## Begin on: Tue Oct 15 13:10:39 CEST 2019

ENUMERATION
No. of records: 422

FAMILY (oriented family) : isomorphism classes
1     [ E1b] : 23 (19 non-degenerate)
2     [ E3b] : 67 (44 non-degenerate)
2*    [E3*b] : 67 (44 non-degenerate)
2ex   [E3*c] : 1 (1 non-degenerate)
2*ex  [ E3c] : 1 (1 non-degenerate)
2P    [  E2] : 9 (8 non-degenerate)
2Pex  [ E1a] : 0
3     [ E5a] : 213 (68 non-degenerate)
4     [  E4] : 16 (6 non-degenerate)
4*    [ E4*] : 16 (6 non-degenerate)
4P    [  E6] : 7 (2 non-degenerate)
5     [ E3a] : 1 (1 non-degenerate)
5*    [E3*a] : 1 (1 non-degenerate)
5P    [ E5b] : 0

E6.1 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {6, 6})
Quotient :: toric
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ A, B, A, B, A, B, A, B, A, B, A, B, S^2, S^-1 * A * S * B, S^-1 * B * S * A, S^-1 * Z * S * Z, Z^6, (Z^-1 * A * B^-1 * A^-1 * B)^6 ]
Map::
	R = (1, 8, 14, 20, 2, 10, 16, 22, 4, 12, 18, 24, 6, 11, 17, 23, 5, 9, 15, 21, 3, 7, 13, 19)
	L = (1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)
	local type(s) :: { ( 24^24 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 12 f = 1
	degree seq :: [ 24 ]

E6.2 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {6, 6})
Quotient :: toric
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ S^2, A^2, B^-1 * A, Z^-3 * A, S * B * S * A, A * Z * A * Z^-1, (S * Z)^2 ]
Map::
	R = (1, 8, 14, 20, 2, 11, 17, 23, 5, 9, 15, 21, 3, 12, 18, 24, 6, 10, 16, 22, 4, 7, 13, 19)
	L = (1, 15)(2, 18)(3, 13)(4, 17)(5, 16)(6, 14)(7, 21)(8, 24)(9, 19)(10, 23)(11, 22)(12, 20)
	local type(s) :: { ( 24^24 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 12 f = 1
	degree seq :: [ 24 ]

E6.3 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {6, 6})
Quotient :: toric
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ S^2, B * A^-1, Z^2 * A^-1, A^3, S * A * S * B, (S * Z)^2, (B^-1 * Z)^6 ]
Map::
	R = (1, 8, 14, 20, 2, 9, 15, 21, 3, 12, 18, 24, 6, 11, 17, 23, 5, 10, 16, 22, 4, 7, 13, 19)
	L = (1, 15)(2, 18)(3, 17)(4, 14)(5, 13)(6, 16)(7, 23)(8, 22)(9, 19)(10, 24)(11, 21)(12, 20)
	local type(s) :: { ( 24^24 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 12 f = 1
	degree seq :: [ 24 ]

E6.4 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Z^2, S^2, B * A^-1, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, A^5 ]
Map::
	R = (1, 12, 22, 32, 2, 11, 21, 31)(3, 15, 25, 35, 5, 13, 23, 33)(4, 16, 26, 36, 6, 14, 24, 34)(7, 19, 29, 39, 9, 17, 27, 37)(8, 20, 30, 40, 10, 18, 28, 38)
	L = (1, 23)(2, 25)(3, 27)(4, 21)(5, 29)(6, 22)(7, 28)(8, 24)(9, 30)(10, 26)(11, 34)(12, 36)(13, 31)(14, 38)(15, 32)(16, 40)(17, 33)(18, 37)(19, 35)(20, 39)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 5 e = 20 f = 5
	degree seq :: [ 8^5 ]

E6.5 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^5 ]
Map::
	R = (1, 12, 22, 32, 2, 11, 21, 31)(3, 15, 25, 35, 5, 13, 23, 33)(4, 16, 26, 36, 6, 14, 24, 34)(7, 19, 29, 39, 9, 17, 27, 37)(8, 20, 30, 40, 10, 18, 28, 38)
	L = (1, 23)(2, 24)(3, 21)(4, 22)(5, 27)(6, 28)(7, 25)(8, 26)(9, 30)(10, 29)(11, 33)(12, 34)(13, 31)(14, 32)(15, 37)(16, 38)(17, 35)(18, 36)(19, 40)(20, 39)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 5 e = 20 f = 5
	degree seq :: [ 8^5 ]

E6.6 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^-1 * B^-1, S * B * S * A, (S * Z)^2, B * Z * A^-1 * Z, A^3 * B^-2 ]
Map:: non-degenerate
	R = (1, 12, 22, 32, 2, 11, 21, 31)(3, 16, 26, 36, 6, 13, 23, 33)(4, 15, 25, 35, 5, 14, 24, 34)(7, 20, 30, 40, 10, 17, 27, 37)(8, 19, 29, 39, 9, 18, 28, 38)
	L = (1, 23)(2, 25)(3, 27)(4, 21)(5, 29)(6, 22)(7, 28)(8, 24)(9, 30)(10, 26)(11, 33)(12, 35)(13, 37)(14, 31)(15, 39)(16, 32)(17, 38)(18, 34)(19, 40)(20, 36)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 5 e = 20 f = 5
	degree seq :: [ 8^5 ]

E6.7 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C10 (small group id <10, 2>)
Aut   = C10 x C2 (small group id <20, 5>)
|r| :: 2
Presentation :: [ Z^2, S^2, B^-1 * A^-1, S * B * S * A, (S * Z)^2, B * Z * B^-1 * Z, A * Z * A^-1 * Z, A^3 * B^-2 ]
Map:: non-degenerate
	R = (1, 12, 22, 32, 2, 11, 21, 31)(3, 15, 25, 35, 5, 13, 23, 33)(4, 16, 26, 36, 6, 14, 24, 34)(7, 19, 29, 39, 9, 17, 27, 37)(8, 20, 30, 40, 10, 18, 28, 38)
	L = (1, 23)(2, 25)(3, 27)(4, 21)(5, 29)(6, 22)(7, 28)(8, 24)(9, 30)(10, 26)(11, 33)(12, 35)(13, 37)(14, 31)(15, 39)(16, 32)(17, 38)(18, 34)(19, 40)(20, 36)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 5 e = 20 f = 5
	degree seq :: [ 8^5 ]

E6.8 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 7, 7, 7})
Quotient :: dipole
Aut^+ = C7 (small group id <7, 1>)
Aut   = D14 (small group id <14, 1>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 8, 2, 9, 6, 13, 5, 12, 3, 10, 7, 14, 4, 11)(15, 22, 17, 24, 16, 23, 21, 28, 20, 27, 18, 25, 19, 26)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.9 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 7, 7, 7})
Quotient :: dipole
Aut^+ = C7 (small group id <7, 1>)
Aut   = D14 (small group id <14, 1>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, Y2 * Y1^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 8, 2, 9, 6, 13, 3, 10, 5, 12, 7, 14, 4, 11)(15, 22, 17, 24, 18, 25, 20, 27, 21, 28, 16, 23, 19, 26)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.10 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 7, 7, 7})
Quotient :: dipole
Aut^+ = C7 (small group id <7, 1>)
Aut   = D14 (small group id <14, 1>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y1 * Y2^2, Y2 * Y1^-3, R * Y2 * R * Y3^-1, (R * Y1)^2, (Y3^-1 * Y1^-1)^7 ]
Map:: non-degenerate
	R = (1, 8, 2, 9, 6, 13, 3, 10, 4, 11, 7, 14, 5, 12)(15, 22, 17, 24, 19, 26, 20, 27, 21, 28, 16, 23, 18, 25)
	L = (1, 18)(2, 21)(3, 15)(4, 16)(5, 17)(6, 19)(7, 20)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.11
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.11 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 7, 7, 7})
Quotient :: dipole
Aut^+ = C7 (small group id <7, 1>)
Aut   = D14 (small group id <14, 1>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2, Y2 * Y1^-2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y1 * Y2^3, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^7 ]
Map:: non-degenerate
	R = (1, 8, 2, 9, 3, 10, 6, 13, 7, 14, 4, 11, 5, 12)(15, 22, 17, 24, 21, 28, 19, 26, 16, 23, 20, 27, 18, 25)
	L = (1, 18)(2, 19)(3, 15)(4, 20)(5, 21)(6, 16)(7, 17)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.10
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.12 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8, 8})
Quotient :: dipole
Aut^+ = C8 (small group id <8, 1>)
Aut   = D16 (small group id <16, 7>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^2 * Y1, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 9, 2, 10, 6, 14, 4, 12)(3, 11, 5, 13, 7, 15, 8, 16)(17, 25, 19, 27, 20, 28, 24, 32, 22, 30, 23, 31, 18, 26, 21, 29)
	L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 3 e = 16 f = 3
	degree seq :: [ 8^2, 16 ]

E6.13 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8, 8})
Quotient :: dipole
Aut^+ = C8 (small group id <8, 1>)
Aut   = D16 (small group id <16, 7>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 9, 2, 10, 6, 14, 4, 12)(3, 11, 7, 15, 8, 16, 5, 13)(17, 25, 19, 27, 18, 26, 23, 31, 22, 30, 24, 32, 20, 28, 21, 29)
	L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 3 e = 16 f = 3
	degree seq :: [ 8^2, 16 ]

E6.14 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8, 8})
Quotient :: dipole
Aut^+ = C8 (small group id <8, 1>)
Aut   = D16 (small group id <16, 7>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y1 * Y2^-1, (R * Y2 * Y3)^2 ]
Map:: non-degenerate
	R = (1, 9, 2, 10, 4, 12, 5, 13)(3, 11, 6, 14, 7, 15, 8, 16)(17, 25, 19, 27, 21, 29, 24, 32, 20, 28, 23, 31, 18, 26, 22, 30)
	L = (1, 20)(2, 21)(3, 23)(4, 17)(5, 18)(6, 24)(7, 19)(8, 22)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.15
Graph:: bipartite
	v = 3 e = 16 f = 3
	degree seq :: [ 8^2, 16 ]

E6.15 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8, 8})
Quotient :: dipole
Aut^+ = C8 (small group id <8, 1>)
Aut   = D16 (small group id <16, 7>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^2 * Y3, Y2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2 ]
Map:: non-degenerate
	R = (1, 9, 2, 10, 4, 12, 5, 13)(3, 11, 7, 15, 8, 16, 6, 14)(17, 25, 19, 27, 18, 26, 23, 31, 20, 28, 24, 32, 21, 29, 22, 30)
	L = (1, 20)(2, 21)(3, 24)(4, 17)(5, 18)(6, 23)(7, 22)(8, 19)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.14
Graph:: bipartite
	v = 3 e = 16 f = 3
	degree seq :: [ 8^2, 16 ]

E6.16 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 9, 9})
Quotient :: dipole
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, Y2^-2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 8, 17)(5, 14, 7, 16, 9, 18)(19, 28, 21, 30, 25, 34, 20, 29, 24, 33, 27, 36, 22, 31, 26, 35, 23, 32)
	L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 18 f = 4
	degree seq :: [ 6^3, 18 ]

E6.17 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 9, 9})
Quotient :: dipole
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, Y2^-3 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 9, 18)(5, 14, 7, 16, 8, 17)(19, 28, 21, 30, 26, 35, 22, 31, 27, 36, 25, 34, 20, 29, 24, 33, 23, 32)
	L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 4 e = 18 f = 4
	degree seq :: [ 6^3, 18 ]

E6.18 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 9, 9})
Quotient :: dipole
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, Y2^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * R)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), (Y3^-1 * Y1^-1)^3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 8, 17)(5, 14, 7, 16, 9, 18)(19, 28, 21, 30, 25, 34, 20, 29, 24, 33, 27, 36, 22, 31, 26, 35, 23, 32)
	L = (1, 20)(2, 22)(3, 24)(4, 19)(5, 25)(6, 26)(7, 27)(8, 21)(9, 23)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.19
Graph:: bipartite
	v = 4 e = 18 f = 4
	degree seq :: [ 6^3, 18 ]

E6.19 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 9, 9})
Quotient :: dipole
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, Y1^-1 * Y2^-3, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * R)^2, (Y1, Y2^-1), (Y3^-1, Y2^-1), (Y3^-1 * Y1^-1)^3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 9, 18)(5, 14, 7, 16, 8, 17)(19, 28, 21, 30, 26, 35, 22, 31, 27, 36, 25, 34, 20, 29, 24, 33, 23, 32)
	L = (1, 20)(2, 22)(3, 24)(4, 19)(5, 25)(6, 27)(7, 26)(8, 23)(9, 21)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6, 18, 6, 18, 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.18
Graph:: bipartite
	v = 4 e = 18 f = 4
	degree seq :: [ 6^3, 18 ]

E6.20 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y2^5, Y3^10, (Y3 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 5, 15)(4, 14, 6, 16)(7, 17, 9, 19)(8, 18, 10, 20)(21, 31, 23, 33, 27, 37, 28, 38, 24, 34)(22, 32, 25, 35, 29, 39, 30, 40, 26, 36)
	L = (1, 24)(2, 26)(3, 21)(4, 28)(5, 22)(6, 30)(7, 23)(8, 27)(9, 25)(10, 29)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.27
Graph:: bipartite
	v = 7 e = 20 f = 3
	degree seq :: [ 4^5, 10^2 ]

E6.21 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, Y2 * Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 7, 17)(4, 14, 8, 18)(5, 15, 9, 19)(6, 16, 10, 20)(21, 31, 23, 33, 24, 34, 26, 36, 25, 35)(22, 32, 27, 37, 28, 38, 30, 40, 29, 39)
	L = (1, 24)(2, 28)(3, 26)(4, 25)(5, 23)(6, 21)(7, 30)(8, 29)(9, 27)(10, 22)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.26
Graph:: bipartite
	v = 7 e = 20 f = 3
	degree seq :: [ 4^5, 10^2 ]

E6.22 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3, Y2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 7, 17)(4, 14, 8, 18)(5, 15, 9, 19)(6, 16, 10, 20)(21, 31, 23, 33, 26, 36, 24, 34, 25, 35)(22, 32, 27, 37, 30, 40, 28, 38, 29, 39)
	L = (1, 24)(2, 28)(3, 25)(4, 23)(5, 26)(6, 21)(7, 29)(8, 27)(9, 30)(10, 22)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.25
Graph:: bipartite
	v = 7 e = 20 f = 3
	degree seq :: [ 4^5, 10^2 ]

E6.23 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y2, Y1 * Y2^-2, Y3 * Y2^-1 * Y3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y3^-1) ]
Map:: non-degenerate
	R = (1, 11, 2, 12, 6, 16, 3, 13, 5, 15)(4, 14, 8, 18, 7, 17, 9, 19, 10, 20)(21, 31, 23, 33, 22, 32, 25, 35, 26, 36)(24, 34, 29, 39, 28, 38, 30, 40, 27, 37)
	L = (1, 24)(2, 28)(3, 29)(4, 23)(5, 30)(6, 27)(7, 21)(8, 25)(9, 22)(10, 26)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.24
Graph:: bipartite
	v = 4 e = 20 f = 6
	degree seq :: [ 10^4 ]

E6.24 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y1^-5 * Y2, (Y3 * Y2)^5, (Y3^-1 * Y1^-1)^5 ]
Map:: non-degenerate
	R = (1, 11, 2, 12, 5, 15, 9, 19, 7, 17, 3, 13, 6, 16, 10, 20, 8, 18, 4, 14)(21, 31, 23, 33)(22, 32, 26, 36)(24, 34, 27, 37)(25, 35, 30, 40)(28, 38, 29, 39)
	L = (1, 22)(2, 25)(3, 26)(4, 21)(5, 29)(6, 30)(7, 23)(8, 24)(9, 27)(10, 28)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 10^4 ), ( 10^20 ) }
Outer automorphisms :: reflexible
Dual of E6.23
Graph:: bipartite
	v = 6 e = 20 f = 4
	degree seq :: [ 4^5, 20 ]

E6.25 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y2^2 * Y1^-2, Y2^4 * Y1, (R * Y2 * Y3^-1)^2, Y1^10, (Y3^-1 * Y1^-1)^5 ]
Map:: non-degenerate
	R = (1, 11, 2, 12, 6, 16, 9, 19, 4, 14)(3, 13, 7, 17, 10, 20, 5, 15, 8, 18)(21, 31, 23, 33, 26, 36, 30, 40, 24, 34, 28, 38, 22, 32, 27, 37, 29, 39, 25, 35)
	L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 29)(7, 30)(8, 23)(9, 24)(10, 25)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.22
Graph:: bipartite
	v = 3 e = 20 f = 7
	degree seq :: [ 10^2, 20 ]

E6.26 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y3^-2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 11, 2, 12, 7, 17, 4, 14, 5, 15)(3, 13, 8, 18, 10, 20, 9, 19, 6, 16)(21, 31, 23, 33, 22, 32, 28, 38, 27, 37, 30, 40, 24, 34, 29, 39, 25, 35, 26, 36)
	L = (1, 24)(2, 25)(3, 29)(4, 22)(5, 27)(6, 30)(7, 21)(8, 26)(9, 28)(10, 23)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.21
Graph:: bipartite
	v = 3 e = 20 f = 7
	degree seq :: [ 10^2, 20 ]

E6.27 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y1^2 * Y3^-1, Y1 * Y2^2, Y1 * Y3^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 11, 2, 12, 4, 14, 7, 17, 5, 15)(3, 13, 6, 16, 8, 18, 10, 20, 9, 19)(21, 31, 23, 33, 25, 35, 29, 39, 27, 37, 30, 40, 24, 34, 28, 38, 22, 32, 26, 36)
	L = (1, 24)(2, 27)(3, 28)(4, 25)(5, 22)(6, 30)(7, 21)(8, 29)(9, 26)(10, 23)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.20
Graph:: bipartite
	v = 3 e = 20 f = 7
	degree seq :: [ 10^2, 20 ]

E6.28 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 4, 4})
Quotient :: edge^2
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3^-1 * Y1^-1, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 13, 4, 16, 10, 22, 5, 17)(2, 14, 6, 18, 11, 23, 7, 19)(3, 15, 8, 20, 12, 24, 9, 21)(25, 26, 27)(28, 32, 30)(29, 33, 31)(34, 35, 36)(37, 39, 38)(40, 42, 44)(41, 43, 45)(46, 48, 47)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 16^3 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E6.30
Graph:: simple bipartite
	v = 11 e = 24 f = 3
	degree seq :: [ 3^8, 8^3 ]

E6.29 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 4, 4})
Quotient :: edge^2
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = C4 x S3 (small group id <24, 5>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y2^4 ]
Map:: non-degenerate
	R = (1, 13, 4, 16, 5, 17)(2, 14, 7, 19, 8, 20)(3, 15, 9, 21, 10, 22)(6, 18, 11, 23, 12, 24)(25, 26, 30, 27)(28, 32, 35, 34)(29, 31, 36, 33)(37, 39, 42, 38)(40, 46, 47, 44)(41, 45, 48, 43)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 12^4 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E6.31
Graph:: simple bipartite
	v = 10 e = 24 f = 4
	degree seq :: [ 4^6, 6^4 ]

E6.30 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 4, 4})
Quotient :: loop^2
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3^-1 * Y1^-1, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 13, 25, 37, 4, 16, 28, 40, 10, 22, 34, 46, 5, 17, 29, 41)(2, 14, 26, 38, 6, 18, 30, 42, 11, 23, 35, 47, 7, 19, 31, 43)(3, 15, 27, 39, 8, 20, 32, 44, 12, 24, 36, 48, 9, 21, 33, 45)
	L = (1, 14)(2, 15)(3, 13)(4, 20)(5, 21)(6, 16)(7, 17)(8, 18)(9, 19)(10, 23)(11, 24)(12, 22)(25, 39)(26, 37)(27, 38)(28, 42)(29, 43)(30, 44)(31, 45)(32, 40)(33, 41)(34, 48)(35, 46)(36, 47)
	local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.28
Transitivity :: VT+
Graph::
	v = 3 e = 24 f = 11
	degree seq :: [ 16^3 ]

E6.31 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 4, 4})
Quotient :: loop^2
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = C4 x S3 (small group id <24, 5>)
|r| :: 2
Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3^3, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y2^4 ]
Map:: non-degenerate
	R = (1, 13, 25, 37, 4, 16, 28, 40, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 8, 20, 32, 44)(3, 15, 27, 39, 9, 21, 33, 45, 10, 22, 34, 46)(6, 18, 30, 42, 11, 23, 35, 47, 12, 24, 36, 48)
	L = (1, 14)(2, 18)(3, 13)(4, 20)(5, 19)(6, 15)(7, 24)(8, 23)(9, 17)(10, 16)(11, 22)(12, 21)(25, 39)(26, 37)(27, 42)(28, 46)(29, 45)(30, 38)(31, 41)(32, 40)(33, 48)(34, 47)(35, 44)(36, 43)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.29
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 24 f = 10
	degree seq :: [ 12^4 ]

E6.32 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 4, 4})
Quotient :: dipole
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 13, 2, 14, 4, 16)(3, 15, 8, 20, 6, 18)(5, 17, 10, 22, 7, 19)(9, 21, 11, 23, 12, 24)(25, 37, 27, 39, 33, 45, 29, 41)(26, 38, 30, 42, 35, 47, 31, 43)(28, 40, 32, 44, 36, 48, 34, 46)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 6^4, 8^3 ]

E6.33 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 4, 4})
Quotient :: dipole
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^4 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 4, 16)(3, 15, 8, 20, 6, 18)(5, 17, 10, 22, 7, 19)(9, 21, 11, 23, 12, 24)(25, 37, 27, 39, 33, 45, 29, 41)(26, 38, 30, 42, 35, 47, 31, 43)(28, 40, 32, 44, 36, 48, 34, 46)
	L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 34)(6, 27)(7, 29)(8, 30)(9, 35)(10, 31)(11, 36)(12, 33)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 6^4, 8^3 ]

E6.34 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 4, 4})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 13, 2, 14, 4, 16)(3, 15, 6, 18, 9, 21)(5, 17, 7, 19, 10, 22)(8, 20, 11, 23, 12, 24)(25, 37, 27, 39, 32, 44, 29, 41)(26, 38, 30, 42, 35, 47, 31, 43)(28, 40, 33, 45, 36, 48, 34, 46)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 6^4, 8^3 ]

E6.35 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 6})
Quotient :: dipole
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3^3, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 7, 19)(6, 18, 8, 20)(9, 21, 12, 24)(10, 22, 11, 23)(25, 37, 27, 39, 26, 38, 29, 41)(28, 40, 34, 46, 31, 43, 35, 47)(30, 42, 33, 45, 32, 44, 36, 48)
	L = (1, 28)(2, 31)(3, 33)(4, 30)(5, 36)(6, 25)(7, 32)(8, 26)(9, 34)(10, 27)(11, 29)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.36
Graph:: bipartite
	v = 9 e = 24 f = 5
	degree seq :: [ 4^6, 8^3 ]

E6.36 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 4, 6})
Quotient :: dipole
Aut^+ = C3 : C4 (small group id <12, 1>)
Aut   = (C6 x C2) : C2 (small group id <24, 8>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y2^2 * Y3, Y3 * Y1^2 * Y2^-1, Y2 * Y1^2 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y3^-1 * Y1^2, Y1^2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 8, 20, 5, 17)(3, 15, 11, 23, 4, 16, 12, 24)(6, 18, 9, 21, 7, 19, 10, 22)(25, 37, 27, 39, 31, 43, 32, 44, 28, 40, 30, 42)(26, 38, 33, 45, 36, 48, 29, 41, 34, 46, 35, 47)
	L = (1, 28)(2, 34)(3, 30)(4, 31)(5, 33)(6, 32)(7, 25)(8, 27)(9, 35)(10, 36)(11, 29)(12, 26)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.35
Graph:: bipartite
	v = 5 e = 24 f = 9
	degree seq :: [ 8^3, 12^2 ]

E6.37 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 6, 6})
Quotient :: dipole
Aut^+ = C6 x C2 (small group id <12, 5>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, Y2 * Y1 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y3)^6 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 5, 17)(3, 15, 6, 18, 9, 21)(4, 16, 8, 20, 7, 19)(10, 22, 12, 24, 11, 23)(25, 37, 27, 39, 29, 41, 33, 45, 26, 38, 30, 42)(28, 40, 34, 46, 31, 43, 35, 47, 32, 44, 36, 48)
	L = (1, 28)(2, 32)(3, 34)(4, 26)(5, 31)(6, 36)(7, 25)(8, 29)(9, 35)(10, 30)(11, 27)(12, 33)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.38
Graph:: bipartite
	v = 6 e = 24 f = 8
	degree seq :: [ 6^4, 12^2 ]

E6.38 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 6, 6})
Quotient :: dipole
Aut^+ = C6 x C2 (small group id <12, 5>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y3 * Y1^2 * Y2, (Y3 * Y1^-1)^2, Y3^-3 * Y2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y3^2 * Y1^-2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 7, 19, 12, 24, 11, 23, 5, 17)(3, 15, 8, 20, 6, 18, 10, 22, 4, 16, 9, 21)(25, 37, 27, 39)(26, 38, 32, 44)(28, 40, 35, 47)(29, 41, 33, 45)(30, 42, 31, 43)(34, 46, 36, 48)
	L = (1, 28)(2, 33)(3, 35)(4, 31)(5, 34)(6, 25)(7, 27)(8, 29)(9, 36)(10, 26)(11, 30)(12, 32)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.37
Graph:: bipartite
	v = 8 e = 24 f = 6
	degree seq :: [ 4^6, 12^2 ]

E6.39 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (Y3^-1, Y2^-1), Y3^-1 * Y2^-1 * Y3^-1 * Y1, Y2 * Y1 * Y3^2, Y2^-1 * Y1 * Y3^-2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * R)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 7, 19)(4, 16, 8, 20)(5, 17, 9, 21)(6, 18, 10, 22)(11, 23, 12, 24)(25, 37, 27, 39, 29, 41)(26, 38, 31, 43, 33, 45)(28, 40, 34, 46, 36, 48)(30, 42, 35, 47, 32, 44)
	L = (1, 28)(2, 32)(3, 34)(4, 33)(5, 36)(6, 25)(7, 30)(8, 29)(9, 35)(10, 26)(11, 27)(12, 31)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.42
Graph:: simple bipartite
	v = 10 e = 24 f = 4
	degree seq :: [ 4^6, 6^4 ]

E6.40 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y2^-2 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y1 * Y2^-2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, Y2^4, (Y3^-1 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 5, 17)(3, 15, 8, 20, 12, 24)(4, 16, 9, 21, 7, 19)(6, 18, 10, 22, 11, 23)(25, 37, 27, 39, 33, 45, 30, 42)(26, 38, 32, 44, 31, 43, 34, 46)(28, 40, 35, 47, 29, 41, 36, 48)
	L = (1, 28)(2, 33)(3, 35)(4, 26)(5, 31)(6, 36)(7, 25)(8, 30)(9, 29)(10, 27)(11, 32)(12, 34)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.41
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 6^4, 8^3 ]

E6.41 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y1^2 * Y3^-1, Y3^-3 * Y2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 4, 16, 8, 20, 11, 23, 10, 22, 3, 15, 7, 19, 9, 21, 12, 24, 6, 18, 5, 17)(25, 37, 27, 39)(26, 38, 31, 43)(28, 40, 33, 45)(29, 41, 34, 46)(30, 42, 35, 47)(32, 44, 36, 48)
	L = (1, 28)(2, 32)(3, 33)(4, 35)(5, 26)(6, 25)(7, 36)(8, 34)(9, 30)(10, 31)(11, 27)(12, 29)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.40
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 4^6, 24 ]

E6.42 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1, Y3^-2 * Y2^-1 * Y1^-1, Y3^3 * Y1^-1, Y2 * Y3^-1 * Y1^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-2 * Y3^2, (R * Y3)^2, Y1^4, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 8, 20, 5, 17)(3, 15, 9, 21, 4, 16, 10, 22)(6, 18, 11, 23, 7, 19, 12, 24)(25, 37, 27, 39, 36, 48, 29, 41, 34, 46, 31, 43, 32, 44, 28, 40, 35, 47, 26, 38, 33, 45, 30, 42)
	L = (1, 28)(2, 34)(3, 35)(4, 36)(5, 33)(6, 32)(7, 25)(8, 27)(9, 31)(10, 30)(11, 29)(12, 26)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.39
Graph:: bipartite
	v = 4 e = 24 f = 10
	degree seq :: [ 8^3, 24 ]

E6.43 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^-1 * Y1 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-2, Y3^-3 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 7, 19)(6, 18, 8, 20)(9, 21, 12, 24)(10, 22, 11, 23)(25, 37, 27, 39, 26, 38, 29, 41)(28, 40, 33, 45, 31, 43, 36, 48)(30, 42, 34, 46, 32, 44, 35, 47)
	L = (1, 28)(2, 31)(3, 33)(4, 35)(5, 36)(6, 25)(7, 34)(8, 26)(9, 30)(10, 27)(11, 29)(12, 32)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.44
Graph:: bipartite
	v = 9 e = 24 f = 5
	degree seq :: [ 4^6, 8^3 ]

E6.44 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 4, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y3 * Y2^2, Y1 * Y3^-2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 5, 17)(3, 15, 8, 20, 11, 23)(4, 16, 9, 21, 7, 19)(6, 18, 10, 22, 12, 24)(25, 37, 27, 39, 31, 43, 36, 48, 29, 41, 35, 47, 33, 45, 34, 46, 26, 38, 32, 44, 28, 40, 30, 42)
	L = (1, 28)(2, 33)(3, 30)(4, 26)(5, 31)(6, 32)(7, 25)(8, 34)(9, 29)(10, 35)(11, 36)(12, 27)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.43
Graph:: bipartite
	v = 5 e = 24 f = 9
	degree seq :: [ 6^4, 24 ]

E6.45 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 12, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^6 * Y1, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 6, 18)(7, 19, 9, 21)(8, 20, 10, 22)(11, 23, 12, 24)(25, 37, 27, 39, 31, 43, 35, 47, 34, 46, 30, 42, 26, 38, 29, 41, 33, 45, 36, 48, 32, 44, 28, 40)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 24 f = 7
	degree seq :: [ 4^6, 24 ]

E6.46 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {13, 13, 13})
Quotient :: edge
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^6, (T2^-1 * T1^-1)^13 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 12, 8, 4, 2, 6, 10, 13, 9, 5)(14, 15, 16, 19, 20, 23, 24, 26, 25, 22, 21, 18, 17)
	L = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.54
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.47 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {13, 13, 13})
Quotient :: edge
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^2, (F * T2)^2, (F * T1)^2, T1 * T2^-6 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 10, 6, 2, 4, 8, 12, 13, 9, 5)(14, 15, 18, 19, 22, 23, 26, 24, 25, 20, 21, 16, 17)
	L = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.51
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.48 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {13, 13, 13})
Quotient :: edge
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 10, 4, 6, 12, 13, 8, 2, 7, 11, 5)(14, 15, 19, 16, 20, 25, 22, 24, 26, 23, 18, 21, 17)
	L = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.53
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.49 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {13, 13, 13})
Quotient :: edge
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^-1 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1 ]
Map:: non-degenerate
	R = (1, 3, 9, 8, 2, 7, 13, 12, 6, 4, 10, 11, 5)(14, 15, 19, 18, 21, 25, 24, 22, 26, 23, 16, 20, 17)
	L = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.52
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.50 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {13, 13, 13})
Quotient :: edge
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^2 * T2 * T1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 6, 12, 4, 10, 8, 2, 7, 11, 13, 5)(14, 15, 19, 26, 23, 16, 20, 25, 18, 21, 22, 24, 17)
	L = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.55
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.51 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {13, 13, 13})
Quotient :: loop
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T2^13, T1^13, (T2^-1 * T1^-1)^13 ]
Map:: non-degenerate
	R = (1, 14, 2, 15, 4, 17, 6, 19, 8, 21, 10, 23, 12, 25, 13, 26, 11, 24, 9, 22, 7, 20, 5, 18, 3, 16)
	L = (1, 15)(2, 17)(3, 14)(4, 19)(5, 16)(6, 21)(7, 18)(8, 23)(9, 20)(10, 25)(11, 22)(12, 26)(13, 24)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.47
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.52 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {13, 13, 13})
Quotient :: loop
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^6, (T2^-1 * T1^-1)^13 ]
Map:: non-degenerate
	R = (1, 14, 3, 16, 7, 20, 11, 24, 12, 25, 8, 21, 4, 17, 2, 15, 6, 19, 10, 23, 13, 26, 9, 22, 5, 18)
	L = (1, 15)(2, 16)(3, 19)(4, 14)(5, 17)(6, 20)(7, 23)(8, 18)(9, 21)(10, 24)(11, 26)(12, 22)(13, 25)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.49
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.53 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {13, 13, 13})
Quotient :: loop
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3 ]
Map:: non-degenerate
	R = (1, 14, 3, 16, 9, 22, 10, 23, 4, 17, 6, 19, 12, 25, 13, 26, 8, 21, 2, 15, 7, 20, 11, 24, 5, 18)
	L = (1, 15)(2, 19)(3, 20)(4, 14)(5, 21)(6, 16)(7, 25)(8, 17)(9, 24)(10, 18)(11, 26)(12, 22)(13, 23)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.48
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.54 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {13, 13, 13})
Quotient :: loop
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^-1 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1 ]
Map:: non-degenerate
	R = (1, 14, 3, 16, 9, 22, 8, 21, 2, 15, 7, 20, 13, 26, 12, 25, 6, 19, 4, 17, 10, 23, 11, 24, 5, 18)
	L = (1, 15)(2, 19)(3, 20)(4, 14)(5, 21)(6, 18)(7, 17)(8, 25)(9, 26)(10, 16)(11, 22)(12, 24)(13, 23)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.46
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.55 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {13, 13, 13})
Quotient :: loop
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ F^2, T2^-1 * T1^-1 * T2^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^2 * T2^-1 * T1^2 ]
Map:: non-degenerate
	R = (1, 14, 3, 16, 9, 22, 4, 17, 10, 23, 13, 26, 11, 24, 6, 19, 12, 25, 8, 21, 2, 15, 7, 20, 5, 18)
	L = (1, 15)(2, 19)(3, 20)(4, 14)(5, 21)(6, 23)(7, 25)(8, 24)(9, 18)(10, 16)(11, 17)(12, 26)(13, 22)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.50
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.56 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^6 * Y2, Y2 * Y1^-6 ]
Map::
	R = (1, 14, 2, 15, 6, 19, 10, 23, 12, 25, 8, 21, 3, 16, 5, 18, 7, 20, 11, 24, 13, 26, 9, 22, 4, 17)(27, 40, 29, 42, 30, 43, 34, 47, 35, 48, 38, 51, 39, 52, 36, 49, 37, 50, 32, 45, 33, 46, 28, 41, 31, 44)
	L = (1, 30)(2, 27)(3, 34)(4, 35)(5, 29)(6, 28)(7, 31)(8, 38)(9, 39)(10, 32)(11, 33)(12, 36)(13, 37)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.61
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.57 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^2 * Y2^-1 * Y1^-2 * Y3 * Y1^-1, Y3^-1 * Y1^4 * Y3^-1 * Y2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ]
Map::
	R = (1, 14, 2, 15, 6, 19, 10, 23, 13, 26, 9, 22, 5, 18, 3, 16, 7, 20, 11, 24, 12, 25, 8, 21, 4, 17)(27, 40, 29, 42, 28, 41, 33, 46, 32, 45, 37, 50, 36, 49, 38, 51, 39, 52, 34, 47, 35, 48, 30, 43, 31, 44)
	L = (1, 30)(2, 27)(3, 31)(4, 34)(5, 35)(6, 28)(7, 29)(8, 38)(9, 39)(10, 32)(11, 33)(12, 37)(13, 36)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.64
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.58 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y2^-1 * Y1^-1 * Y2^-2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), Y2^-1 * Y1^2 * Y3^-2, Y1^3 * Y2^-1 * Y3^-1, Y3 * Y2^2 * Y3 * Y2 * Y3 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 14, 2, 15, 6, 19, 10, 23, 3, 16, 7, 20, 12, 25, 13, 26, 9, 22, 5, 18, 8, 21, 11, 24, 4, 17)(27, 40, 29, 42, 35, 48, 30, 43, 36, 49, 39, 52, 37, 50, 32, 45, 38, 51, 34, 47, 28, 41, 33, 46, 31, 44)
	L = (1, 30)(2, 27)(3, 36)(4, 37)(5, 35)(6, 28)(7, 29)(8, 31)(9, 39)(10, 32)(11, 34)(12, 33)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.65
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.59 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y1^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1^2 * Y3^-2, Y1^2 * Y2 * Y1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^2 ]
Map::
	R = (1, 14, 2, 15, 6, 19, 11, 24, 5, 18, 8, 21, 12, 25, 13, 26, 9, 22, 3, 16, 7, 20, 10, 23, 4, 17)(27, 40, 29, 42, 34, 47, 28, 41, 33, 46, 38, 51, 32, 45, 36, 49, 39, 52, 37, 50, 30, 43, 35, 48, 31, 44)
	L = (1, 30)(2, 27)(3, 35)(4, 36)(5, 37)(6, 28)(7, 29)(8, 31)(9, 39)(10, 33)(11, 32)(12, 34)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.63
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.60 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y2^-3 * Y1^2, Y1 * Y2^2 * Y3^-2, Y2 * Y1^8 ]
Map::
	R = (1, 14, 2, 15, 6, 19, 13, 26, 10, 23, 3, 16, 7, 20, 12, 25, 5, 18, 8, 21, 9, 22, 11, 24, 4, 17)(27, 40, 29, 42, 35, 48, 32, 45, 38, 51, 30, 43, 36, 49, 34, 47, 28, 41, 33, 46, 37, 50, 39, 52, 31, 44)
	L = (1, 30)(2, 27)(3, 36)(4, 37)(5, 38)(6, 28)(7, 29)(8, 31)(9, 34)(10, 39)(11, 35)(12, 33)(13, 32)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.62
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.61 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^13, (Y3^-1 * Y1^-1)^13, (Y3 * Y2^-1)^13 ]
Map::
	R = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40, 28, 41, 30, 43, 32, 45, 34, 47, 36, 49, 38, 51, 39, 52, 37, 50, 35, 48, 33, 46, 31, 44, 29, 42)
	L = (1, 29)(2, 27)(3, 31)(4, 28)(5, 33)(6, 30)(7, 35)(8, 32)(9, 37)(10, 34)(11, 39)(12, 36)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.56
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.62 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^-6, (Y3 * Y2^-1)^13, (Y3^-1 * Y1^-1)^13 ]
Map::
	R = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40, 28, 41, 31, 44, 32, 45, 35, 48, 36, 49, 39, 52, 37, 50, 38, 51, 33, 46, 34, 47, 29, 42, 30, 43)
	L = (1, 29)(2, 30)(3, 33)(4, 34)(5, 27)(6, 28)(7, 37)(8, 38)(9, 31)(10, 32)(11, 36)(12, 39)(13, 35)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.60
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.63 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^-1 * Y3^-1 * Y2^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3 * Y2^-1 * Y3^3, (Y3^-1 * Y1^-1)^13 ]
Map::
	R = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40, 28, 41, 32, 45, 31, 44, 34, 47, 38, 51, 37, 50, 35, 48, 39, 52, 36, 49, 29, 42, 33, 46, 30, 43)
	L = (1, 29)(2, 33)(3, 35)(4, 36)(5, 27)(6, 30)(7, 39)(8, 28)(9, 34)(10, 37)(11, 31)(12, 32)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.59
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.64 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3^-2 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^2 * Y3 * Y2^2, (Y3^-1 * Y1^-1)^13 ]
Map::
	R = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40, 28, 41, 32, 45, 37, 50, 31, 44, 34, 47, 38, 51, 39, 52, 35, 48, 29, 42, 33, 46, 36, 49, 30, 43)
	L = (1, 29)(2, 33)(3, 34)(4, 35)(5, 27)(6, 36)(7, 38)(8, 28)(9, 31)(10, 39)(11, 30)(12, 32)(13, 37)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.57
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.65 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {13, 13, 13})
Quotient :: dipole
Aut^+ = C13 (small group id <13, 1>)
Aut   = D26 (small group id <26, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^3 * Y3^-2, Y2 * Y3 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^13 ]
Map::
	R = (1, 14)(2, 15)(3, 16)(4, 17)(5, 18)(6, 19)(7, 20)(8, 21)(9, 22)(10, 23)(11, 24)(12, 25)(13, 26)(27, 40, 28, 41, 32, 45, 35, 48, 38, 51, 31, 44, 34, 47, 36, 49, 29, 42, 33, 46, 39, 52, 37, 50, 30, 43)
	L = (1, 29)(2, 33)(3, 35)(4, 36)(5, 27)(6, 39)(7, 38)(8, 28)(9, 37)(10, 32)(11, 34)(12, 30)(13, 31)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.58
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.66 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: halfedge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y2, Y1^7 ]
Map::
	R = (1, 16, 2, 19, 5, 23, 9, 26, 12, 22, 8, 18, 4, 15)(3, 21, 7, 25, 11, 28, 14, 27, 13, 24, 10, 20, 6, 17)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 13)(12, 14)(15, 17)(16, 20)(18, 21)(19, 24)(22, 25)(23, 27)(26, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.67 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: halfedge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y3 * Y1^-3 * Y2, Y2 * Y1^-1 * Y3 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 16, 2, 20, 6, 24, 10, 26, 12, 27, 13, 19, 5, 15)(3, 23, 9, 22, 8, 18, 4, 25, 11, 28, 14, 21, 7, 17)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 13)(10, 11)(15, 18)(16, 22)(17, 24)(19, 25)(20, 23)(21, 26)(27, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.68
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.68 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: halfedge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y2 * Y1^-3 * Y3, Y3 * Y1^-1 * Y2 * Y3 * Y2 ]
Map:: non-degenerate
	R = (1, 16, 2, 20, 6, 26, 12, 24, 10, 27, 13, 19, 5, 15)(3, 23, 9, 28, 14, 22, 8, 18, 4, 25, 11, 21, 7, 17)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 11)(8, 10)(13, 14)(15, 18)(16, 22)(17, 24)(19, 25)(20, 28)(21, 27)(23, 26)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.67
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.69 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: edge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^7 ]
Map::
	R = (1, 15, 3, 17, 7, 21, 11, 25, 12, 26, 8, 22, 4, 18)(2, 16, 5, 19, 9, 23, 13, 27, 14, 28, 10, 24, 6, 20)(29, 30)(31, 34)(32, 33)(35, 38)(36, 37)(39, 42)(40, 41)(43, 44)(45, 48)(46, 47)(49, 52)(50, 51)(53, 56)(54, 55)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.73
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.70 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: edge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3^-2, Y1 * Y2 * Y3 * Y1 * Y2 ]
Map::
	R = (1, 15, 4, 18, 12, 26, 6, 20, 9, 23, 13, 27, 5, 19)(2, 16, 7, 21, 11, 25, 3, 17, 10, 24, 14, 28, 8, 22)(29, 30)(31, 37)(32, 36)(33, 35)(34, 38)(39, 41)(40, 42)(43, 45)(44, 48)(46, 53)(47, 52)(49, 54)(50, 51)(55, 56)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.75
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.71 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: edge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3 * Y2 * Y1 * Y2, Y1 * Y3^-3 * Y2 ]
Map::
	R = (1, 15, 4, 18, 12, 26, 9, 23, 6, 20, 13, 27, 5, 19)(2, 16, 7, 21, 14, 28, 11, 25, 3, 17, 10, 24, 8, 22)(29, 30)(31, 37)(32, 36)(33, 35)(34, 39)(38, 40)(41, 42)(43, 45)(44, 48)(46, 53)(47, 52)(49, 51)(50, 55)(54, 56)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.74
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.72 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 7, 7})
Quotient :: edge^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^7, Y1^7 ]
Map:: non-degenerate
	R = (1, 15, 4, 18)(2, 16, 6, 20)(3, 17, 8, 22)(5, 19, 10, 24)(7, 21, 12, 26)(9, 23, 13, 27)(11, 25, 14, 28)(29, 30, 33, 37, 39, 35, 31)(32, 36, 40, 42, 41, 38, 34)(43, 45, 49, 53, 51, 47, 44)(46, 48, 52, 55, 56, 54, 50)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 8^4 ), ( 8^7 ) }
Outer automorphisms :: reflexible
Dual of E6.76
Graph:: simple bipartite
	v = 11 e = 28 f = 7
	degree seq :: [ 4^7, 7^4 ]

E6.73 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 7, 7})
Quotient :: loop^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^7 ]
Map::
	R = (1, 15, 29, 43, 3, 17, 31, 45, 7, 21, 35, 49, 11, 25, 39, 53, 12, 26, 40, 54, 8, 22, 36, 50, 4, 18, 32, 46)(2, 16, 30, 44, 5, 19, 33, 47, 9, 23, 37, 51, 13, 27, 41, 55, 14, 28, 42, 56, 10, 24, 38, 52, 6, 20, 34, 48)
	L = (1, 16)(2, 15)(3, 20)(4, 19)(5, 18)(6, 17)(7, 24)(8, 23)(9, 22)(10, 21)(11, 28)(12, 27)(13, 26)(14, 25)(29, 44)(30, 43)(31, 48)(32, 47)(33, 46)(34, 45)(35, 52)(36, 51)(37, 50)(38, 49)(39, 56)(40, 55)(41, 54)(42, 53)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.69
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.74 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 7, 7})
Quotient :: loop^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3^-2, Y1 * Y2 * Y3 * Y1 * Y2 ]
Map::
	R = (1, 15, 29, 43, 4, 18, 32, 46, 12, 26, 40, 54, 6, 20, 34, 48, 9, 23, 37, 51, 13, 27, 41, 55, 5, 19, 33, 47)(2, 16, 30, 44, 7, 21, 35, 49, 11, 25, 39, 53, 3, 17, 31, 45, 10, 24, 38, 52, 14, 28, 42, 56, 8, 22, 36, 50)
	L = (1, 16)(2, 15)(3, 23)(4, 22)(5, 21)(6, 24)(7, 19)(8, 18)(9, 17)(10, 20)(11, 27)(12, 28)(13, 25)(14, 26)(29, 45)(30, 48)(31, 43)(32, 53)(33, 52)(34, 44)(35, 54)(36, 51)(37, 50)(38, 47)(39, 46)(40, 49)(41, 56)(42, 55)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.71
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.75 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 7, 7})
Quotient :: loop^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y1 * Y3 * Y2 * Y1 * Y2, Y1 * Y3^-3 * Y2 ]
Map::
	R = (1, 15, 29, 43, 4, 18, 32, 46, 12, 26, 40, 54, 9, 23, 37, 51, 6, 20, 34, 48, 13, 27, 41, 55, 5, 19, 33, 47)(2, 16, 30, 44, 7, 21, 35, 49, 14, 28, 42, 56, 11, 25, 39, 53, 3, 17, 31, 45, 10, 24, 38, 52, 8, 22, 36, 50)
	L = (1, 16)(2, 15)(3, 23)(4, 22)(5, 21)(6, 25)(7, 19)(8, 18)(9, 17)(10, 26)(11, 20)(12, 24)(13, 28)(14, 27)(29, 45)(30, 48)(31, 43)(32, 53)(33, 52)(34, 44)(35, 51)(36, 55)(37, 49)(38, 47)(39, 46)(40, 56)(41, 50)(42, 54)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.70
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.76 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 7, 7})
Quotient :: loop^2
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^7, Y1^7 ]
Map:: non-degenerate
	R = (1, 15, 29, 43, 4, 18, 32, 46)(2, 16, 30, 44, 6, 20, 34, 48)(3, 17, 31, 45, 8, 22, 36, 50)(5, 19, 33, 47, 10, 24, 38, 52)(7, 21, 35, 49, 12, 26, 40, 54)(9, 23, 37, 51, 13, 27, 41, 55)(11, 25, 39, 53, 14, 28, 42, 56)
	L = (1, 16)(2, 19)(3, 15)(4, 22)(5, 23)(6, 18)(7, 17)(8, 26)(9, 25)(10, 20)(11, 21)(12, 28)(13, 24)(14, 27)(29, 45)(30, 43)(31, 49)(32, 48)(33, 44)(34, 52)(35, 53)(36, 46)(37, 47)(38, 55)(39, 51)(40, 50)(41, 56)(42, 54)
	local type(s) :: { ( 4, 7, 4, 7, 4, 7, 4, 7 ) }
Outer automorphisms :: reflexible
Dual of E6.72
Transitivity :: VT+
Graph::
	v = 7 e = 28 f = 11
	degree seq :: [ 8^7 ]

E6.77 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^7, (Y3 * Y2^-1)^7 ]
Map::
	R = (1, 15, 2, 16)(3, 17, 5, 19)(4, 18, 6, 20)(7, 21, 9, 23)(8, 22, 10, 24)(11, 25, 13, 27)(12, 26, 14, 28)(29, 43, 31, 45, 35, 49, 39, 53, 40, 54, 36, 50, 32, 46)(30, 44, 33, 47, 37, 51, 41, 55, 42, 56, 38, 52, 34, 48)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.78 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^7, (Y3 * Y2^-1)^7 ]
Map::
	R = (1, 15, 2, 16)(3, 17, 6, 20)(4, 18, 5, 19)(7, 21, 10, 24)(8, 22, 9, 23)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 35, 49, 39, 53, 40, 54, 36, 50, 32, 46)(30, 44, 33, 47, 37, 51, 41, 55, 42, 56, 38, 52, 34, 48)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.79 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^7, (Y3 * Y2^-1)^7 ]
Map:: non-degenerate
	R = (1, 15, 2, 16)(3, 17, 6, 20)(4, 18, 5, 19)(7, 21, 10, 24)(8, 22, 9, 23)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 35, 49, 39, 53, 40, 54, 36, 50, 32, 46)(30, 44, 33, 47, 37, 51, 41, 55, 42, 56, 38, 52, 34, 48)
	L = (1, 32)(2, 34)(3, 29)(4, 36)(5, 30)(6, 38)(7, 31)(8, 40)(9, 33)(10, 42)(11, 35)(12, 39)(13, 37)(14, 41)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.83
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.80 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-2, (Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 15, 2, 16)(3, 17, 9, 23)(4, 18, 10, 24)(5, 19, 7, 21)(6, 20, 8, 22)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 32, 46, 39, 53, 40, 54, 34, 48, 33, 47)(30, 44, 35, 49, 36, 50, 41, 55, 42, 56, 38, 52, 37, 51)
	L = (1, 32)(2, 36)(3, 39)(4, 40)(5, 31)(6, 29)(7, 41)(8, 42)(9, 35)(10, 30)(11, 34)(12, 33)(13, 38)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.81 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y2 * Y3^-3, (Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 15, 2, 16)(3, 17, 9, 23)(4, 18, 10, 24)(5, 19, 7, 21)(6, 20, 8, 22)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 34, 48, 39, 53, 40, 54, 32, 46, 33, 47)(30, 44, 35, 49, 38, 52, 41, 55, 42, 56, 36, 50, 37, 51)
	L = (1, 32)(2, 36)(3, 33)(4, 39)(5, 40)(6, 29)(7, 37)(8, 41)(9, 42)(10, 30)(11, 31)(12, 34)(13, 35)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.82
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.82 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (Y2 * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2 ]
Map:: non-degenerate
	R = (1, 15, 2, 16)(3, 17, 9, 23)(4, 18, 10, 24)(5, 19, 7, 21)(6, 20, 8, 22)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 39, 53, 32, 46, 34, 48, 40, 54, 33, 47)(30, 44, 35, 49, 41, 55, 36, 50, 38, 52, 42, 56, 37, 51)
	L = (1, 32)(2, 36)(3, 34)(4, 33)(5, 39)(6, 29)(7, 38)(8, 37)(9, 41)(10, 30)(11, 40)(12, 31)(13, 42)(14, 35)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.81
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.83 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 7, 7})
Quotient :: dipole
Aut^+ = D14 (small group id <14, 1>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (Y2 * Y1)^2, Y2^-2 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 15, 2, 16)(3, 17, 9, 23)(4, 18, 10, 24)(5, 19, 7, 21)(6, 20, 8, 22)(11, 25, 14, 28)(12, 26, 13, 27)(29, 43, 31, 45, 39, 53, 34, 48, 32, 46, 40, 54, 33, 47)(30, 44, 35, 49, 41, 55, 38, 52, 36, 50, 42, 56, 37, 51)
	L = (1, 32)(2, 36)(3, 40)(4, 31)(5, 34)(6, 29)(7, 42)(8, 35)(9, 38)(10, 30)(11, 33)(12, 39)(13, 37)(14, 41)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.79
Graph:: bipartite
	v = 9 e = 28 f = 9
	degree seq :: [ 4^7, 14^2 ]

E6.84 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^2 * T1 * T2^4, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 6, 12, 13, 10, 4, 8, 2, 7, 11, 14, 9, 5)(15, 16, 20, 25, 27, 23, 18)(17, 21, 26, 28, 24, 19, 22)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 28^7 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.94
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 14 f = 1
	degree seq :: [ 7^2, 14 ]

E6.85 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^7 ]
Map:: non-degenerate
	R = (1, 3, 4, 8, 9, 12, 13, 14, 10, 11, 6, 7, 2, 5)(15, 16, 20, 24, 27, 23, 18)(17, 19, 21, 25, 28, 26, 22)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 28^7 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.92
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 14 f = 1
	degree seq :: [ 7^2, 14 ]

E6.86 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^7, (T2^-1 * T1^-1)^14 ]
Map:: non-degenerate
	R = (1, 3, 2, 7, 6, 11, 10, 14, 12, 13, 8, 9, 4, 5)(15, 16, 20, 24, 26, 22, 18)(17, 21, 25, 28, 27, 23, 19)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 28^7 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.95
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 14 f = 1
	degree seq :: [ 7^2, 14 ]

E6.87 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-1 * T1, T2 * T1 * T2^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 12, 4, 10, 6, 14, 11, 8, 2, 7, 13, 5)(15, 16, 20, 23, 27, 25, 18)(17, 21, 28, 26, 19, 22, 24)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 28^7 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.91
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 14 f = 1
	degree seq :: [ 7^2, 14 ]

E6.88 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-4 ]
Map:: non-degenerate
	R = (1, 3, 9, 8, 2, 7, 11, 14, 6, 12, 4, 10, 13, 5)(15, 16, 20, 27, 23, 25, 18)(17, 21, 26, 19, 22, 28, 24)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 28^7 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.93
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 14 f = 1
	degree seq :: [ 7^2, 14 ]

E6.89 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^4, (T2^-1 * T1^-1)^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 14, 8, 2, 7, 13, 10, 4, 6, 12, 11, 5)(15, 16, 20, 17, 21, 26, 23, 27, 25, 28, 24, 19, 22, 18)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.96
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.90 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {7, 14, 14})
Quotient :: edge
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T2^-4 * T1^2, T2^-2 * T1 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 12, 6, 4, 10, 14, 8, 2, 7, 13, 11, 5)(15, 16, 20, 19, 22, 26, 25, 28, 23, 27, 24, 17, 21, 18)
	L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.97
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.91 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^2 * T1 * T2^4, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 6, 20, 12, 26, 13, 27, 10, 24, 4, 18, 8, 22, 2, 16, 7, 21, 11, 25, 14, 28, 9, 23, 5, 19)
	L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 22)(6, 25)(7, 26)(8, 17)(9, 18)(10, 19)(11, 27)(12, 28)(13, 23)(14, 24)
	local type(s) :: { ( 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.87
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 14 f = 3
	degree seq :: [ 28 ]

E6.92 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1, (F * T2)^2, (F * T1)^2, T1^7 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 4, 18, 8, 22, 9, 23, 12, 26, 13, 27, 14, 28, 10, 24, 11, 25, 6, 20, 7, 21, 2, 16, 5, 19)
	L = (1, 16)(2, 20)(3, 19)(4, 15)(5, 21)(6, 24)(7, 25)(8, 17)(9, 18)(10, 27)(11, 28)(12, 22)(13, 23)(14, 26)
	local type(s) :: { ( 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.85
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 14 f = 3
	degree seq :: [ 28 ]

E6.93 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^7, (T2^-1 * T1^-1)^14 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 2, 16, 7, 21, 6, 20, 11, 25, 10, 24, 14, 28, 12, 26, 13, 27, 8, 22, 9, 23, 4, 18, 5, 19)
	L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 17)(6, 24)(7, 25)(8, 18)(9, 19)(10, 26)(11, 28)(12, 22)(13, 23)(14, 27)
	local type(s) :: { ( 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.88
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 14 f = 3
	degree seq :: [ 28 ]

E6.94 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-1 * T1, T2 * T1 * T2^3 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 9, 23, 12, 26, 4, 18, 10, 24, 6, 20, 14, 28, 11, 25, 8, 22, 2, 16, 7, 21, 13, 27, 5, 19)
	L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 22)(6, 23)(7, 28)(8, 24)(9, 27)(10, 17)(11, 18)(12, 19)(13, 25)(14, 26)
	local type(s) :: { ( 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.84
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 14 f = 3
	degree seq :: [ 28 ]

E6.95 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-4 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 9, 23, 8, 22, 2, 16, 7, 21, 11, 25, 14, 28, 6, 20, 12, 26, 4, 18, 10, 24, 13, 27, 5, 19)
	L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 22)(6, 27)(7, 26)(8, 28)(9, 25)(10, 17)(11, 18)(12, 19)(13, 23)(14, 24)
	local type(s) :: { ( 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.86
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 14 f = 3
	degree seq :: [ 28 ]

E6.96 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (T2 * T1^-1)^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, T1^2 * T2^5, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^2 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 6, 20, 12, 26, 14, 28, 9, 23, 5, 19)(2, 16, 7, 21, 11, 25, 13, 27, 10, 24, 4, 18, 8, 22)
	L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 22)(6, 25)(7, 26)(8, 17)(9, 18)(10, 19)(11, 28)(12, 27)(13, 23)(14, 24)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.89
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.97 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {7, 14, 14})
Quotient :: loop
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^7, (T2^-1 * T1^-1)^14 ]
Map:: non-degenerate
	R = (1, 15, 3, 17, 7, 21, 11, 25, 13, 27, 9, 23, 5, 19)(2, 16, 6, 20, 10, 24, 14, 28, 12, 26, 8, 22, 4, 18)
	L = (1, 16)(2, 17)(3, 20)(4, 15)(5, 18)(6, 21)(7, 24)(8, 19)(9, 22)(10, 25)(11, 28)(12, 23)(13, 26)(14, 27)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible
Dual of E6.90
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.98 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^2 * Y2 * Y1 * Y2 * Y3^-2, Y1^7, (Y1 * Y3^-1)^7, (Y3 * Y2^-1)^14 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 11, 25, 13, 27, 9, 23, 4, 18)(3, 17, 7, 21, 12, 26, 14, 28, 10, 24, 5, 19, 8, 22)(29, 43, 31, 45, 34, 48, 40, 54, 41, 55, 38, 52, 32, 46, 36, 50, 30, 44, 35, 49, 39, 53, 42, 56, 37, 51, 33, 47)
	L = (1, 32)(2, 29)(3, 36)(4, 37)(5, 38)(6, 30)(7, 31)(8, 33)(9, 41)(10, 42)(11, 34)(12, 35)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.110
Graph:: bipartite
	v = 3 e = 28 f = 15
	degree seq :: [ 14^2, 28 ]

E6.99 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^7, Y1^7 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 10, 24, 13, 27, 9, 23, 4, 18)(3, 17, 5, 19, 7, 21, 11, 25, 14, 28, 12, 26, 8, 22)(29, 43, 31, 45, 32, 46, 36, 50, 37, 51, 40, 54, 41, 55, 42, 56, 38, 52, 39, 53, 34, 48, 35, 49, 30, 44, 33, 47)
	L = (1, 32)(2, 29)(3, 36)(4, 37)(5, 31)(6, 30)(7, 33)(8, 40)(9, 41)(10, 34)(11, 35)(12, 42)(13, 38)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.108
Graph:: bipartite
	v = 3 e = 28 f = 15
	degree seq :: [ 14^2, 28 ]

E6.100 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y1^7, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 10, 24, 12, 26, 8, 22, 4, 18)(3, 17, 7, 21, 11, 25, 14, 28, 13, 27, 9, 23, 5, 19)(29, 43, 31, 45, 30, 44, 35, 49, 34, 48, 39, 53, 38, 52, 42, 56, 40, 54, 41, 55, 36, 50, 37, 51, 32, 46, 33, 47)
	L = (1, 32)(2, 29)(3, 33)(4, 36)(5, 37)(6, 30)(7, 31)(8, 40)(9, 41)(10, 34)(11, 35)(12, 38)(13, 42)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.111
Graph:: bipartite
	v = 3 e = 28 f = 15
	degree seq :: [ 14^2, 28 ]

E6.101 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2^-4 * Y1, Y1^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 13, 27, 9, 23, 11, 25, 4, 18)(3, 17, 7, 21, 12, 26, 5, 19, 8, 22, 14, 28, 10, 24)(29, 43, 31, 45, 37, 51, 36, 50, 30, 44, 35, 49, 39, 53, 42, 56, 34, 48, 40, 54, 32, 46, 38, 52, 41, 55, 33, 47)
	L = (1, 32)(2, 29)(3, 38)(4, 39)(5, 40)(6, 30)(7, 31)(8, 33)(9, 41)(10, 42)(11, 37)(12, 35)(13, 34)(14, 36)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.109
Graph:: bipartite
	v = 3 e = 28 f = 15
	degree seq :: [ 14^2, 28 ]

E6.102 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^-2 * Y1 * Y3^-2, Y1 * Y2^4, Y1^7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 9, 23, 13, 27, 11, 25, 4, 18)(3, 17, 7, 21, 14, 28, 12, 26, 5, 19, 8, 22, 10, 24)(29, 43, 31, 45, 37, 51, 40, 54, 32, 46, 38, 52, 34, 48, 42, 56, 39, 53, 36, 50, 30, 44, 35, 49, 41, 55, 33, 47)
	L = (1, 32)(2, 29)(3, 38)(4, 39)(5, 40)(6, 30)(7, 31)(8, 33)(9, 34)(10, 36)(11, 41)(12, 42)(13, 37)(14, 35)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.107
Graph:: bipartite
	v = 3 e = 28 f = 15
	degree seq :: [ 14^2, 28 ]

E6.103 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^3 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, Y1 * Y2^-1 * Y1^4, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 12, 26, 9, 23, 3, 17, 7, 21, 13, 27, 11, 25, 5, 19, 8, 22, 14, 28, 10, 24, 4, 18)(29, 43, 31, 45, 36, 50, 30, 44, 35, 49, 42, 56, 34, 48, 41, 55, 38, 52, 40, 54, 39, 53, 32, 46, 37, 51, 33, 47)
	L = (1, 31)(2, 35)(3, 36)(4, 37)(5, 29)(6, 41)(7, 42)(8, 30)(9, 33)(10, 40)(11, 32)(12, 39)(13, 38)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.105
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.104 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2, (R * Y1)^2, (Y2^-1, Y1^-1), R * Y2 * R * Y3, Y2^-1 * Y1^-5, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 12, 26, 9, 23, 5, 19, 8, 22, 14, 28, 10, 24, 3, 17, 7, 21, 13, 27, 11, 25, 4, 18)(29, 43, 31, 45, 37, 51, 32, 46, 38, 52, 40, 54, 39, 53, 42, 56, 34, 48, 41, 55, 36, 50, 30, 44, 35, 49, 33, 47)
	L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 41)(7, 33)(8, 30)(9, 32)(10, 40)(11, 42)(12, 39)(13, 36)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.106
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.105 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2 * Y3^2 * Y2, Y2^-2 * Y3^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^-1 * Y3^6, Y2^7, (Y3^-1 * Y1^-1)^14 ]
Map::
	R = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43, 30, 44, 34, 48, 39, 53, 42, 56, 37, 51, 32, 46)(31, 45, 35, 49, 33, 47, 36, 50, 40, 54, 41, 55, 38, 52)
	L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 33)(7, 32)(8, 30)(9, 41)(10, 42)(11, 36)(12, 34)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.103
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.106 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^7, (Y3^-1 * Y1^-1)^14, (Y3 * Y2^-1)^14 ]
Map::
	R = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43, 30, 44, 34, 48, 38, 52, 41, 55, 37, 51, 32, 46)(31, 45, 33, 47, 35, 49, 39, 53, 42, 56, 40, 54, 36, 50)
	L = (1, 31)(2, 33)(3, 32)(4, 36)(5, 29)(6, 35)(7, 30)(8, 37)(9, 40)(10, 39)(11, 34)(12, 41)(13, 42)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.104
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.107 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2 * Y1^-2, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^6, Y3^7, (Y3 * Y2^-1)^7, Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^3 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 11, 25, 14, 28, 10, 24, 5, 19, 8, 22, 3, 17, 7, 21, 12, 26, 13, 27, 9, 23, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)
	L = (1, 31)(2, 35)(3, 34)(4, 36)(5, 29)(6, 40)(7, 39)(8, 30)(9, 33)(10, 32)(11, 41)(12, 42)(13, 38)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.102
Graph:: bipartite
	v = 15 e = 28 f = 3
	degree seq :: [ 2^14, 28 ]

E6.108 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^7, (Y3^3 * Y1^-1)^2, (Y3 * Y2^-1)^7 ]
Map::
	R = (1, 15, 2, 16, 5, 19, 6, 20, 9, 23, 10, 24, 13, 27, 14, 28, 11, 25, 12, 26, 7, 21, 8, 22, 3, 17, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)
	L = (1, 31)(2, 32)(3, 35)(4, 36)(5, 29)(6, 30)(7, 39)(8, 40)(9, 33)(10, 34)(11, 41)(12, 42)(13, 37)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.99
Graph:: bipartite
	v = 15 e = 28 f = 3
	degree seq :: [ 2^14, 28 ]

E6.109 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^7, (Y3 * Y2^-1)^7, (Y3^-1 * Y1^-1)^14 ]
Map::
	R = (1, 15, 2, 16, 3, 17, 6, 20, 7, 21, 10, 24, 11, 25, 14, 28, 13, 27, 12, 26, 9, 23, 8, 22, 5, 19, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)
	L = (1, 31)(2, 34)(3, 35)(4, 30)(5, 29)(6, 38)(7, 39)(8, 32)(9, 33)(10, 42)(11, 41)(12, 36)(13, 37)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.101
Graph:: bipartite
	v = 15 e = 28 f = 3
	degree seq :: [ 2^14, 28 ]

E6.110 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-1 * Y1 * Y3^-2 * Y1, Y1^2 * Y3 * Y1^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 12, 26, 5, 19, 8, 22, 9, 23, 14, 28, 13, 27, 10, 24, 3, 17, 7, 21, 11, 25, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)
	L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 39)(7, 42)(8, 30)(9, 34)(10, 36)(11, 41)(12, 32)(13, 33)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.98
Graph:: bipartite
	v = 15 e = 28 f = 3
	degree seq :: [ 2^14, 28 ]

E6.111 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {7, 14, 14})
Quotient :: dipole
Aut^+ = C14 (small group id <14, 2>)
Aut   = D28 (small group id <28, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^3 * Y1^2, Y3 * Y1^-4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7 ]
Map::
	R = (1, 15, 2, 16, 6, 20, 10, 24, 3, 17, 7, 21, 13, 27, 14, 28, 9, 23, 12, 26, 5, 19, 8, 22, 11, 25, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56)
	L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 41)(7, 40)(8, 30)(9, 39)(10, 42)(11, 34)(12, 32)(13, 33)(14, 36)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28, 14, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.100
Graph:: bipartite
	v = 15 e = 28 f = 3
	degree seq :: [ 2^14, 28 ]

E6.112 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 15, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^5, T1^-1 * T2 * T1^-1 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 11, 15, 8, 2, 7, 12, 4, 10, 14, 6, 13, 5)(16, 17, 21, 26, 19)(18, 22, 28, 30, 25)(20, 23, 29, 24, 27)
	L = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)
	local type(s) :: { ( 30^5 ), ( 30^15 ) }
Outer automorphisms :: reflexible
Dual of E6.118
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 15 f = 1
	degree seq :: [ 5^3, 15 ]

E6.113 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 15, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, (T1^-1 * T2^-1)^15 ]
Map:: non-degenerate
	R = (1, 3, 8, 2, 7, 13, 6, 12, 15, 10, 14, 11, 4, 9, 5)(16, 17, 21, 25, 19)(18, 22, 27, 29, 24)(20, 23, 28, 30, 26)
	L = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)
	local type(s) :: { ( 30^5 ), ( 30^15 ) }
Outer automorphisms :: reflexible
Dual of E6.117
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 15 f = 1
	degree seq :: [ 5^3, 15 ]

E6.114 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 15, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, (T1^2 * T2)^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 4, 10, 14, 11, 15, 13, 6, 12, 8, 2, 7, 5)(16, 17, 21, 26, 19)(18, 22, 27, 30, 25)(20, 23, 28, 29, 24)
	L = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)
	local type(s) :: { ( 30^5 ), ( 30^15 ) }
Outer automorphisms :: reflexible
Dual of E6.116
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 15 f = 1
	degree seq :: [ 5^3, 15 ]

E6.115 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 15, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^7, (T2^-1 * T1^-1)^5 ]
Map:: non-degenerate
	R = (1, 3, 7, 11, 15, 12, 8, 4, 2, 6, 10, 14, 13, 9, 5)(16, 17, 18, 21, 22, 25, 26, 29, 30, 28, 27, 24, 23, 20, 19)
	L = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)
	local type(s) :: { ( 10^15 ) }
Outer automorphisms :: reflexible
Dual of E6.119
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 15 f = 3
	degree seq :: [ 15^2 ]

E6.116 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 15, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^5, T1^-1 * T2 * T1^-1 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 9, 24, 11, 26, 15, 30, 8, 23, 2, 17, 7, 22, 12, 27, 4, 19, 10, 25, 14, 29, 6, 21, 13, 28, 5, 20)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 26)(7, 28)(8, 29)(9, 27)(10, 18)(11, 19)(12, 20)(13, 30)(14, 24)(15, 25)
	local type(s) :: { ( 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15 ) }
Outer automorphisms :: reflexible
Dual of E6.114
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 15 f = 4
	degree seq :: [ 30 ]

E6.117 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 15, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, (T1^-1 * T2^-1)^15 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 8, 23, 2, 17, 7, 22, 13, 28, 6, 21, 12, 27, 15, 30, 10, 25, 14, 29, 11, 26, 4, 19, 9, 24, 5, 20)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 25)(7, 27)(8, 28)(9, 18)(10, 19)(11, 20)(12, 29)(13, 30)(14, 24)(15, 26)
	local type(s) :: { ( 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15 ) }
Outer automorphisms :: reflexible
Dual of E6.113
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 15 f = 4
	degree seq :: [ 30 ]

E6.118 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 15, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, (T1^2 * T2)^3 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 9, 24, 4, 19, 10, 25, 14, 29, 11, 26, 15, 30, 13, 28, 6, 21, 12, 27, 8, 23, 2, 17, 7, 22, 5, 20)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 26)(7, 27)(8, 28)(9, 20)(10, 18)(11, 19)(12, 30)(13, 29)(14, 24)(15, 25)
	local type(s) :: { ( 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15, 5, 15 ) }
Outer automorphisms :: reflexible
Dual of E6.112
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 15 f = 4
	degree seq :: [ 30 ]

E6.119 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 15, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T2^5, T2 * T1^-1 * T2^2 * T1^-2 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 9, 24, 13, 28, 5, 20)(2, 17, 7, 22, 11, 26, 15, 30, 8, 23)(4, 19, 10, 25, 14, 29, 6, 21, 12, 27)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 28)(7, 27)(8, 29)(9, 26)(10, 18)(11, 19)(12, 20)(13, 30)(14, 24)(15, 25)
	local type(s) :: { ( 15^10 ) }
Outer automorphisms :: reflexible
Dual of E6.115
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 15 f = 2
	degree seq :: [ 10^3 ]

E6.120 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y3^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y2)^2, Y2 * Y3 * Y2^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^5, Y2^2 * Y1 * Y2 * Y3^-1, Y2^6 * Y1^-1, Y3^10 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 13, 28, 15, 30, 10, 25)(5, 20, 8, 23, 14, 29, 9, 24, 12, 27)(31, 46, 33, 48, 39, 54, 41, 56, 45, 60, 38, 53, 32, 47, 37, 52, 42, 57, 34, 49, 40, 55, 44, 59, 36, 51, 43, 58, 35, 50)
	L = (1, 34)(2, 31)(3, 40)(4, 41)(5, 42)(6, 32)(7, 33)(8, 35)(9, 44)(10, 45)(11, 36)(12, 39)(13, 37)(14, 38)(15, 43)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.127
Graph:: bipartite
	v = 4 e = 30 f = 16
	degree seq :: [ 10^3, 30 ]

E6.121 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y1^5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 10, 25, 4, 19)(3, 18, 7, 22, 12, 27, 14, 29, 9, 24)(5, 20, 8, 23, 13, 28, 15, 30, 11, 26)(31, 46, 33, 48, 38, 53, 32, 47, 37, 52, 43, 58, 36, 51, 42, 57, 45, 60, 40, 55, 44, 59, 41, 56, 34, 49, 39, 54, 35, 50)
	L = (1, 34)(2, 31)(3, 39)(4, 40)(5, 41)(6, 32)(7, 33)(8, 35)(9, 44)(10, 36)(11, 45)(12, 37)(13, 38)(14, 42)(15, 43)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.126
Graph:: bipartite
	v = 4 e = 30 f = 16
	degree seq :: [ 10^3, 30 ]

E6.122 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y1^5, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 12, 27, 15, 30, 10, 25)(5, 20, 8, 23, 13, 28, 14, 29, 9, 24)(31, 46, 33, 48, 39, 54, 34, 49, 40, 55, 44, 59, 41, 56, 45, 60, 43, 58, 36, 51, 42, 57, 38, 53, 32, 47, 37, 52, 35, 50)
	L = (1, 34)(2, 31)(3, 40)(4, 41)(5, 39)(6, 32)(7, 33)(8, 35)(9, 44)(10, 45)(11, 36)(12, 37)(13, 38)(14, 43)(15, 42)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.125
Graph:: bipartite
	v = 4 e = 30 f = 16
	degree seq :: [ 10^3, 30 ]

E6.123 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^7, (Y3^-1 * Y1^-1)^5 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 10, 25, 14, 29, 13, 28, 9, 24, 5, 20, 3, 18, 7, 22, 11, 26, 15, 30, 12, 27, 8, 23, 4, 19)(31, 46, 33, 48, 32, 47, 37, 52, 36, 51, 41, 56, 40, 55, 45, 60, 44, 59, 42, 57, 43, 58, 38, 53, 39, 54, 34, 49, 35, 50)
	L = (1, 33)(2, 37)(3, 32)(4, 35)(5, 31)(6, 41)(7, 36)(8, 39)(9, 34)(10, 45)(11, 40)(12, 43)(13, 38)(14, 42)(15, 44)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.124
Graph:: bipartite
	v = 2 e = 30 f = 18
	degree seq :: [ 30^2 ]

E6.124 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^2 * Y3^-3, Y2^5, (Y3^-1 * Y1^-1)^15 ]
Map::
	R = (1, 16)(2, 17)(3, 18)(4, 19)(5, 20)(6, 21)(7, 22)(8, 23)(9, 24)(10, 25)(11, 26)(12, 27)(13, 28)(14, 29)(15, 30)(31, 46, 32, 47, 36, 51, 41, 56, 34, 49)(33, 48, 37, 52, 44, 59, 43, 58, 40, 55)(35, 50, 38, 53, 39, 54, 45, 60, 42, 57)
	L = (1, 33)(2, 37)(3, 39)(4, 40)(5, 31)(6, 44)(7, 45)(8, 32)(9, 36)(10, 38)(11, 43)(12, 34)(13, 35)(14, 42)(15, 41)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 30, 30 ), ( 30^10 ) }
Outer automorphisms :: reflexible
Dual of E6.123
Graph:: simple bipartite
	v = 18 e = 30 f = 2
	degree seq :: [ 2^15, 10^3 ]

E6.125 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^5, Y1^3 * Y3^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 13, 28, 15, 30, 10, 25, 3, 18, 7, 22, 12, 27, 5, 20, 8, 23, 14, 29, 9, 24, 11, 26, 4, 19)(31, 46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)
	L = (1, 33)(2, 37)(3, 39)(4, 40)(5, 31)(6, 42)(7, 41)(8, 32)(9, 43)(10, 44)(11, 45)(12, 34)(13, 35)(14, 36)(15, 38)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.122
Graph:: bipartite
	v = 16 e = 30 f = 4
	degree seq :: [ 2^15, 30 ]

E6.126 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, (Y1^-1 * Y3^-1)^15 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 3, 18, 7, 22, 12, 27, 9, 24, 13, 28, 15, 30, 11, 26, 14, 29, 10, 25, 5, 20, 8, 23, 4, 19)(31, 46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)
	L = (1, 33)(2, 37)(3, 39)(4, 36)(5, 31)(6, 42)(7, 43)(8, 32)(9, 41)(10, 34)(11, 35)(12, 45)(13, 44)(14, 38)(15, 40)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.121
Graph:: bipartite
	v = 16 e = 30 f = 4
	degree seq :: [ 2^15, 30 ]

E6.127 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 15, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^-1 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 5, 20, 8, 23, 12, 27, 11, 26, 14, 29, 15, 30, 9, 24, 13, 28, 10, 25, 3, 18, 7, 22, 4, 19)(31, 46)(32, 47)(33, 48)(34, 49)(35, 50)(36, 51)(37, 52)(38, 53)(39, 54)(40, 55)(41, 56)(42, 57)(43, 58)(44, 59)(45, 60)
	L = (1, 33)(2, 37)(3, 39)(4, 40)(5, 31)(6, 34)(7, 43)(8, 32)(9, 41)(10, 45)(11, 35)(12, 36)(13, 44)(14, 38)(15, 42)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.120
Graph:: bipartite
	v = 16 e = 30 f = 4
	degree seq :: [ 2^15, 30 ]

E6.128 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 8})
Quotient :: halfedge^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y1^8 ]
Map:: non-degenerate
	R = (1, 18, 2, 22, 6, 26, 10, 30, 14, 29, 13, 25, 9, 21, 5, 17)(3, 24, 8, 28, 12, 32, 16, 31, 15, 27, 11, 23, 7, 20, 4, 19)
	L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 12)(10, 11)(13, 16)(14, 15)(17, 20)(18, 23)(19, 21)(22, 27)(24, 25)(26, 31)(28, 29)(30, 32)
	local type(s) :: { ( 8^16 ) }
Outer automorphisms :: reflexible
Dual of E6.129
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 16 f = 4
	degree seq :: [ 16^2 ]

E6.129 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 4, 8})
Quotient :: halfedge^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^4, (Y1^-1 * Y3)^2, Y1^-1 * Y2 * Y3 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 18, 2, 22, 6, 21, 5, 17)(3, 25, 9, 29, 13, 23, 7, 19)(4, 27, 11, 30, 14, 24, 8, 20)(10, 31, 15, 32, 16, 28, 12, 26)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 13)(8, 10)(11, 16)(14, 15)(17, 20)(18, 24)(19, 26)(21, 27)(22, 30)(23, 31)(25, 28)(29, 32)
	local type(s) :: { ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E6.128
Transitivity :: VT+ AT
Graph:: bipartite
	v = 4 e = 16 f = 2
	degree seq :: [ 8^4 ]

E6.130 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 8})
Quotient :: edge^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y2)^2, Y3^4, Y1 * Y2 * Y3^-1 * Y1 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^2 ]
Map::
	R = (1, 17, 4, 20, 12, 28, 5, 21)(2, 18, 7, 23, 14, 30, 8, 24)(3, 19, 10, 26, 16, 32, 11, 27)(6, 22, 13, 29, 15, 31, 9, 25)(33, 34)(35, 41)(36, 40)(37, 39)(38, 43)(42, 47)(44, 46)(45, 48)(49, 51)(50, 54)(52, 59)(53, 58)(55, 57)(56, 61)(60, 64)(62, 63)
	L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 32, 32 ), ( 32^8 ) }
Outer automorphisms :: reflexible
Dual of E6.133
Graph:: simple bipartite
	v = 20 e = 32 f = 2
	degree seq :: [ 2^16, 8^4 ]

E6.131 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 8})
Quotient :: edge^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^8 ]
Map::
	R = (1, 17, 4, 20, 8, 24, 12, 28, 16, 32, 13, 29, 9, 25, 5, 21)(2, 18, 3, 19, 7, 23, 11, 27, 15, 31, 14, 30, 10, 26, 6, 22)(33, 34)(35, 37)(36, 38)(39, 41)(40, 42)(43, 45)(44, 46)(47, 48)(49, 51)(50, 52)(53, 55)(54, 56)(57, 59)(58, 60)(61, 63)(62, 64)
	L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 16, 16 ), ( 16^16 ) }
Outer automorphisms :: reflexible
Dual of E6.132
Graph:: simple bipartite
	v = 18 e = 32 f = 4
	degree seq :: [ 2^16, 16^2 ]

E6.132 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 8})
Quotient :: loop^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y2)^2, Y3^4, Y1 * Y2 * Y3^-1 * Y1 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y3^2 ]
Map::
	R = (1, 17, 33, 49, 4, 20, 36, 52, 12, 28, 44, 60, 5, 21, 37, 53)(2, 18, 34, 50, 7, 23, 39, 55, 14, 30, 46, 62, 8, 24, 40, 56)(3, 19, 35, 51, 10, 26, 42, 58, 16, 32, 48, 64, 11, 27, 43, 59)(6, 22, 38, 54, 13, 29, 45, 61, 15, 31, 47, 63, 9, 25, 41, 57)
	L = (1, 18)(2, 17)(3, 25)(4, 24)(5, 23)(6, 27)(7, 21)(8, 20)(9, 19)(10, 31)(11, 22)(12, 30)(13, 32)(14, 28)(15, 26)(16, 29)(33, 51)(34, 54)(35, 49)(36, 59)(37, 58)(38, 50)(39, 57)(40, 61)(41, 55)(42, 53)(43, 52)(44, 64)(45, 56)(46, 63)(47, 62)(48, 60)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.131
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 32 f = 18
	degree seq :: [ 16^4 ]

E6.133 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 8})
Quotient :: loop^2
Aut^+ = D16 (small group id <16, 7>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^8 ]
Map::
	R = (1, 17, 33, 49, 4, 20, 36, 52, 8, 24, 40, 56, 12, 28, 44, 60, 16, 32, 48, 64, 13, 29, 45, 61, 9, 25, 41, 57, 5, 21, 37, 53)(2, 18, 34, 50, 3, 19, 35, 51, 7, 23, 39, 55, 11, 27, 43, 59, 15, 31, 47, 63, 14, 30, 46, 62, 10, 26, 42, 58, 6, 22, 38, 54)
	L = (1, 18)(2, 17)(3, 21)(4, 22)(5, 19)(6, 20)(7, 25)(8, 26)(9, 23)(10, 24)(11, 29)(12, 30)(13, 27)(14, 28)(15, 32)(16, 31)(33, 51)(34, 52)(35, 49)(36, 50)(37, 55)(38, 56)(39, 53)(40, 54)(41, 59)(42, 60)(43, 57)(44, 58)(45, 63)(46, 64)(47, 61)(48, 62)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.130
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 32 f = 20
	degree seq :: [ 32^2 ]

E6.134 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 6, 22)(4, 20, 9, 25)(5, 21, 10, 26)(7, 23, 11, 27)(8, 24, 12, 28)(13, 29, 16, 32)(14, 30, 15, 31)(33, 49, 35, 51)(34, 50, 38, 54)(36, 52, 37, 53)(39, 55, 40, 56)(41, 57, 42, 58)(43, 59, 44, 60)(45, 61, 46, 62)(47, 63, 48, 64)
	L = (1, 36)(2, 39)(3, 37)(4, 35)(5, 33)(6, 40)(7, 38)(8, 34)(9, 45)(10, 46)(11, 47)(12, 48)(13, 42)(14, 41)(15, 44)(16, 43)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.143
Graph:: simple bipartite
	v = 16 e = 32 f = 6
	degree seq :: [ 4^16 ]

E6.135 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = D16 (small group id <16, 7>)
Aut   = C2 x D16 (small group id <32, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^4, (Y2^-1 * Y1)^2, (Y3 * Y2^-1)^8 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 10, 26)(5, 21, 7, 23)(6, 22, 8, 24)(11, 27, 14, 30)(12, 28, 16, 32)(13, 29, 15, 31)(33, 49, 35, 51, 43, 59, 37, 53)(34, 50, 39, 55, 46, 62, 41, 57)(36, 52, 38, 54, 44, 60, 45, 61)(40, 56, 42, 58, 47, 63, 48, 64)
	L = (1, 36)(2, 40)(3, 38)(4, 37)(5, 45)(6, 33)(7, 42)(8, 41)(9, 48)(10, 34)(11, 44)(12, 35)(13, 43)(14, 47)(15, 39)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.140
Graph:: simple bipartite
	v = 12 e = 32 f = 10
	degree seq :: [ 4^8, 8^4 ]

E6.136 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = D16 (small group id <16, 7>)
Aut   = C2 x D16 (small group id <32, 39>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 10, 26)(5, 21, 7, 23)(6, 22, 8, 24)(11, 27, 14, 30)(12, 28, 16, 32)(13, 29, 15, 31)(33, 49, 35, 51, 43, 59, 37, 53)(34, 50, 39, 55, 46, 62, 41, 57)(36, 52, 44, 60, 45, 61, 38, 54)(40, 56, 47, 63, 48, 64, 42, 58)
	L = (1, 36)(2, 40)(3, 44)(4, 35)(5, 38)(6, 33)(7, 47)(8, 39)(9, 42)(10, 34)(11, 45)(12, 43)(13, 37)(14, 48)(15, 46)(16, 41)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.139
Graph:: simple bipartite
	v = 12 e = 32 f = 10
	degree seq :: [ 4^8, 8^4 ]

E6.137 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y1 * Y2^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 5, 21)(4, 20, 6, 22)(7, 23, 10, 26)(8, 24, 9, 25)(11, 27, 12, 28)(13, 29, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 34, 50, 37, 53)(36, 52, 40, 56, 38, 54, 41, 57)(39, 55, 43, 59, 42, 58, 44, 60)(45, 61, 48, 64, 46, 62, 47, 63)
	L = (1, 36)(2, 38)(3, 39)(4, 33)(5, 42)(6, 34)(7, 35)(8, 45)(9, 46)(10, 37)(11, 47)(12, 48)(13, 40)(14, 41)(15, 43)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.142
Graph:: bipartite
	v = 12 e = 32 f = 10
	degree seq :: [ 4^8, 8^4 ]

E6.138 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, Y2^4, Y1 * Y2^2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 9, 25)(4, 20, 7, 23)(5, 21, 10, 26)(6, 22, 11, 27)(8, 24, 12, 28)(13, 29, 16, 32)(14, 30, 15, 31)(33, 49, 35, 51, 39, 55, 37, 53)(34, 50, 38, 54, 36, 52, 40, 56)(41, 57, 45, 61, 42, 58, 46, 62)(43, 59, 47, 63, 44, 60, 48, 64)
	L = (1, 36)(2, 39)(3, 42)(4, 33)(5, 41)(6, 44)(7, 34)(8, 43)(9, 37)(10, 35)(11, 40)(12, 38)(13, 47)(14, 48)(15, 45)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.141
Graph:: bipartite
	v = 12 e = 32 f = 10
	degree seq :: [ 4^8, 8^4 ]

E6.139 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = D16 (small group id <16, 7>)
Aut   = C2 x D16 (small group id <32, 39>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3^-1 * Y1^-1)^4 ]
Map:: non-degenerate
	R = (1, 17, 2, 18, 5, 21, 9, 25, 13, 29, 12, 28, 8, 24, 4, 20)(3, 19, 7, 23, 11, 27, 15, 31, 16, 32, 14, 30, 10, 26, 6, 22)(33, 49, 35, 51)(34, 50, 38, 54)(36, 52, 39, 55)(37, 53, 42, 58)(40, 56, 43, 59)(41, 57, 46, 62)(44, 60, 47, 63)(45, 61, 48, 64)
	L = (1, 34)(2, 37)(3, 39)(4, 33)(5, 41)(6, 35)(7, 43)(8, 36)(9, 45)(10, 38)(11, 47)(12, 40)(13, 44)(14, 42)(15, 48)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.136
Graph:: bipartite
	v = 10 e = 32 f = 12
	degree seq :: [ 4^8, 16^2 ]

E6.140 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = D16 (small group id <16, 7>)
Aut   = C2 x D16 (small group id <32, 39>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y1^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1^-3, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 17, 2, 18, 7, 23, 6, 22, 10, 26, 4, 20, 9, 25, 5, 21)(3, 19, 11, 27, 16, 32, 13, 29, 15, 31, 12, 28, 14, 30, 8, 24)(33, 49, 35, 51)(34, 50, 40, 56)(36, 52, 45, 61)(37, 53, 43, 59)(38, 54, 44, 60)(39, 55, 46, 62)(41, 57, 48, 64)(42, 58, 47, 63)
	L = (1, 36)(2, 41)(3, 44)(4, 39)(5, 42)(6, 33)(7, 37)(8, 47)(9, 38)(10, 34)(11, 46)(12, 48)(13, 35)(14, 45)(15, 43)(16, 40)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.135
Graph:: bipartite
	v = 10 e = 32 f = 12
	degree seq :: [ 4^8, 16^2 ]

E6.141 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^4, Y2 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 17, 2, 18, 6, 22, 10, 26, 3, 19, 7, 23, 14, 30, 5, 21)(4, 20, 11, 27, 16, 32, 8, 24, 9, 25, 13, 29, 15, 31, 12, 28)(33, 49, 35, 51)(34, 50, 39, 55)(36, 52, 41, 57)(37, 53, 42, 58)(38, 54, 46, 62)(40, 56, 44, 60)(43, 59, 45, 61)(47, 63, 48, 64)
	L = (1, 36)(2, 40)(3, 41)(4, 33)(5, 45)(6, 47)(7, 44)(8, 34)(9, 35)(10, 43)(11, 42)(12, 39)(13, 37)(14, 48)(15, 38)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.138
Graph:: bipartite
	v = 10 e = 32 f = 12
	degree seq :: [ 4^8, 16^2 ]

E6.142 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y3, (Y3 * Y2)^2, (R * Y1)^2, Y1^-1 * Y3 * Y2 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 17, 2, 18, 6, 22, 13, 29, 10, 26, 16, 32, 12, 28, 5, 21)(3, 19, 9, 25, 15, 31, 7, 23, 4, 20, 11, 27, 14, 30, 8, 24)(33, 49, 35, 51)(34, 50, 39, 55)(36, 52, 42, 58)(37, 53, 43, 59)(38, 54, 46, 62)(40, 56, 48, 64)(41, 57, 45, 61)(44, 60, 47, 63)
	L = (1, 36)(2, 40)(3, 42)(4, 33)(5, 41)(6, 47)(7, 48)(8, 34)(9, 37)(10, 35)(11, 45)(12, 46)(13, 43)(14, 44)(15, 38)(16, 39)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.137
Graph:: bipartite
	v = 10 e = 32 f = 12
	degree seq :: [ 4^8, 16^2 ]

E6.143 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 4, 8})
Quotient :: dipole
Aut^+ = QD16 (small group id <16, 8>)
Aut   = (C2 x D8) : C2 (small group id <32, 43>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1^4, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2^-4 * Y1^-1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 9, 25, 13, 29, 8, 24)(5, 21, 11, 27, 14, 30, 7, 23)(10, 26, 16, 32, 12, 28, 15, 31)(33, 49, 35, 51, 42, 58, 46, 62, 38, 54, 45, 61, 44, 60, 37, 53)(34, 50, 39, 55, 47, 63, 41, 57, 36, 52, 43, 59, 48, 64, 40, 56)
	L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 43)(6, 36)(7, 37)(8, 35)(9, 45)(10, 48)(11, 46)(12, 47)(13, 40)(14, 39)(15, 42)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 4^8 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E6.134
Graph:: bipartite
	v = 6 e = 32 f = 16
	degree seq :: [ 8^4, 16^2 ]

E6.144 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 16, 16})
Quotient :: edge
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T1 * T2^4, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 11, 4, 10, 16, 14, 6, 13, 15, 8, 2, 7, 12, 5)(17, 18, 22, 20)(19, 23, 29, 26)(21, 24, 30, 27)(25, 28, 31, 32)
	L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 32^4 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E6.148
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 16 f = 1
	degree seq :: [ 4^4, 16 ]

E6.145 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 16, 16})
Quotient :: edge
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^4 * T1^-1, (T1^-1 * T2^-1)^16 ]
Map:: non-degenerate
	R = (1, 3, 9, 8, 2, 7, 15, 14, 6, 13, 16, 11, 4, 10, 12, 5)(17, 18, 22, 20)(19, 23, 29, 26)(21, 24, 30, 27)(25, 31, 32, 28)
	L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 32^4 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E6.147
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 16 f = 1
	degree seq :: [ 4^4, 16 ]

E6.146 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 16, 16})
Quotient :: edge
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^5, T2^3 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 10, 4, 6, 12, 16, 14, 8, 2, 7, 13, 11, 5)(17, 18, 22, 19, 23, 28, 25, 29, 32, 31, 27, 30, 26, 21, 24, 20)
	L = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)
	local type(s) :: { ( 8^16 ) }
Outer automorphisms :: reflexible
Dual of E6.149
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 16 f = 4
	degree seq :: [ 16^2 ]

E6.147 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 16, 16})
Quotient :: loop
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T1 * T2^4, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 17, 3, 19, 9, 25, 11, 27, 4, 20, 10, 26, 16, 32, 14, 30, 6, 22, 13, 29, 15, 31, 8, 24, 2, 18, 7, 23, 12, 28, 5, 21)
	L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 24)(6, 20)(7, 29)(8, 30)(9, 28)(10, 19)(11, 21)(12, 31)(13, 26)(14, 27)(15, 32)(16, 25)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.145
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 16 f = 5
	degree seq :: [ 32 ]

E6.148 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 16, 16})
Quotient :: loop
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^4 * T1^-1, (T1^-1 * T2^-1)^16 ]
Map:: non-degenerate
	R = (1, 17, 3, 19, 9, 25, 8, 24, 2, 18, 7, 23, 15, 31, 14, 30, 6, 22, 13, 29, 16, 32, 11, 27, 4, 20, 10, 26, 12, 28, 5, 21)
	L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 24)(6, 20)(7, 29)(8, 30)(9, 31)(10, 19)(11, 21)(12, 25)(13, 26)(14, 27)(15, 32)(16, 28)
	local type(s) :: { ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.144
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 16 f = 5
	degree seq :: [ 32 ]

E6.149 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 16, 16})
Quotient :: loop
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4 ]
Map:: non-degenerate
	R = (1, 17, 3, 19, 9, 25, 5, 21)(2, 18, 7, 23, 14, 30, 8, 24)(4, 20, 10, 26, 15, 31, 12, 28)(6, 22, 11, 27, 16, 32, 13, 29)
	L = (1, 18)(2, 22)(3, 23)(4, 17)(5, 24)(6, 28)(7, 27)(8, 29)(9, 30)(10, 19)(11, 20)(12, 21)(13, 31)(14, 32)(15, 25)(16, 26)
	local type(s) :: { ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E6.146
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 16 f = 2
	degree seq :: [ 8^4 ]

E6.150 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y3^4, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 7, 23, 13, 29, 10, 26)(5, 21, 8, 24, 14, 30, 11, 27)(9, 25, 15, 31, 16, 32, 12, 28)(33, 49, 35, 51, 41, 57, 40, 56, 34, 50, 39, 55, 47, 63, 46, 62, 38, 54, 45, 61, 48, 64, 43, 59, 36, 52, 42, 58, 44, 60, 37, 53)
	L = (1, 36)(2, 33)(3, 42)(4, 38)(5, 43)(6, 34)(7, 35)(8, 37)(9, 44)(10, 45)(11, 46)(12, 48)(13, 39)(14, 40)(15, 41)(16, 47)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) }
Outer automorphisms :: reflexible
Dual of E6.154
Graph:: bipartite
	v = 5 e = 32 f = 17
	degree seq :: [ 8^4, 32 ]

E6.151 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^4, (Y2, Y1^-1), Y2^4 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 7, 23, 13, 29, 10, 26)(5, 21, 8, 24, 14, 30, 11, 27)(9, 25, 12, 28, 15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 43, 59, 36, 52, 42, 58, 48, 64, 46, 62, 38, 54, 45, 61, 47, 63, 40, 56, 34, 50, 39, 55, 44, 60, 37, 53)
	L = (1, 36)(2, 33)(3, 42)(4, 38)(5, 43)(6, 34)(7, 35)(8, 37)(9, 48)(10, 45)(11, 46)(12, 41)(13, 39)(14, 40)(15, 44)(16, 47)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) }
Outer automorphisms :: reflexible
Dual of E6.155
Graph:: bipartite
	v = 5 e = 32 f = 17
	degree seq :: [ 8^4, 32 ]

E6.152 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^3 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^5, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 12, 28, 11, 27, 5, 21, 8, 24, 14, 30, 16, 32, 15, 31, 9, 25, 3, 19, 7, 23, 13, 29, 10, 26, 4, 20)(33, 49, 35, 51, 40, 56, 34, 50, 39, 55, 46, 62, 38, 54, 45, 61, 48, 64, 44, 60, 42, 58, 47, 63, 43, 59, 36, 52, 41, 57, 37, 53)
	L = (1, 35)(2, 39)(3, 40)(4, 41)(5, 33)(6, 45)(7, 46)(8, 34)(9, 37)(10, 47)(11, 36)(12, 42)(13, 48)(14, 38)(15, 43)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.153
Graph:: bipartite
	v = 2 e = 32 f = 20
	degree seq :: [ 32^2 ]

E6.153 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2, Y3^-1), Y2 * Y3^4, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^16 ]
Map::
	R = (1, 17)(2, 18)(3, 19)(4, 20)(5, 21)(6, 22)(7, 23)(8, 24)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32)(33, 49, 34, 50, 38, 54, 36, 52)(35, 51, 39, 55, 45, 61, 42, 58)(37, 53, 40, 56, 46, 62, 43, 59)(41, 57, 44, 60, 47, 63, 48, 64)
	L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 45)(7, 44)(8, 34)(9, 43)(10, 48)(11, 36)(12, 37)(13, 47)(14, 38)(15, 40)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 32, 32 ), ( 32^8 ) }
Outer automorphisms :: reflexible
Dual of E6.152
Graph:: simple bipartite
	v = 20 e = 32 f = 2
	degree seq :: [ 2^16, 8^4 ]

E6.154 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 12, 28, 5, 21, 8, 24, 13, 29, 15, 31, 9, 25, 14, 30, 16, 32, 10, 26, 3, 19, 7, 23, 11, 27, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64)
	L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 43)(7, 46)(8, 34)(9, 37)(10, 47)(11, 48)(12, 36)(13, 38)(14, 40)(15, 44)(16, 45)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E6.150
Graph:: bipartite
	v = 17 e = 32 f = 5
	degree seq :: [ 2^16, 32 ]

E6.155 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y1^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, (Y1^-1 * Y3^-1)^16 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 10, 26, 3, 19, 7, 23, 13, 29, 15, 31, 9, 25, 14, 30, 16, 32, 12, 28, 5, 21, 8, 24, 11, 27, 4, 20)(33, 49)(34, 50)(35, 51)(36, 52)(37, 53)(38, 54)(39, 55)(40, 56)(41, 57)(42, 58)(43, 59)(44, 60)(45, 61)(46, 62)(47, 63)(48, 64)
	L = (1, 35)(2, 39)(3, 41)(4, 42)(5, 33)(6, 45)(7, 46)(8, 34)(9, 37)(10, 47)(11, 38)(12, 36)(13, 48)(14, 40)(15, 44)(16, 43)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)
	local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E6.151
Graph:: bipartite
	v = 17 e = 32 f = 5
	degree seq :: [ 2^16, 32 ]

E6.156 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 3, 9})
Quotient :: halfedge^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^-4 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 20, 2, 24, 6, 32, 14, 28, 10, 30, 12, 35, 17, 31, 13, 23, 5, 19)(3, 27, 9, 34, 16, 26, 8, 22, 4, 29, 11, 36, 18, 33, 15, 25, 7, 21)
	L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 17)(10, 11)(13, 16)(14, 18)(19, 22)(20, 26)(21, 28)(23, 29)(24, 34)(25, 30)(27, 32)(31, 36)(33, 35)
	local type(s) :: { ( 6^18 ) }
Outer automorphisms :: reflexible
Dual of E6.157
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 18 f = 6
	degree seq :: [ 18^2 ]

E6.157 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 3, 9})
Quotient :: halfedge^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, (Y2 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-2, Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3 ]
Map:: non-degenerate
	R = (1, 20, 2, 23, 5, 19)(3, 26, 8, 24, 6, 21)(4, 28, 10, 25, 7, 22)(9, 30, 12, 32, 14, 27)(11, 31, 13, 34, 16, 29)(15, 36, 18, 35, 17, 33)
	L = (1, 3)(2, 6)(4, 11)(5, 8)(7, 13)(9, 15)(10, 16)(12, 17)(14, 18)(19, 22)(20, 25)(21, 27)(23, 28)(24, 30)(26, 32)(29, 35)(31, 36)(33, 34)
	local type(s) :: { ( 18^6 ) }
Outer automorphisms :: reflexible
Dual of E6.156
Transitivity :: VT+ AT
Graph:: bipartite
	v = 6 e = 18 f = 2
	degree seq :: [ 6^6 ]

E6.158 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 9})
Quotient :: edge^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y2 * Y1 * Y3^2 * Y1 * Y2, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ]
Map::
	R = (1, 19, 4, 22, 5, 23)(2, 20, 7, 25, 8, 26)(3, 21, 10, 28, 11, 29)(6, 24, 13, 31, 14, 32)(9, 27, 16, 34, 17, 35)(12, 30, 18, 36, 15, 33)(37, 38)(39, 45)(40, 44)(41, 43)(42, 48)(46, 53)(47, 52)(49, 51)(50, 54)(55, 57)(56, 60)(58, 65)(59, 64)(61, 68)(62, 67)(63, 69)(66, 71)(70, 72)
	L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 36, 36 ), ( 36^6 ) }
Outer automorphisms :: reflexible
Dual of E6.161
Graph:: simple bipartite
	v = 24 e = 36 f = 2
	degree seq :: [ 2^18, 6^6 ]

E6.159 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 9})
Quotient :: edge^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y2 * Y3^-1 * Y1 * Y2 * Y1, Y3^2 * Y1 * Y3^-2 * Y2 ]
Map::
	R = (1, 19, 4, 22, 12, 30, 17, 35, 9, 27, 6, 24, 14, 32, 13, 31, 5, 23)(2, 20, 7, 25, 15, 33, 18, 36, 11, 29, 3, 21, 10, 28, 16, 34, 8, 26)(37, 38)(39, 45)(40, 44)(41, 43)(42, 47)(46, 53)(48, 52)(49, 51)(50, 54)(55, 57)(56, 60)(58, 65)(59, 64)(61, 63)(62, 68)(66, 72)(67, 70)(69, 71)
	L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 12, 12 ), ( 12^18 ) }
Outer automorphisms :: reflexible
Dual of E6.160
Graph:: simple bipartite
	v = 20 e = 36 f = 6
	degree seq :: [ 2^18, 18^2 ]

E6.160 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 9})
Quotient :: loop^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y2 * Y1 * Y3^2 * Y1 * Y2, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ]
Map::
	R = (1, 19, 37, 55, 4, 22, 40, 58, 5, 23, 41, 59)(2, 20, 38, 56, 7, 25, 43, 61, 8, 26, 44, 62)(3, 21, 39, 57, 10, 28, 46, 64, 11, 29, 47, 65)(6, 24, 42, 60, 13, 31, 49, 67, 14, 32, 50, 68)(9, 27, 45, 63, 16, 34, 52, 70, 17, 35, 53, 71)(12, 30, 48, 66, 18, 36, 54, 72, 15, 33, 51, 69)
	L = (1, 20)(2, 19)(3, 27)(4, 26)(5, 25)(6, 30)(7, 23)(8, 22)(9, 21)(10, 35)(11, 34)(12, 24)(13, 33)(14, 36)(15, 31)(16, 29)(17, 28)(18, 32)(37, 57)(38, 60)(39, 55)(40, 65)(41, 64)(42, 56)(43, 68)(44, 67)(45, 69)(46, 59)(47, 58)(48, 71)(49, 62)(50, 61)(51, 63)(52, 72)(53, 66)(54, 70)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.159
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 36 f = 20
	degree seq :: [ 12^6 ]

E6.161 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 9})
Quotient :: loop^2
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y2 * Y3^-1 * Y1 * Y2 * Y1, Y3^2 * Y1 * Y3^-2 * Y2 ]
Map::
	R = (1, 19, 37, 55, 4, 22, 40, 58, 12, 30, 48, 66, 17, 35, 53, 71, 9, 27, 45, 63, 6, 24, 42, 60, 14, 32, 50, 68, 13, 31, 49, 67, 5, 23, 41, 59)(2, 20, 38, 56, 7, 25, 43, 61, 15, 33, 51, 69, 18, 36, 54, 72, 11, 29, 47, 65, 3, 21, 39, 57, 10, 28, 46, 64, 16, 34, 52, 70, 8, 26, 44, 62)
	L = (1, 20)(2, 19)(3, 27)(4, 26)(5, 25)(6, 29)(7, 23)(8, 22)(9, 21)(10, 35)(11, 24)(12, 34)(13, 33)(14, 36)(15, 31)(16, 30)(17, 28)(18, 32)(37, 57)(38, 60)(39, 55)(40, 65)(41, 64)(42, 56)(43, 63)(44, 68)(45, 61)(46, 59)(47, 58)(48, 72)(49, 70)(50, 62)(51, 71)(52, 67)(53, 69)(54, 66)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.158
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 36 f = 24
	degree seq :: [ 36^2 ]

E6.162 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 9})
Quotient :: dipole
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y2^-1 * Y3^3, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 19, 2, 20)(3, 21, 9, 27)(4, 22, 10, 28)(5, 23, 7, 25)(6, 24, 8, 26)(11, 29, 18, 36)(12, 30, 17, 35)(13, 31, 16, 34)(14, 32, 15, 33)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 49, 67)(42, 60, 48, 66, 50, 68)(44, 62, 51, 69, 53, 71)(46, 64, 52, 70, 54, 72)
	L = (1, 40)(2, 44)(3, 47)(4, 48)(5, 49)(6, 37)(7, 51)(8, 52)(9, 53)(10, 38)(11, 50)(12, 39)(13, 42)(14, 41)(15, 54)(16, 43)(17, 46)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.164
Graph:: simple bipartite
	v = 15 e = 36 f = 11
	degree seq :: [ 4^9, 6^6 ]

E6.163 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 9})
Quotient :: dipole
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y2^-1 * Y3^-3, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ]
Map:: non-degenerate
	R = (1, 19, 2, 20)(3, 21, 9, 27)(4, 22, 10, 28)(5, 23, 7, 25)(6, 24, 8, 26)(11, 29, 17, 35)(12, 30, 18, 36)(13, 31, 15, 33)(14, 32, 16, 34)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 47, 65, 50, 68)(42, 60, 48, 66, 49, 67)(44, 62, 51, 69, 54, 72)(46, 64, 52, 70, 53, 71)
	L = (1, 40)(2, 44)(3, 47)(4, 49)(5, 50)(6, 37)(7, 51)(8, 53)(9, 54)(10, 38)(11, 42)(12, 39)(13, 41)(14, 48)(15, 46)(16, 43)(17, 45)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 4, 18, 4, 18 ), ( 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.165
Graph:: simple bipartite
	v = 15 e = 36 f = 11
	degree seq :: [ 4^9, 6^6 ]

E6.164 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 9})
Quotient :: dipole
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y1 * Y3^-2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^3 * Y3 * Y1, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 19, 2, 20, 7, 25, 14, 32, 6, 24, 4, 22, 9, 27, 13, 31, 5, 23)(3, 21, 10, 28, 17, 35, 16, 34, 12, 30, 11, 29, 18, 36, 15, 33, 8, 26)(37, 55, 39, 57)(38, 56, 44, 62)(40, 58, 48, 66)(41, 59, 46, 64)(42, 60, 47, 65)(43, 61, 51, 69)(45, 63, 52, 70)(49, 67, 53, 71)(50, 68, 54, 72)
	L = (1, 40)(2, 45)(3, 47)(4, 38)(5, 42)(6, 37)(7, 49)(8, 48)(9, 43)(10, 54)(11, 46)(12, 39)(13, 50)(14, 41)(15, 52)(16, 44)(17, 51)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.162
Graph:: bipartite
	v = 11 e = 36 f = 15
	degree seq :: [ 4^9, 18^2 ]

E6.165 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 9})
Quotient :: dipole
Aut^+ = D18 (small group id <18, 1>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (Y1 * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1 * Y3^4, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 19, 2, 20, 4, 22, 8, 26, 12, 30, 14, 32, 13, 31, 6, 24, 5, 23)(3, 21, 9, 27, 10, 28, 16, 34, 17, 35, 18, 36, 15, 33, 11, 29, 7, 25)(37, 55, 39, 57)(38, 56, 43, 61)(40, 58, 47, 65)(41, 59, 45, 63)(42, 60, 46, 64)(44, 62, 51, 69)(48, 66, 54, 72)(49, 67, 52, 70)(50, 68, 53, 71)
	L = (1, 40)(2, 44)(3, 46)(4, 48)(5, 38)(6, 37)(7, 45)(8, 50)(9, 52)(10, 53)(11, 39)(12, 49)(13, 41)(14, 42)(15, 43)(16, 54)(17, 51)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.163
Graph:: bipartite
	v = 11 e = 36 f = 15
	degree seq :: [ 4^9, 18^2 ]

E6.166 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 18, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^6 * T1, (T1^-1 * T2^-1)^18 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 16, 10, 4, 9, 15, 18, 13, 7, 2, 6, 12, 17, 11, 5)(19, 20, 22)(21, 24, 27)(23, 25, 28)(26, 30, 33)(29, 31, 34)(32, 35, 36)
	L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 36^3 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E6.170
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 18 f = 1
	degree seq :: [ 3^6, 18 ]

E6.167 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 18, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-6 * T1, (T1^-1 * T2^-1)^18 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 13, 7, 2, 6, 12, 18, 16, 10, 4, 9, 15, 17, 11, 5)(19, 20, 22)(21, 24, 27)(23, 25, 28)(26, 30, 33)(29, 31, 34)(32, 36, 35)
	L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 36^3 ), ( 36^18 ) }
Outer automorphisms :: reflexible
Dual of E6.169
Transitivity :: ET+
Graph:: bipartite
	v = 7 e = 18 f = 1
	degree seq :: [ 3^6, 18 ]

E6.168 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 18, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, (T2, T1), (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1 * T2 * T1 * T2^2 * T1, T2^2 * T1^-1 * T2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 16, 6, 15, 12, 4, 10, 18, 8, 2, 7, 17, 11, 14, 13, 5)(19, 20, 24, 32, 28, 21, 25, 33, 31, 36, 27, 35, 30, 23, 26, 34, 29, 22)
	L = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6^18 ) }
Outer automorphisms :: reflexible
Dual of E6.171
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 18 f = 6
	degree seq :: [ 18^2 ]

E6.169 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 18, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^6 * T1, (T1^-1 * T2^-1)^18 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 8, 26, 14, 32, 16, 34, 10, 28, 4, 22, 9, 27, 15, 33, 18, 36, 13, 31, 7, 25, 2, 20, 6, 24, 12, 30, 17, 35, 11, 29, 5, 23)
	L = (1, 20)(2, 22)(3, 24)(4, 19)(5, 25)(6, 27)(7, 28)(8, 30)(9, 21)(10, 23)(11, 31)(12, 33)(13, 34)(14, 35)(15, 26)(16, 29)(17, 36)(18, 32)
	local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.167
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 18 f = 7
	degree seq :: [ 36 ]

E6.170 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 18, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-6 * T1, (T1^-1 * T2^-1)^18 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 8, 26, 14, 32, 13, 31, 7, 25, 2, 20, 6, 24, 12, 30, 18, 36, 16, 34, 10, 28, 4, 22, 9, 27, 15, 33, 17, 35, 11, 29, 5, 23)
	L = (1, 20)(2, 22)(3, 24)(4, 19)(5, 25)(6, 27)(7, 28)(8, 30)(9, 21)(10, 23)(11, 31)(12, 33)(13, 34)(14, 36)(15, 26)(16, 29)(17, 32)(18, 35)
	local type(s) :: { ( 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18, 3, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.166
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 18 f = 7
	degree seq :: [ 36 ]

E6.171 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 18, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^6, (T1^-1 * T2^-1)^18 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 5, 23)(2, 20, 7, 25, 8, 26)(4, 22, 9, 27, 11, 29)(6, 24, 13, 31, 14, 32)(10, 28, 15, 33, 17, 35)(12, 30, 16, 34, 18, 36)
	L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 30)(7, 31)(8, 32)(9, 21)(10, 22)(11, 23)(12, 35)(13, 34)(14, 36)(15, 27)(16, 28)(17, 29)(18, 33)
	local type(s) :: { ( 18^6 ) }
Outer automorphisms :: reflexible
Dual of E6.168
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 18 f = 2
	degree seq :: [ 6^6 ]

E6.172 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^6, Y2^-3 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 18, 36, 17, 35)(37, 55, 39, 57, 44, 62, 50, 68, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 54, 72, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 53, 71, 47, 65, 41, 59)
	L = (1, 40)(2, 37)(3, 45)(4, 38)(5, 46)(6, 39)(7, 41)(8, 51)(9, 42)(10, 43)(11, 52)(12, 44)(13, 47)(14, 53)(15, 48)(16, 49)(17, 54)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E6.176
Graph:: bipartite
	v = 7 e = 36 f = 19
	degree seq :: [ 6^6, 36 ]

E6.173 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y1^-2, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^6 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 17, 35, 18, 36)(37, 55, 39, 57, 44, 62, 50, 68, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 54, 72, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 53, 71, 47, 65, 41, 59)
	L = (1, 40)(2, 37)(3, 45)(4, 38)(5, 46)(6, 39)(7, 41)(8, 51)(9, 42)(10, 43)(11, 52)(12, 44)(13, 47)(14, 54)(15, 48)(16, 49)(17, 50)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 2, 36, 2, 36, 2, 36 ), ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) }
Outer automorphisms :: reflexible
Dual of E6.177
Graph:: bipartite
	v = 7 e = 36 f = 19
	degree seq :: [ 6^6, 36 ]

E6.174 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y2 * Y1^2, Y1^-1 * Y2 * Y1^-3 * Y2, (Y3^-1 * Y1^-1)^3 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 14, 32, 9, 27, 17, 35, 12, 30, 5, 23, 8, 26, 16, 34, 10, 28, 3, 21, 7, 25, 15, 33, 13, 31, 18, 36, 11, 29, 4, 22)(37, 55, 39, 57, 45, 63, 54, 72, 44, 62, 38, 56, 43, 61, 53, 71, 47, 65, 52, 70, 42, 60, 51, 69, 48, 66, 40, 58, 46, 64, 50, 68, 49, 67, 41, 59)
	L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 51)(7, 53)(8, 38)(9, 54)(10, 50)(11, 52)(12, 40)(13, 41)(14, 49)(15, 48)(16, 42)(17, 47)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.175
Graph:: bipartite
	v = 2 e = 36 f = 24
	degree seq :: [ 36^2 ]

E6.175 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2 * Y3^6, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^18 ]
Map::
	R = (1, 19)(2, 20)(3, 21)(4, 22)(5, 23)(6, 24)(7, 25)(8, 26)(9, 27)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)(37, 55, 38, 56, 40, 58)(39, 57, 42, 60, 45, 63)(41, 59, 43, 61, 46, 64)(44, 62, 48, 66, 51, 69)(47, 65, 49, 67, 52, 70)(50, 68, 53, 71, 54, 72)
	L = (1, 39)(2, 42)(3, 44)(4, 45)(5, 37)(6, 48)(7, 38)(8, 50)(9, 51)(10, 40)(11, 41)(12, 53)(13, 43)(14, 52)(15, 54)(16, 46)(17, 47)(18, 49)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 36, 36 ), ( 36^6 ) }
Outer automorphisms :: reflexible
Dual of E6.174
Graph:: simple bipartite
	v = 24 e = 36 f = 2
	degree seq :: [ 2^18, 6^6 ]

E6.176 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^6, (Y1^-1 * Y3^-1)^18 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 12, 30, 17, 35, 11, 29, 5, 23, 8, 26, 14, 32, 18, 36, 15, 33, 9, 27, 3, 21, 7, 25, 13, 31, 16, 34, 10, 28, 4, 22)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72)
	L = (1, 39)(2, 43)(3, 41)(4, 45)(5, 37)(6, 49)(7, 44)(8, 38)(9, 47)(10, 51)(11, 40)(12, 52)(13, 50)(14, 42)(15, 53)(16, 54)(17, 46)(18, 48)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) }
Outer automorphisms :: reflexible
Dual of E6.172
Graph:: bipartite
	v = 19 e = 36 f = 7
	degree seq :: [ 2^18, 36 ]

E6.177 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 18, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^6, (Y1^-1 * Y3^-1)^18 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 12, 30, 15, 33, 9, 27, 3, 21, 7, 25, 13, 31, 18, 36, 17, 35, 11, 29, 5, 23, 8, 26, 14, 32, 16, 34, 10, 28, 4, 22)(37, 55)(38, 56)(39, 57)(40, 58)(41, 59)(42, 60)(43, 61)(44, 62)(45, 63)(46, 64)(47, 65)(48, 66)(49, 67)(50, 68)(51, 69)(52, 70)(53, 71)(54, 72)
	L = (1, 39)(2, 43)(3, 41)(4, 45)(5, 37)(6, 49)(7, 44)(8, 38)(9, 47)(10, 51)(11, 40)(12, 54)(13, 50)(14, 42)(15, 53)(16, 48)(17, 46)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) }
Outer automorphisms :: reflexible
Dual of E6.173
Graph:: bipartite
	v = 19 e = 36 f = 7
	degree seq :: [ 2^18, 36 ]

E6.178 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2^4, Y1^2 * Y2^-2, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1, Y2^2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 21, 4, 24)(2, 22, 6, 26)(3, 23, 7, 27)(5, 25, 10, 30)(8, 28, 16, 36)(9, 29, 17, 37)(11, 31, 19, 39)(12, 32, 14, 34)(13, 33, 15, 35)(18, 38, 20, 40)(41, 42, 45, 43)(44, 48, 55, 49)(46, 51, 56, 52)(47, 53, 60, 54)(50, 58, 59, 57)(61, 63, 65, 62)(64, 69, 75, 68)(66, 72, 76, 71)(67, 74, 80, 73)(70, 77, 79, 78)
	L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E6.181
Graph:: simple bipartite
	v = 20 e = 40 f = 10
	degree seq :: [ 4^20 ]

E6.179 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 4, 4})
Quotient :: edge^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^4, Y2^4, Y3 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 21, 4, 24)(2, 22, 6, 26)(3, 23, 7, 27)(5, 25, 10, 30)(8, 28, 16, 36)(9, 29, 17, 37)(11, 31, 13, 33)(12, 32, 15, 35)(14, 34, 20, 40)(18, 38, 19, 39)(41, 42, 45, 43)(44, 48, 55, 49)(46, 51, 59, 52)(47, 53, 57, 54)(50, 56, 60, 58)(61, 63, 65, 62)(64, 69, 75, 68)(66, 72, 79, 71)(67, 74, 77, 73)(70, 78, 80, 76)
	L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E6.180
Graph:: simple bipartite
	v = 20 e = 40 f = 10
	degree seq :: [ 4^20 ]

E6.180 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y2^4, Y1^2 * Y2^-2, R * Y2 * R * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1, Y2^2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 ]
Map:: non-degenerate
	R = (1, 21, 41, 61, 4, 24, 44, 64)(2, 22, 42, 62, 6, 26, 46, 66)(3, 23, 43, 63, 7, 27, 47, 67)(5, 25, 45, 65, 10, 30, 50, 70)(8, 28, 48, 68, 16, 36, 56, 76)(9, 29, 49, 69, 17, 37, 57, 77)(11, 31, 51, 71, 19, 39, 59, 79)(12, 32, 52, 72, 14, 34, 54, 74)(13, 33, 53, 73, 15, 35, 55, 75)(18, 38, 58, 78, 20, 40, 60, 80)
	L = (1, 22)(2, 25)(3, 21)(4, 28)(5, 23)(6, 31)(7, 33)(8, 35)(9, 24)(10, 38)(11, 36)(12, 26)(13, 40)(14, 27)(15, 29)(16, 32)(17, 30)(18, 39)(19, 37)(20, 34)(41, 63)(42, 61)(43, 65)(44, 69)(45, 62)(46, 72)(47, 74)(48, 64)(49, 75)(50, 77)(51, 66)(52, 76)(53, 67)(54, 80)(55, 68)(56, 71)(57, 79)(58, 70)(59, 78)(60, 73)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.179
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 40 f = 20
	degree seq :: [ 8^10 ]

E6.181 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 4, 4})
Quotient :: loop^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y1^4, Y2^4, Y3 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 ]
Map:: non-degenerate
	R = (1, 21, 41, 61, 4, 24, 44, 64)(2, 22, 42, 62, 6, 26, 46, 66)(3, 23, 43, 63, 7, 27, 47, 67)(5, 25, 45, 65, 10, 30, 50, 70)(8, 28, 48, 68, 16, 36, 56, 76)(9, 29, 49, 69, 17, 37, 57, 77)(11, 31, 51, 71, 13, 33, 53, 73)(12, 32, 52, 72, 15, 35, 55, 75)(14, 34, 54, 74, 20, 40, 60, 80)(18, 38, 58, 78, 19, 39, 59, 79)
	L = (1, 22)(2, 25)(3, 21)(4, 28)(5, 23)(6, 31)(7, 33)(8, 35)(9, 24)(10, 36)(11, 39)(12, 26)(13, 37)(14, 27)(15, 29)(16, 40)(17, 34)(18, 30)(19, 32)(20, 38)(41, 63)(42, 61)(43, 65)(44, 69)(45, 62)(46, 72)(47, 74)(48, 64)(49, 75)(50, 78)(51, 66)(52, 79)(53, 67)(54, 77)(55, 68)(56, 70)(57, 73)(58, 80)(59, 71)(60, 76)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.178
Transitivity :: VT+
Graph:: bipartite
	v = 10 e = 40 f = 20
	degree seq :: [ 8^10 ]

E6.182 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 5, 20})
Quotient :: edge
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^5 ]
Map:: non-degenerate
	R = (1, 3, 9, 12, 5)(2, 7, 15, 16, 8)(4, 10, 17, 18, 11)(6, 13, 19, 20, 14)(21, 22, 26, 24)(23, 27, 33, 30)(25, 28, 34, 31)(29, 35, 39, 37)(32, 36, 40, 38)
	L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 40^4 ), ( 40^5 ) }
Outer automorphisms :: reflexible
Dual of E6.186
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 20 f = 1
	degree seq :: [ 4^5, 5^4 ]

E6.183 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 5, 20})
Quotient :: edge
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^5, (T1^-1 * T2^-1)^4 ]
Map:: non-degenerate
	R = (1, 3, 9, 8, 2, 7, 16, 15, 6, 14, 20, 18, 11, 17, 19, 12, 4, 10, 13, 5)(21, 22, 26, 31, 24)(23, 27, 34, 37, 30)(25, 28, 35, 38, 32)(29, 36, 40, 39, 33)
	L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 8^5 ), ( 8^20 ) }
Outer automorphisms :: reflexible
Dual of E6.187
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 20 f = 5
	degree seq :: [ 5^4, 20 ]

E6.184 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 5, 20})
Quotient :: edge
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T1^5 * T2 ]
Map:: non-degenerate
	R = (1, 3, 9, 5)(2, 7, 16, 8)(4, 10, 17, 12)(6, 14, 20, 15)(11, 18, 19, 13)(21, 22, 26, 33, 32, 25, 28, 35, 39, 37, 29, 36, 40, 38, 30, 23, 27, 34, 31, 24)
	L = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	local type(s) :: { ( 10^4 ), ( 10^20 ) }
Outer automorphisms :: reflexible
Dual of E6.185
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 20 f = 4
	degree seq :: [ 4^5, 20 ]

E6.185 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 5, 20})
Quotient :: loop
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^5 ]
Map:: non-degenerate
	R = (1, 21, 3, 23, 9, 29, 12, 32, 5, 25)(2, 22, 7, 27, 15, 35, 16, 36, 8, 28)(4, 24, 10, 30, 17, 37, 18, 38, 11, 31)(6, 26, 13, 33, 19, 39, 20, 40, 14, 34)
	L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 24)(7, 33)(8, 34)(9, 35)(10, 23)(11, 25)(12, 36)(13, 30)(14, 31)(15, 39)(16, 40)(17, 29)(18, 32)(19, 37)(20, 38)
	local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.184
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 20 f = 6
	degree seq :: [ 10^4 ]

E6.186 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 5, 20})
Quotient :: loop
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^5, (T1^-1 * T2^-1)^4 ]
Map:: non-degenerate
	R = (1, 21, 3, 23, 9, 29, 8, 28, 2, 22, 7, 27, 16, 36, 15, 35, 6, 26, 14, 34, 20, 40, 18, 38, 11, 31, 17, 37, 19, 39, 12, 32, 4, 24, 10, 30, 13, 33, 5, 25)
	L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 31)(7, 34)(8, 35)(9, 36)(10, 23)(11, 24)(12, 25)(13, 29)(14, 37)(15, 38)(16, 40)(17, 30)(18, 32)(19, 33)(20, 39)
	local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5 ) }
Outer automorphisms :: reflexible
Dual of E6.182
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 20 f = 9
	degree seq :: [ 40 ]

E6.187 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 5, 20})
Quotient :: loop
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T1^5 * T2 ]
Map:: non-degenerate
	R = (1, 21, 3, 23, 9, 29, 5, 25)(2, 22, 7, 27, 16, 36, 8, 28)(4, 24, 10, 30, 17, 37, 12, 32)(6, 26, 14, 34, 20, 40, 15, 35)(11, 31, 18, 38, 19, 39, 13, 33)
	L = (1, 22)(2, 26)(3, 27)(4, 21)(5, 28)(6, 33)(7, 34)(8, 35)(9, 36)(10, 23)(11, 24)(12, 25)(13, 32)(14, 31)(15, 39)(16, 40)(17, 29)(18, 30)(19, 37)(20, 38)
	local type(s) :: { ( 5, 20, 5, 20, 5, 20, 5, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.183
Transitivity :: ET+ VT+ AT
Graph::
	v = 5 e = 20 f = 5
	degree seq :: [ 8^5 ]

E6.188 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y1^4, (Y2, Y1^-1), Y2^5, Y3^20 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 17, 37)(12, 32, 16, 36, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 56, 76, 48, 68)(44, 64, 50, 70, 57, 77, 58, 78, 51, 71)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74)
	L = (1, 44)(2, 41)(3, 50)(4, 46)(5, 51)(6, 42)(7, 43)(8, 45)(9, 57)(10, 53)(11, 54)(12, 58)(13, 47)(14, 48)(15, 49)(16, 52)(17, 59)(18, 60)(19, 55)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) }
Outer automorphisms :: reflexible
Dual of E6.191
Graph:: bipartite
	v = 9 e = 40 f = 21
	degree seq :: [ 8^5, 10^4 ]

E6.189 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^-1 * Y2^4, Y1^5, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 17, 37, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 20, 40, 19, 39, 13, 33)(41, 61, 43, 63, 49, 69, 48, 68, 42, 62, 47, 67, 56, 76, 55, 75, 46, 66, 54, 74, 60, 80, 58, 78, 51, 71, 57, 77, 59, 79, 52, 72, 44, 64, 50, 70, 53, 73, 45, 65)
	L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 48)(10, 53)(11, 57)(12, 44)(13, 45)(14, 60)(15, 46)(16, 55)(17, 59)(18, 51)(19, 52)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.190
Graph:: bipartite
	v = 5 e = 40 f = 25
	degree seq :: [ 10^4, 40 ]

E6.190 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^4, Y2^-1 * Y3^5, (Y3^-1 * Y1^-1)^20 ]
Map::
	R = (1, 21)(2, 22)(3, 23)(4, 24)(5, 25)(6, 26)(7, 27)(8, 28)(9, 29)(10, 30)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)(41, 61, 42, 62, 46, 66, 44, 64)(43, 63, 47, 67, 53, 73, 50, 70)(45, 65, 48, 68, 54, 74, 51, 71)(49, 69, 55, 75, 59, 79, 57, 77)(52, 72, 56, 76, 60, 80, 58, 78)
	L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 53)(7, 55)(8, 42)(9, 56)(10, 57)(11, 44)(12, 45)(13, 59)(14, 46)(15, 60)(16, 48)(17, 52)(18, 51)(19, 58)(20, 54)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 10, 40 ), ( 10, 40, 10, 40, 10, 40, 10, 40 ) }
Outer automorphisms :: reflexible
Dual of E6.189
Graph:: simple bipartite
	v = 25 e = 40 f = 5
	degree seq :: [ 2^20, 8^5 ]

E6.191 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-1 * Y1^-5, Y1 * Y3^-2 * Y1^-1 * Y3^-2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 13, 33, 12, 32, 5, 25, 8, 28, 15, 35, 19, 39, 17, 37, 9, 29, 16, 36, 20, 40, 18, 38, 10, 30, 3, 23, 7, 27, 14, 34, 11, 31, 4, 24)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)
	L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 45)(10, 57)(11, 58)(12, 44)(13, 51)(14, 60)(15, 46)(16, 48)(17, 52)(18, 59)(19, 53)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.188
Graph:: bipartite
	v = 21 e = 40 f = 9
	degree seq :: [ 2^20, 40 ]

E6.192 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * Y2^-5, Y2^-1 * Y3^2 * Y2^2 * Y3^2 * Y2^-1 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 18, 38)(12, 32, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 57, 77, 51, 71, 44, 64, 50, 70, 58, 78, 60, 80, 54, 74, 46, 66, 53, 73, 59, 79, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 52, 72, 45, 65)
	L = (1, 44)(2, 41)(3, 50)(4, 46)(5, 51)(6, 42)(7, 43)(8, 45)(9, 58)(10, 53)(11, 54)(12, 57)(13, 47)(14, 48)(15, 49)(16, 52)(17, 60)(18, 59)(19, 55)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.193
Graph:: bipartite
	v = 6 e = 40 f = 24
	degree seq :: [ 8^5, 40 ]

E6.193 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 5, 20})
Quotient :: dipole
Aut^+ = C20 (small group id <20, 2>)
Aut   = D40 (small group id <40, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y1^-1 * Y3^4, Y1^5, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^4, (Y3 * Y2^-1)^20 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 11, 31, 4, 24)(3, 23, 7, 27, 14, 34, 17, 37, 10, 30)(5, 25, 8, 28, 15, 35, 18, 38, 12, 32)(9, 29, 16, 36, 20, 40, 19, 39, 13, 33)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(55, 75)(56, 76)(57, 77)(58, 78)(59, 79)(60, 80)
	L = (1, 43)(2, 47)(3, 49)(4, 50)(5, 41)(6, 54)(7, 56)(8, 42)(9, 48)(10, 53)(11, 57)(12, 44)(13, 45)(14, 60)(15, 46)(16, 55)(17, 59)(18, 51)(19, 52)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)
	local type(s) :: { ( 8, 40 ), ( 8, 40, 8, 40, 8, 40, 8, 40, 8, 40 ) }
Outer automorphisms :: reflexible
Dual of E6.192
Graph:: simple bipartite
	v = 24 e = 40 f = 6
	degree seq :: [ 2^20, 10^4 ]

E6.194 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 7, 21})
Quotient :: edge
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^7 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 17, 11, 5)(2, 6, 12, 18, 19, 13, 7)(4, 9, 15, 20, 21, 16, 10)(22, 23, 25)(24, 27, 30)(26, 28, 31)(29, 33, 36)(32, 34, 37)(35, 39, 41)(38, 40, 42)
	L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)
	local type(s) :: { ( 42^3 ), ( 42^7 ) }
Outer automorphisms :: reflexible
Dual of E6.198
Transitivity :: ET+
Graph:: simple bipartite
	v = 10 e = 21 f = 1
	degree seq :: [ 3^7, 7^3 ]

E6.195 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 7, 21})
Quotient :: edge
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T1^-1 * T2^6, T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1, T1^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 11, 21, 16, 6, 15, 12, 4, 10, 20, 14, 13, 5)(22, 23, 27, 35, 40, 32, 25)(24, 28, 36, 34, 39, 42, 31)(26, 29, 37, 41, 30, 38, 33)
	L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)
	local type(s) :: { ( 6^7 ), ( 6^21 ) }
Outer automorphisms :: reflexible
Dual of E6.199
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 21 f = 7
	degree seq :: [ 7^3, 21 ]

E6.196 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 7, 21})
Quotient :: edge
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-7, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 15, 17)(12, 19, 20)(16, 21, 18)(22, 23, 27, 33, 39, 38, 32, 26, 29, 35, 41, 42, 36, 30, 24, 28, 34, 40, 37, 31, 25)
	L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)
	local type(s) :: { ( 14^3 ), ( 14^21 ) }
Outer automorphisms :: reflexible
Dual of E6.197
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 21 f = 3
	degree seq :: [ 3^7, 21 ]

E6.197 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 7, 21})
Quotient :: loop
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^7 ]
Map:: non-degenerate
	R = (1, 22, 3, 24, 8, 29, 14, 35, 17, 38, 11, 32, 5, 26)(2, 23, 6, 27, 12, 33, 18, 39, 19, 40, 13, 34, 7, 28)(4, 25, 9, 30, 15, 36, 20, 41, 21, 42, 16, 37, 10, 31)
	L = (1, 23)(2, 25)(3, 27)(4, 22)(5, 28)(6, 30)(7, 31)(8, 33)(9, 24)(10, 26)(11, 34)(12, 36)(13, 37)(14, 39)(15, 29)(16, 32)(17, 40)(18, 41)(19, 42)(20, 35)(21, 38)
	local type(s) :: { ( 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21, 3, 21 ) }
Outer automorphisms :: reflexible
Dual of E6.196
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 21 f = 8
	degree seq :: [ 14^3 ]

E6.198 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 7, 21})
Quotient :: loop
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^-3, T1^-1 * T2^6, T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1, T1^7 ]
Map:: non-degenerate
	R = (1, 22, 3, 24, 9, 30, 19, 40, 18, 39, 8, 29, 2, 23, 7, 28, 17, 38, 11, 32, 21, 42, 16, 37, 6, 27, 15, 36, 12, 33, 4, 25, 10, 31, 20, 41, 14, 35, 13, 34, 5, 26)
	L = (1, 23)(2, 27)(3, 28)(4, 22)(5, 29)(6, 35)(7, 36)(8, 37)(9, 38)(10, 24)(11, 25)(12, 26)(13, 39)(14, 40)(15, 34)(16, 41)(17, 33)(18, 42)(19, 32)(20, 30)(21, 31)
	local type(s) :: { ( 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7 ) }
Outer automorphisms :: reflexible
Dual of E6.194
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 21 f = 10
	degree seq :: [ 42 ]

E6.199 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 7, 21})
Quotient :: loop
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-7, (T1^-1 * T2^-1)^7 ]
Map:: non-degenerate
	R = (1, 22, 3, 24, 5, 26)(2, 23, 7, 28, 8, 29)(4, 25, 9, 30, 11, 32)(6, 27, 13, 34, 14, 35)(10, 31, 15, 36, 17, 38)(12, 33, 19, 40, 20, 41)(16, 37, 21, 42, 18, 39)
	L = (1, 23)(2, 27)(3, 28)(4, 22)(5, 29)(6, 33)(7, 34)(8, 35)(9, 24)(10, 25)(11, 26)(12, 39)(13, 40)(14, 41)(15, 30)(16, 31)(17, 32)(18, 38)(19, 37)(20, 42)(21, 36)
	local type(s) :: { ( 7, 21, 7, 21, 7, 21 ) }
Outer automorphisms :: reflexible
Dual of E6.195
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 21 f = 4
	degree seq :: [ 6^7 ]

E6.200 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^7, Y3^21 ]
Map::
	R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 20, 41)(17, 38, 19, 40, 21, 42)(43, 64, 45, 66, 50, 71, 56, 77, 59, 80, 53, 74, 47, 68)(44, 65, 48, 69, 54, 75, 60, 81, 61, 82, 55, 76, 49, 70)(46, 67, 51, 72, 57, 78, 62, 83, 63, 84, 58, 79, 52, 73)
	L = (1, 46)(2, 43)(3, 51)(4, 44)(5, 52)(6, 45)(7, 47)(8, 57)(9, 48)(10, 49)(11, 58)(12, 50)(13, 53)(14, 62)(15, 54)(16, 55)(17, 63)(18, 56)(19, 59)(20, 60)(21, 61)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 2, 42, 2, 42, 2, 42 ), ( 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42, 2, 42 ) }
Outer automorphisms :: reflexible
Dual of E6.203
Graph:: bipartite
	v = 10 e = 42 f = 22
	degree seq :: [ 6^7, 14^3 ]

E6.201 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1^-1, Y2^-1), Y1^-3 * Y2^-3, (Y3^-1 * Y1^-1)^3, Y1^-1 * Y2^6, Y1^7 ]
Map::
	R = (1, 22, 2, 23, 6, 27, 14, 35, 19, 40, 11, 32, 4, 25)(3, 24, 7, 28, 15, 36, 13, 34, 18, 39, 21, 42, 10, 31)(5, 26, 8, 29, 16, 37, 20, 41, 9, 30, 17, 38, 12, 33)(43, 64, 45, 66, 51, 72, 61, 82, 60, 81, 50, 71, 44, 65, 49, 70, 59, 80, 53, 74, 63, 84, 58, 79, 48, 69, 57, 78, 54, 75, 46, 67, 52, 73, 62, 83, 56, 77, 55, 76, 47, 68)
	L = (1, 45)(2, 49)(3, 51)(4, 52)(5, 43)(6, 57)(7, 59)(8, 44)(9, 61)(10, 62)(11, 63)(12, 46)(13, 47)(14, 55)(15, 54)(16, 48)(17, 53)(18, 50)(19, 60)(20, 56)(21, 58)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.202
Graph:: bipartite
	v = 4 e = 42 f = 28
	degree seq :: [ 14^3, 42 ]

E6.202 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^7, (Y3^-1 * Y1^-1)^21 ]
Map::
	R = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)(43, 64, 44, 65, 46, 67)(45, 66, 48, 69, 51, 72)(47, 68, 49, 70, 52, 73)(50, 71, 54, 75, 57, 78)(53, 74, 55, 76, 58, 79)(56, 77, 60, 81, 62, 83)(59, 80, 61, 82, 63, 84)
	L = (1, 45)(2, 48)(3, 50)(4, 51)(5, 43)(6, 54)(7, 44)(8, 56)(9, 57)(10, 46)(11, 47)(12, 60)(13, 49)(14, 61)(15, 62)(16, 52)(17, 53)(18, 63)(19, 55)(20, 59)(21, 58)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 14, 42 ), ( 14, 42, 14, 42, 14, 42 ) }
Outer automorphisms :: reflexible
Dual of E6.201
Graph:: simple bipartite
	v = 28 e = 42 f = 4
	degree seq :: [ 2^21, 6^7 ]

E6.203 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^-7, (Y1^-1 * Y3^-1)^7 ]
Map::
	R = (1, 22, 2, 23, 6, 27, 12, 33, 18, 39, 17, 38, 11, 32, 5, 26, 8, 29, 14, 35, 20, 41, 21, 42, 15, 36, 9, 30, 3, 24, 7, 28, 13, 34, 19, 40, 16, 37, 10, 31, 4, 25)(43, 64)(44, 65)(45, 66)(46, 67)(47, 68)(48, 69)(49, 70)(50, 71)(51, 72)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(61, 82)(62, 83)(63, 84)
	L = (1, 45)(2, 49)(3, 47)(4, 51)(5, 43)(6, 55)(7, 50)(8, 44)(9, 53)(10, 57)(11, 46)(12, 61)(13, 56)(14, 48)(15, 59)(16, 63)(17, 52)(18, 58)(19, 62)(20, 54)(21, 60)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.200
Graph:: bipartite
	v = 22 e = 42 f = 10
	degree seq :: [ 2^21, 42 ]

E6.204 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^-7 ]
Map::
	R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 21, 42)(17, 38, 19, 40, 20, 41)(43, 64, 45, 66, 50, 71, 56, 77, 62, 83, 58, 79, 52, 73, 46, 67, 51, 72, 57, 78, 63, 84, 61, 82, 55, 76, 49, 70, 44, 65, 48, 69, 54, 75, 60, 81, 59, 80, 53, 74, 47, 68)
	L = (1, 46)(2, 43)(3, 51)(4, 44)(5, 52)(6, 45)(7, 47)(8, 57)(9, 48)(10, 49)(11, 58)(12, 50)(13, 53)(14, 63)(15, 54)(16, 55)(17, 62)(18, 56)(19, 59)(20, 61)(21, 60)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.205
Graph:: bipartite
	v = 8 e = 42 f = 24
	degree seq :: [ 6^7, 42 ]

E6.205 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 7, 21})
Quotient :: dipole
Aut^+ = C21 (small group id <21, 2>)
Aut   = D42 (small group id <42, 5>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y3^-1), Y1^-3 * Y3^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^6, Y1^2 * Y3^-1 * Y1^2 * Y3^-2, Y1^7, (Y3 * Y2^-1)^21 ]
Map::
	R = (1, 22, 2, 23, 6, 27, 14, 35, 19, 40, 11, 32, 4, 25)(3, 24, 7, 28, 15, 36, 13, 34, 18, 39, 21, 42, 10, 31)(5, 26, 8, 29, 16, 37, 20, 41, 9, 30, 17, 38, 12, 33)(43, 64)(44, 65)(45, 66)(46, 67)(47, 68)(48, 69)(49, 70)(50, 71)(51, 72)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(61, 82)(62, 83)(63, 84)
	L = (1, 45)(2, 49)(3, 51)(4, 52)(5, 43)(6, 57)(7, 59)(8, 44)(9, 61)(10, 62)(11, 63)(12, 46)(13, 47)(14, 55)(15, 54)(16, 48)(17, 53)(18, 50)(19, 60)(20, 56)(21, 58)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)
	local type(s) :: { ( 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) }
Outer automorphisms :: reflexible
Dual of E6.204
Graph:: simple bipartite
	v = 24 e = 42 f = 8
	degree seq :: [ 2^21, 14^3 ]

E6.206 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-3, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y1 * Y2)^2, (Y3^-1 * Y1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 12, 36)(5, 29, 13, 37)(6, 30, 14, 38)(7, 31, 17, 41)(8, 32, 18, 42)(10, 34, 16, 40)(11, 35, 15, 39)(19, 43, 22, 46)(20, 44, 24, 48)(21, 45, 23, 47)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 58, 82)(53, 77, 59, 83)(55, 79, 63, 87)(56, 80, 64, 88)(57, 81, 67, 91)(60, 84, 69, 93)(61, 85, 68, 92)(62, 86, 70, 94)(65, 89, 72, 96)(66, 90, 71, 95)
	L = (1, 52)(2, 55)(3, 58)(4, 59)(5, 49)(6, 63)(7, 64)(8, 50)(9, 68)(10, 53)(11, 51)(12, 67)(13, 69)(14, 71)(15, 56)(16, 54)(17, 70)(18, 72)(19, 61)(20, 60)(21, 57)(22, 66)(23, 65)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.211
Graph:: simple bipartite
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.207 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = D24 (small group id <24, 6>)
Aut   = C2 x D24 (small group id <48, 36>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^-4 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 10, 34)(5, 29, 7, 31)(6, 30, 8, 32)(11, 35, 21, 45)(12, 36, 20, 44)(13, 37, 22, 46)(14, 38, 18, 42)(15, 39, 17, 41)(16, 40, 19, 43)(23, 47, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 59, 83, 62, 86)(54, 78, 60, 84, 63, 87)(56, 80, 65, 89, 68, 92)(58, 82, 66, 90, 69, 93)(61, 85, 71, 95, 64, 88)(67, 91, 72, 96, 70, 94)
	L = (1, 52)(2, 56)(3, 59)(4, 61)(5, 62)(6, 49)(7, 65)(8, 67)(9, 68)(10, 50)(11, 71)(12, 51)(13, 60)(14, 64)(15, 53)(16, 54)(17, 72)(18, 55)(19, 66)(20, 70)(21, 57)(22, 58)(23, 63)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.209
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.208 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^4 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 10, 34)(5, 29, 7, 31)(6, 30, 8, 32)(11, 35, 20, 44)(12, 36, 18, 42)(13, 37, 17, 41)(14, 38, 19, 43)(15, 39, 16, 40)(21, 45, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 61, 85, 59, 83)(54, 78, 63, 87, 60, 84)(56, 80, 66, 90, 64, 88)(58, 82, 68, 92, 65, 89)(62, 86, 69, 93, 70, 94)(67, 91, 71, 95, 72, 96)
	L = (1, 52)(2, 56)(3, 59)(4, 62)(5, 61)(6, 49)(7, 64)(8, 67)(9, 66)(10, 50)(11, 69)(12, 51)(13, 70)(14, 54)(15, 53)(16, 71)(17, 55)(18, 72)(19, 58)(20, 57)(21, 60)(22, 63)(23, 65)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.210
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.209 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = D24 (small group id <24, 6>)
Aut   = C2 x D24 (small group id <48, 36>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y3^3 * Y1^-1, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^4, (Y1^-1 * Y2)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 16, 40, 8, 32)(4, 28, 9, 33, 17, 41, 14, 38)(6, 30, 10, 34, 18, 42, 15, 39)(12, 36, 21, 45, 23, 47, 19, 43)(13, 37, 22, 46, 24, 48, 20, 44)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 61, 85)(53, 77, 59, 83)(54, 78, 60, 84)(55, 79, 64, 88)(57, 81, 68, 92)(58, 82, 67, 91)(62, 86, 70, 94)(63, 87, 69, 93)(65, 89, 72, 96)(66, 90, 71, 95)
	L = (1, 52)(2, 57)(3, 60)(4, 58)(5, 62)(6, 49)(7, 65)(8, 67)(9, 66)(10, 50)(11, 69)(12, 70)(13, 51)(14, 54)(15, 53)(16, 71)(17, 63)(18, 55)(19, 61)(20, 56)(21, 72)(22, 59)(23, 68)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.207
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.210 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y1^-2 * Y3^-2, Y3^4, Y1^4, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y3^-1 * Y1^2 * Y3^-1, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 16, 40, 8, 32)(4, 28, 14, 38, 6, 30, 15, 39)(9, 33, 19, 43, 10, 34, 20, 44)(12, 36, 21, 45, 13, 37, 22, 46)(17, 41, 23, 47, 18, 42, 24, 48)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 61, 85)(53, 77, 59, 83)(54, 78, 60, 84)(55, 79, 64, 88)(57, 81, 66, 90)(58, 82, 65, 89)(62, 86, 69, 93)(63, 87, 70, 94)(67, 91, 71, 95)(68, 92, 72, 96)
	L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 58)(6, 49)(7, 54)(8, 65)(9, 53)(10, 50)(11, 66)(12, 64)(13, 51)(14, 68)(15, 67)(16, 61)(17, 59)(18, 56)(19, 62)(20, 63)(21, 71)(22, 72)(23, 70)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.208
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.211 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y1^3, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 5, 29)(3, 27, 10, 34, 7, 31)(4, 28, 13, 37, 8, 32)(6, 30, 15, 39, 9, 33)(11, 35, 16, 40, 19, 43)(12, 36, 17, 41, 20, 44)(14, 38, 18, 42, 22, 46)(21, 45, 24, 48, 23, 47)(49, 73, 51, 75, 59, 83, 54, 78)(50, 74, 55, 79, 64, 88, 57, 81)(52, 76, 62, 86, 69, 93, 60, 84)(53, 77, 58, 82, 67, 91, 63, 87)(56, 80, 66, 90, 71, 95, 65, 89)(61, 85, 70, 94, 72, 96, 68, 92)
	L = (1, 52)(2, 56)(3, 60)(4, 49)(5, 61)(6, 62)(7, 65)(8, 50)(9, 66)(10, 68)(11, 69)(12, 51)(13, 53)(14, 54)(15, 70)(16, 71)(17, 55)(18, 57)(19, 72)(20, 58)(21, 59)(22, 63)(23, 64)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^6 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.206
Graph:: simple bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 6^8, 8^6 ]

E6.212 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = C2 x ((C6 x C2) : C2) (small group id <48, 43>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^4 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 10, 34)(5, 29, 9, 33)(6, 30, 8, 32)(11, 35, 17, 41)(12, 36, 16, 40)(13, 37, 20, 44)(14, 38, 19, 43)(15, 39, 18, 42)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 61, 85, 59, 83)(54, 78, 63, 87, 60, 84)(56, 80, 66, 90, 64, 88)(58, 82, 68, 92, 65, 89)(62, 86, 69, 93, 70, 94)(67, 91, 71, 95, 72, 96)
	L = (1, 52)(2, 56)(3, 59)(4, 62)(5, 61)(6, 49)(7, 64)(8, 67)(9, 66)(10, 50)(11, 69)(12, 51)(13, 70)(14, 54)(15, 53)(16, 71)(17, 55)(18, 72)(19, 58)(20, 57)(21, 60)(22, 63)(23, 65)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.213
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.213 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = (C6 x C2) : C2 (small group id <24, 8>)
Aut   = C2 x ((C6 x C2) : C2) (small group id <48, 43>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y3 * Y1^-2 * Y3, Y1^4, (R * Y1)^2, Y3^-1 * Y1^2 * Y3^-1, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1^-1, (Y2 * Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 18, 42, 13, 37)(4, 28, 15, 39, 6, 30, 16, 40)(8, 32, 19, 43, 17, 41, 21, 45)(9, 33, 23, 47, 10, 34, 24, 48)(12, 36, 22, 46, 14, 38, 20, 44)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 62, 86)(53, 77, 65, 89)(54, 78, 60, 84)(55, 79, 66, 90)(57, 81, 70, 94)(58, 82, 68, 92)(59, 83, 72, 96)(61, 85, 71, 95)(63, 87, 67, 91)(64, 88, 69, 93)
	L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 58)(6, 49)(7, 54)(8, 68)(9, 53)(10, 50)(11, 67)(12, 66)(13, 69)(14, 51)(15, 72)(16, 71)(17, 70)(18, 62)(19, 61)(20, 65)(21, 59)(22, 56)(23, 63)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.212
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.214 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y2 * Y1 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 12, 36)(5, 29, 14, 38)(6, 30, 16, 40)(7, 31, 11, 35)(8, 32, 13, 37)(10, 34, 18, 42)(15, 39, 17, 41)(19, 43, 23, 47)(20, 44, 21, 45)(22, 46, 24, 48)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 61, 85)(53, 77, 63, 87)(55, 79, 62, 86)(56, 80, 66, 90)(57, 81, 67, 91)(58, 82, 69, 93)(59, 83, 70, 94)(60, 84, 68, 92)(64, 88, 71, 95)(65, 89, 72, 96)
	L = (1, 52)(2, 55)(3, 58)(4, 53)(5, 49)(6, 65)(7, 56)(8, 50)(9, 62)(10, 59)(11, 51)(12, 54)(13, 70)(14, 68)(15, 71)(16, 61)(17, 60)(18, 67)(19, 72)(20, 57)(21, 63)(22, 64)(23, 69)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.223
Graph:: simple bipartite
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.215 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2, (R * Y2 * Y3)^2, (Y2 * Y3 * Y1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 7, 31)(5, 29, 13, 37)(6, 30, 15, 39)(8, 32, 19, 43)(10, 34, 18, 42)(11, 35, 20, 44)(12, 36, 16, 40)(14, 38, 17, 41)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 59, 83, 60, 84)(55, 79, 65, 89, 66, 90)(57, 81, 67, 91, 69, 93)(58, 82, 70, 94, 68, 92)(61, 85, 71, 95, 63, 87)(62, 86, 64, 88, 72, 96)
	L = (1, 52)(2, 55)(3, 58)(4, 49)(5, 62)(6, 64)(7, 50)(8, 68)(9, 66)(10, 51)(11, 67)(12, 63)(13, 65)(14, 53)(15, 60)(16, 54)(17, 61)(18, 57)(19, 59)(20, 56)(21, 72)(22, 71)(23, 70)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.220
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.216 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2 * Y3)^2, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y2^-1)^4 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 8, 32)(4, 28, 7, 31)(5, 29, 6, 30)(9, 33, 16, 40)(10, 34, 15, 39)(11, 35, 14, 38)(12, 36, 13, 37)(17, 41, 24, 48)(18, 42, 19, 43)(20, 44, 21, 45)(22, 46, 23, 47)(49, 73, 51, 75, 53, 77)(50, 74, 54, 78, 56, 80)(52, 76, 58, 82, 59, 83)(55, 79, 62, 86, 63, 87)(57, 81, 65, 89, 66, 90)(60, 84, 69, 93, 70, 94)(61, 85, 71, 95, 68, 92)(64, 88, 67, 91, 72, 96)
	L = (1, 52)(2, 55)(3, 57)(4, 49)(5, 60)(6, 61)(7, 50)(8, 64)(9, 51)(10, 67)(11, 68)(12, 53)(13, 54)(14, 69)(15, 66)(16, 56)(17, 71)(18, 63)(19, 58)(20, 59)(21, 62)(22, 72)(23, 65)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.219
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.217 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2^-1)^2, Y3^4, Y3^2 * Y2 * Y1 * Y2^-1, R * Y2 * Y1 * R * Y2^-1, (Y2 * Y1)^3 ]
Map:: non-degenerate
	R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 17, 41)(6, 30, 8, 32)(7, 31, 20, 44)(9, 33, 23, 47)(12, 36, 21, 45)(13, 37, 16, 40)(14, 38, 19, 43)(15, 39, 22, 46)(18, 42, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 62, 86, 64, 88)(54, 78, 67, 91, 60, 84)(56, 80, 66, 90, 61, 85)(58, 82, 72, 96, 69, 93)(59, 83, 71, 95, 63, 87)(65, 89, 70, 94, 68, 92)
	L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 66)(6, 49)(7, 69)(8, 70)(9, 62)(10, 50)(11, 64)(12, 68)(13, 51)(14, 53)(15, 54)(16, 55)(17, 67)(18, 57)(19, 71)(20, 61)(21, 59)(22, 58)(23, 72)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.221
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.218 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y1)^2, Y3^4, Y1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 11, 35)(4, 28, 10, 34)(5, 29, 17, 41)(6, 30, 8, 32)(7, 31, 20, 44)(9, 33, 24, 48)(12, 36, 16, 40)(13, 37, 23, 47)(14, 38, 21, 45)(15, 39, 22, 46)(18, 42, 19, 43)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 62, 86, 64, 88)(54, 78, 67, 91, 60, 84)(56, 80, 69, 93, 71, 95)(58, 82, 66, 90, 61, 85)(59, 83, 72, 96, 70, 94)(63, 87, 68, 92, 65, 89)
	L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 66)(6, 49)(7, 61)(8, 70)(9, 67)(10, 50)(11, 71)(12, 55)(13, 51)(14, 53)(15, 54)(16, 59)(17, 69)(18, 72)(19, 65)(20, 64)(21, 57)(22, 58)(23, 68)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.222
Graph:: simple bipartite
	v = 20 e = 48 f = 18
	degree seq :: [ 4^12, 6^8 ]

E6.219 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y3 * Y1^-1)^3, Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 6, 30, 5, 29)(3, 27, 9, 33, 14, 38, 7, 31)(4, 28, 11, 35, 22, 46, 12, 36)(8, 32, 17, 41, 19, 43, 18, 42)(10, 34, 20, 44, 15, 39, 21, 45)(13, 37, 24, 48, 16, 40, 23, 47)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 57, 81)(54, 78, 62, 86)(56, 80, 64, 88)(59, 83, 69, 93)(60, 84, 68, 92)(61, 85, 67, 91)(63, 87, 70, 94)(65, 89, 72, 96)(66, 90, 71, 95)
	L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 61)(6, 63)(7, 64)(8, 50)(9, 67)(10, 51)(11, 71)(12, 65)(13, 53)(14, 70)(15, 54)(16, 55)(17, 60)(18, 69)(19, 57)(20, 72)(21, 66)(22, 62)(23, 59)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.216
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.220 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1, Y2 * Y1^2 * Y3 * Y1^-2, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 6, 30, 5, 29)(3, 27, 9, 33, 17, 41, 11, 35)(4, 28, 12, 36, 16, 40, 13, 37)(7, 31, 18, 42, 15, 39, 20, 44)(8, 32, 21, 45, 14, 38, 22, 46)(10, 34, 23, 47, 24, 48, 19, 43)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 62, 86)(54, 78, 64, 88)(56, 80, 67, 91)(57, 81, 69, 93)(59, 83, 66, 90)(60, 84, 70, 94)(61, 85, 68, 92)(63, 87, 71, 95)(65, 89, 72, 96)
	L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 63)(6, 65)(7, 67)(8, 50)(9, 68)(10, 51)(11, 70)(12, 66)(13, 69)(14, 71)(15, 53)(16, 72)(17, 54)(18, 60)(19, 55)(20, 57)(21, 61)(22, 59)(23, 62)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.215
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.221 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y2^2, R^2, Y2 * Y3^-1 * Y1^-2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y3 * Y2)^2, (Y3^-1 * Y1)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y2 * Y1^-1)^2 ]
Map:: non-degenerate
	R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 6, 30, 13, 37)(4, 28, 14, 38, 18, 42, 16, 40)(8, 32, 19, 43, 10, 34, 21, 45)(9, 33, 22, 46, 17, 41, 24, 48)(12, 36, 23, 47, 15, 39, 20, 44)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 55, 79)(53, 77, 57, 81)(54, 78, 60, 84)(58, 82, 68, 92)(59, 83, 72, 96)(61, 85, 67, 91)(62, 86, 69, 93)(63, 87, 66, 90)(64, 88, 70, 94)(65, 89, 71, 95)
	L = (1, 52)(2, 57)(3, 60)(4, 63)(5, 56)(6, 49)(7, 51)(8, 68)(9, 71)(10, 50)(11, 67)(12, 66)(13, 72)(14, 70)(15, 54)(16, 69)(17, 53)(18, 55)(19, 62)(20, 65)(21, 61)(22, 59)(23, 58)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.217
Graph:: bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.222 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y2^2, R^2, (Y3 * Y2)^2, Y3^-1 * Y2 * Y1^2, Y3^-1 * Y2 * Y1^-2, (R * Y3)^2, (R * Y1)^2, Y3^4, (Y3 * Y2)^2, Y1 * Y3^-2 * Y1^-1 * Y2 * Y3^-1, (Y3 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 4, 28, 12, 36)(6, 30, 16, 40, 18, 42, 17, 41)(8, 32, 19, 43, 9, 33, 20, 44)(10, 34, 23, 47, 15, 39, 24, 48)(13, 37, 22, 46, 14, 38, 21, 45)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 61, 85)(53, 77, 58, 82)(54, 78, 55, 79)(57, 81, 69, 93)(59, 83, 72, 96)(60, 84, 67, 91)(62, 86, 66, 90)(63, 87, 70, 94)(64, 88, 68, 92)(65, 89, 71, 95)
	L = (1, 52)(2, 57)(3, 55)(4, 62)(5, 63)(6, 49)(7, 66)(8, 53)(9, 70)(10, 50)(11, 71)(12, 68)(13, 51)(14, 54)(15, 69)(16, 67)(17, 72)(18, 61)(19, 59)(20, 65)(21, 56)(22, 58)(23, 64)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.218
Graph:: simple bipartite
	v = 18 e = 48 f = 20
	degree seq :: [ 4^12, 8^6 ]

E6.223 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 4})
Quotient :: dipole
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ R^2, Y3^3, Y1^3, Y2^2 * Y3^-1 * Y1^-1, Y2 * Y1 * Y3 * Y2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1 * Y2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2 ]
Map:: non-degenerate
	R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 10, 34)(4, 28, 14, 38, 16, 40)(6, 30, 13, 37, 19, 43)(7, 31, 20, 44, 9, 33)(8, 32, 21, 45, 15, 39)(11, 35, 23, 47, 17, 41)(18, 42, 24, 48, 22, 46)(49, 73, 51, 75, 57, 81, 54, 78)(50, 74, 56, 80, 65, 89, 58, 82)(52, 76, 63, 87, 53, 77, 61, 85)(55, 79, 66, 90, 64, 88, 67, 91)(59, 83, 70, 94, 68, 92, 60, 84)(62, 86, 72, 96, 71, 95, 69, 93)
	L = (1, 52)(2, 57)(3, 56)(4, 55)(5, 65)(6, 66)(7, 49)(8, 61)(9, 59)(10, 70)(11, 50)(12, 54)(13, 51)(14, 53)(15, 72)(16, 71)(17, 62)(18, 60)(19, 63)(20, 64)(21, 58)(22, 69)(23, 68)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^6 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.214
Graph:: bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 6^8, 8^6 ]

E6.224 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 6})
Quotient :: edge
Aut^+ = SL(2,3) (small group id <24, 3>)
Aut   = GL(2,3) (small group id <48, 29>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-3 * T1^-1, T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 3, 10, 6, 16, 5)(2, 7, 13, 4, 12, 8)(9, 20, 22, 11, 19, 21)(14, 23, 18, 15, 24, 17)(25, 26, 30, 28)(27, 33, 40, 35)(29, 38, 34, 39)(31, 41, 36, 42)(32, 43, 37, 44)(45, 47, 46, 48)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 12^4 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E6.225
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 24 f = 4
	degree seq :: [ 4^6, 6^4 ]

E6.225 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 6})
Quotient :: loop
Aut^+ = SL(2,3) (small group id <24, 3>)
Aut   = GL(2,3) (small group id <48, 29>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-3 * T1^-1, T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 25, 3, 27, 10, 34, 6, 30, 16, 40, 5, 29)(2, 26, 7, 31, 13, 37, 4, 28, 12, 36, 8, 32)(9, 33, 20, 44, 22, 46, 11, 35, 19, 43, 21, 45)(14, 38, 23, 47, 18, 42, 15, 39, 24, 48, 17, 41)
	L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 38)(6, 28)(7, 41)(8, 43)(9, 40)(10, 39)(11, 27)(12, 42)(13, 44)(14, 34)(15, 29)(16, 35)(17, 36)(18, 31)(19, 37)(20, 32)(21, 47)(22, 48)(23, 46)(24, 45)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.224
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 24 f = 10
	degree seq :: [ 12^4 ]

E6.226 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 6})
Quotient :: dipole
Aut^+ = SL(2,3) (small group id <24, 3>)
Aut   = GL(2,3) (small group id <48, 29>)
|r| :: 2
Presentation :: [ R^2, Y1 * Y3, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^4, Y1^2 * Y3^-2, (R * Y3)^2, Y2^-3 * Y3^-1 * Y1, (Y1^-1 * Y2)^3, Y1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y2 * Y3^-1 * R * Y2^-2 * R * Y1 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 16, 40, 11, 35)(5, 29, 14, 38, 10, 34, 15, 39)(7, 31, 17, 41, 12, 36, 18, 42)(8, 32, 19, 43, 13, 37, 20, 44)(21, 45, 23, 47, 22, 46, 24, 48)(49, 73, 51, 75, 58, 82, 54, 78, 64, 88, 53, 77)(50, 74, 55, 79, 61, 85, 52, 76, 60, 84, 56, 80)(57, 81, 68, 92, 70, 94, 59, 83, 67, 91, 69, 93)(62, 86, 71, 95, 66, 90, 63, 87, 72, 96, 65, 89)
	L = (1, 52)(2, 49)(3, 59)(4, 54)(5, 63)(6, 50)(7, 66)(8, 68)(9, 51)(10, 62)(11, 64)(12, 65)(13, 67)(14, 53)(15, 58)(16, 57)(17, 55)(18, 60)(19, 56)(20, 61)(21, 72)(22, 71)(23, 69)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.227
Graph:: bipartite
	v = 10 e = 48 f = 28
	degree seq :: [ 8^6, 12^4 ]

E6.227 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 6})
Quotient :: dipole
Aut^+ = SL(2,3) (small group id <24, 3>)
Aut   = GL(2,3) (small group id <48, 29>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^4, Y1^2 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 10, 34, 13, 37, 4, 28)(3, 27, 9, 33, 16, 40, 5, 29, 15, 39, 11, 35)(7, 31, 17, 41, 20, 44, 8, 32, 19, 43, 18, 42)(12, 36, 23, 47, 22, 46, 14, 38, 24, 48, 21, 45)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)
	L = (1, 51)(2, 55)(3, 58)(4, 60)(5, 49)(6, 62)(7, 61)(8, 50)(9, 69)(10, 53)(11, 67)(12, 54)(13, 56)(14, 52)(15, 70)(16, 65)(17, 59)(18, 71)(19, 64)(20, 72)(21, 63)(22, 57)(23, 68)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.226
Graph:: simple bipartite
	v = 28 e = 48 f = 10
	degree seq :: [ 2^24, 12^4 ]

E6.228 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 6})
Quotient :: edge
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^6 ]
Map:: non-degenerate
	R = (1, 3, 10, 18, 12, 5)(2, 7, 15, 22, 16, 8)(4, 9, 17, 23, 19, 11)(6, 13, 20, 24, 21, 14)(25, 26, 30, 28)(27, 33, 37, 31)(29, 35, 38, 32)(34, 39, 44, 41)(36, 40, 45, 43)(42, 47, 48, 46)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 12^4 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E6.229
Transitivity :: ET+
Graph:: simple bipartite
	v = 10 e = 24 f = 4
	degree seq :: [ 4^6, 6^4 ]

E6.229 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 6})
Quotient :: loop
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^6 ]
Map:: non-degenerate
	R = (1, 25, 3, 27, 10, 34, 18, 42, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 22, 46, 16, 40, 8, 32)(4, 28, 9, 33, 17, 41, 23, 47, 19, 43, 11, 35)(6, 30, 13, 37, 20, 44, 24, 48, 21, 45, 14, 38)
	L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 35)(6, 28)(7, 27)(8, 29)(9, 37)(10, 39)(11, 38)(12, 40)(13, 31)(14, 32)(15, 44)(16, 45)(17, 34)(18, 47)(19, 36)(20, 41)(21, 43)(22, 42)(23, 48)(24, 46)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.228
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 24 f = 10
	degree seq :: [ 12^4 ]

E6.230 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 6})
Quotient :: dipole
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^6, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 7, 31)(5, 29, 11, 35, 14, 38, 8, 32)(10, 34, 15, 39, 20, 44, 17, 41)(12, 36, 16, 40, 21, 45, 19, 43)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86)
	L = (1, 52)(2, 49)(3, 55)(4, 54)(5, 56)(6, 50)(7, 61)(8, 62)(9, 51)(10, 65)(11, 53)(12, 67)(13, 57)(14, 59)(15, 58)(16, 60)(17, 68)(18, 70)(19, 69)(20, 63)(21, 64)(22, 72)(23, 66)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.231
Graph:: bipartite
	v = 10 e = 48 f = 28
	degree seq :: [ 8^6, 12^4 ]

E6.231 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 6})
Quotient :: dipole
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 13, 37, 12, 36, 4, 28)(3, 27, 8, 32, 14, 38, 21, 45, 18, 42, 10, 34)(5, 29, 7, 31, 15, 39, 20, 44, 19, 43, 11, 35)(9, 33, 16, 40, 22, 46, 24, 48, 23, 47, 17, 41)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)
	L = (1, 51)(2, 55)(3, 57)(4, 59)(5, 49)(6, 62)(7, 64)(8, 50)(9, 53)(10, 52)(11, 65)(12, 66)(13, 68)(14, 70)(15, 54)(16, 56)(17, 58)(18, 71)(19, 60)(20, 72)(21, 61)(22, 63)(23, 67)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.230
Graph:: simple bipartite
	v = 28 e = 48 f = 10
	degree seq :: [ 2^24, 12^4 ]

E6.232 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 8, 8})
Quotient :: edge
Aut^+ = C3 : C8 (small group id <24, 1>)
Aut   = (C3 x D8) : C2 (small group id <48, 15>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^8 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 21, 17, 11, 5)(2, 6, 12, 18, 23, 19, 13, 7)(4, 8, 14, 20, 24, 22, 16, 10)(25, 26, 28)(27, 32, 30)(29, 34, 31)(33, 36, 38)(35, 37, 40)(39, 44, 42)(41, 46, 43)(45, 47, 48)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 16^3 ), ( 16^8 ) }
Outer automorphisms :: reflexible
Dual of E6.233
Transitivity :: ET+
Graph:: simple bipartite
	v = 11 e = 24 f = 3
	degree seq :: [ 3^8, 8^3 ]

E6.233 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 8, 8})
Quotient :: loop
Aut^+ = C3 : C8 (small group id <24, 1>)
Aut   = (C3 x D8) : C2 (small group id <48, 15>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^8 ]
Map:: non-degenerate
	R = (1, 25, 3, 27, 9, 33, 15, 39, 21, 45, 17, 41, 11, 35, 5, 29)(2, 26, 6, 30, 12, 36, 18, 42, 23, 47, 19, 43, 13, 37, 7, 31)(4, 28, 8, 32, 14, 38, 20, 44, 24, 48, 22, 46, 16, 40, 10, 34)
	L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 34)(6, 27)(7, 29)(8, 30)(9, 36)(10, 31)(11, 37)(12, 38)(13, 40)(14, 33)(15, 44)(16, 35)(17, 46)(18, 39)(19, 41)(20, 42)(21, 47)(22, 43)(23, 48)(24, 45)
	local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.232
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 24 f = 11
	degree seq :: [ 16^3 ]

E6.234 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 8, 8})
Quotient :: dipole
Aut^+ = C3 : C8 (small group id <24, 1>)
Aut   = (C3 x D8) : C2 (small group id <48, 15>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-1 * Y1)^8 ]
Map::
	R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 6, 30)(5, 29, 10, 34, 7, 31)(9, 33, 12, 36, 14, 38)(11, 35, 13, 37, 16, 40)(15, 39, 20, 44, 18, 42)(17, 41, 22, 46, 19, 43)(21, 45, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 63, 87, 69, 93, 65, 89, 59, 83, 53, 77)(50, 74, 54, 78, 60, 84, 66, 90, 71, 95, 67, 91, 61, 85, 55, 79)(52, 76, 56, 80, 62, 86, 68, 92, 72, 96, 70, 94, 64, 88, 58, 82)
	L = (1, 52)(2, 49)(3, 54)(4, 50)(5, 55)(6, 56)(7, 58)(8, 51)(9, 62)(10, 53)(11, 64)(12, 57)(13, 59)(14, 60)(15, 66)(16, 61)(17, 67)(18, 68)(19, 70)(20, 63)(21, 72)(22, 65)(23, 69)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.235
Graph:: bipartite
	v = 11 e = 48 f = 27
	degree seq :: [ 6^8, 16^3 ]

E6.235 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 8, 8})
Quotient :: dipole
Aut^+ = C3 : C8 (small group id <24, 1>)
Aut   = (C3 x D8) : C2 (small group id <48, 15>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^8 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 12, 36, 18, 42, 17, 41, 11, 35, 4, 28)(3, 27, 8, 32, 13, 37, 20, 44, 23, 47, 21, 45, 15, 39, 9, 33)(5, 29, 7, 31, 14, 38, 19, 43, 24, 48, 22, 46, 16, 40, 10, 34)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)
	L = (1, 51)(2, 55)(3, 53)(4, 58)(5, 49)(6, 61)(7, 56)(8, 50)(9, 52)(10, 57)(11, 63)(12, 67)(13, 62)(14, 54)(15, 64)(16, 59)(17, 70)(18, 71)(19, 68)(20, 60)(21, 65)(22, 69)(23, 72)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.234
Graph:: simple bipartite
	v = 27 e = 48 f = 11
	degree seq :: [ 2^24, 16^3 ]

E6.236 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 12})
Quotient :: dipole
Aut^+ = D24 (small group id <24, 6>)
Aut   = C2 x D24 (small group id <48, 36>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 25, 2, 26)(3, 27, 5, 29)(4, 28, 8, 32)(6, 30, 10, 34)(7, 31, 11, 35)(9, 33, 13, 37)(12, 36, 16, 40)(14, 38, 18, 42)(15, 39, 19, 43)(17, 41, 21, 45)(20, 44, 24, 48)(22, 46, 23, 47)(49, 73, 51, 75)(50, 74, 53, 77)(52, 76, 55, 79)(54, 78, 57, 81)(56, 80, 59, 83)(58, 82, 61, 85)(60, 84, 63, 87)(62, 86, 65, 89)(64, 88, 67, 91)(66, 90, 69, 93)(68, 92, 71, 95)(70, 94, 72, 96)
	L = (1, 52)(2, 54)(3, 55)(4, 49)(5, 57)(6, 50)(7, 51)(8, 60)(9, 53)(10, 62)(11, 63)(12, 56)(13, 65)(14, 58)(15, 59)(16, 68)(17, 61)(18, 70)(19, 71)(20, 64)(21, 72)(22, 66)(23, 67)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.237
Graph:: simple bipartite
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.237 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 12})
Quotient :: dipole
Aut^+ = D24 (small group id <24, 6>)
Aut   = C2 x D24 (small group id <48, 36>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, Y2 * Y3 * Y1^6, Y1^-1 * Y2 * Y1^2 * Y3 * Y1^-3 ]
Map:: non-degenerate
	R = (1, 25, 2, 26, 6, 30, 13, 37, 21, 45, 18, 42, 10, 34, 16, 40, 24, 48, 20, 44, 12, 36, 5, 29)(3, 27, 9, 33, 17, 41, 23, 47, 15, 39, 8, 32, 4, 28, 11, 35, 19, 43, 22, 46, 14, 38, 7, 31)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 57, 81)(54, 78, 62, 86)(56, 80, 64, 88)(59, 83, 66, 90)(60, 84, 65, 89)(61, 85, 70, 94)(63, 87, 72, 96)(67, 91, 69, 93)(68, 92, 71, 95)
	L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 59)(6, 63)(7, 64)(8, 50)(9, 66)(10, 51)(11, 53)(12, 67)(13, 71)(14, 72)(15, 54)(16, 55)(17, 69)(18, 57)(19, 60)(20, 70)(21, 65)(22, 68)(23, 61)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^4 ), ( 4^24 ) }
Outer automorphisms :: reflexible
Dual of E6.236
Graph:: bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 4^12, 24^2 ]

E6.238 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 12})
Quotient :: edge
Aut^+ = C3 : Q8 (small group id <24, 4>)
Aut   = (C12 x C2) : C2 (small group id <48, 37>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2^4 * T1^-1 * T2^-2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 22, 14, 6, 13, 21, 20, 12, 5)(2, 7, 15, 23, 18, 10, 4, 11, 19, 24, 16, 8)(25, 26, 30, 28)(27, 32, 37, 34)(29, 31, 38, 35)(33, 40, 45, 42)(36, 39, 46, 43)(41, 48, 44, 47)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 8^4 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E6.239
Transitivity :: ET+
Graph:: bipartite
	v = 8 e = 24 f = 6
	degree seq :: [ 4^6, 12^2 ]

E6.239 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 12})
Quotient :: loop
Aut^+ = C3 : Q8 (small group id <24, 4>)
Aut   = (C12 x C2) : C2 (small group id <48, 37>)
|r| :: 2
Presentation :: [ F^2, T1^-2 * T2^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-2 * T2^-1, T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 ]
Map:: non-degenerate
	R = (1, 25, 3, 27, 6, 30, 5, 29)(2, 26, 7, 31, 4, 28, 8, 32)(9, 33, 13, 37, 10, 34, 14, 38)(11, 35, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48)
	L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 34)(6, 28)(7, 35)(8, 36)(9, 29)(10, 27)(11, 32)(12, 31)(13, 41)(14, 42)(15, 43)(16, 44)(17, 38)(18, 37)(19, 40)(20, 39)(21, 48)(22, 47)(23, 45)(24, 46)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.238
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 24 f = 8
	degree seq :: [ 8^6 ]

E6.240 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 12})
Quotient :: dipole
Aut^+ = C3 : Q8 (small group id <24, 4>)
Aut   = (C12 x C2) : C2 (small group id <48, 37>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 8, 32, 13, 37, 10, 34)(5, 29, 7, 31, 14, 38, 11, 35)(9, 33, 16, 40, 21, 45, 18, 42)(12, 36, 15, 39, 22, 46, 19, 43)(17, 41, 24, 48, 20, 44, 23, 47)(49, 73, 51, 75, 57, 81, 65, 89, 70, 94, 62, 86, 54, 78, 61, 85, 69, 93, 68, 92, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 71, 95, 66, 90, 58, 82, 52, 76, 59, 83, 67, 91, 72, 96, 64, 88, 56, 80)
	L = (1, 51)(2, 55)(3, 57)(4, 59)(5, 49)(6, 61)(7, 63)(8, 50)(9, 65)(10, 52)(11, 67)(12, 53)(13, 69)(14, 54)(15, 71)(16, 56)(17, 70)(18, 58)(19, 72)(20, 60)(21, 68)(22, 62)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.241
Graph:: bipartite
	v = 8 e = 48 f = 30
	degree seq :: [ 8^6, 24^2 ]

E6.241 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 12})
Quotient :: dipole
Aut^+ = C3 : Q8 (small group id <24, 4>)
Aut   = (C12 x C2) : C2 (small group id <48, 37>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-6 * Y2^-1, (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(49, 73, 50, 74, 54, 78, 52, 76)(51, 75, 56, 80, 61, 85, 58, 82)(53, 77, 55, 79, 62, 86, 59, 83)(57, 81, 64, 88, 69, 93, 66, 90)(60, 84, 63, 87, 70, 94, 67, 91)(65, 89, 72, 96, 68, 92, 71, 95)
	L = (1, 51)(2, 55)(3, 57)(4, 59)(5, 49)(6, 61)(7, 63)(8, 50)(9, 65)(10, 52)(11, 67)(12, 53)(13, 69)(14, 54)(15, 71)(16, 56)(17, 70)(18, 58)(19, 72)(20, 60)(21, 68)(22, 62)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.240
Graph:: simple bipartite
	v = 30 e = 48 f = 8
	degree seq :: [ 2^24, 8^6 ]

E6.242 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 24, 24})
Quotient :: regular
Aut^+ = C24 (small group id <24, 2>)
Aut   = D48 (small group id <48, 7>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^12 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 24, 20, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 24)
	local type(s) :: { ( 24^24 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 12 f = 1
	degree seq :: [ 24 ]

E6.243 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 24, 24})
Quotient :: edge
Aut^+ = C24 (small group id <24, 2>)
Aut   = D48 (small group id <48, 7>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^12 * T1 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 24, 20, 16, 12, 8, 4)(25, 26)(27, 29)(28, 30)(31, 33)(32, 34)(35, 37)(36, 38)(39, 41)(40, 42)(43, 45)(44, 46)(47, 48)
	L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)
	local type(s) :: { ( 48, 48 ), ( 48^24 ) }
Outer automorphisms :: reflexible
Dual of E6.244
Transitivity :: ET+
Graph:: bipartite
	v = 13 e = 24 f = 1
	degree seq :: [ 2^12, 24 ]

E6.244 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 24, 24})
Quotient :: loop
Aut^+ = C24 (small group id <24, 2>)
Aut   = D48 (small group id <48, 7>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^12 * T1 ]
Map::
	R = (1, 25, 3, 27, 7, 31, 11, 35, 15, 39, 19, 43, 23, 47, 22, 46, 18, 42, 14, 38, 10, 34, 6, 30, 2, 26, 5, 29, 9, 33, 13, 37, 17, 41, 21, 45, 24, 48, 20, 44, 16, 40, 12, 36, 8, 32, 4, 28)
	L = (1, 26)(2, 25)(3, 29)(4, 30)(5, 27)(6, 28)(7, 33)(8, 34)(9, 31)(10, 32)(11, 37)(12, 38)(13, 35)(14, 36)(15, 41)(16, 42)(17, 39)(18, 40)(19, 45)(20, 46)(21, 43)(22, 44)(23, 48)(24, 47)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.243
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 24 f = 13
	degree seq :: [ 48 ]

E6.245 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 24, 24})
Quotient :: dipole
Aut^+ = C24 (small group id <24, 2>)
Aut   = D48 (small group id <48, 7>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^12 * Y1, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 25, 2, 26)(3, 27, 5, 29)(4, 28, 6, 30)(7, 31, 9, 33)(8, 32, 10, 34)(11, 35, 13, 37)(12, 36, 14, 38)(15, 39, 17, 41)(16, 40, 18, 42)(19, 43, 21, 45)(20, 44, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 55, 79, 59, 83, 63, 87, 67, 91, 71, 95, 70, 94, 66, 90, 62, 86, 58, 82, 54, 78, 50, 74, 53, 77, 57, 81, 61, 85, 65, 89, 69, 93, 72, 96, 68, 92, 64, 88, 60, 84, 56, 80, 52, 76)
	L = (1, 50)(2, 49)(3, 53)(4, 54)(5, 51)(6, 52)(7, 57)(8, 58)(9, 55)(10, 56)(11, 61)(12, 62)(13, 59)(14, 60)(15, 65)(16, 66)(17, 63)(18, 64)(19, 69)(20, 70)(21, 67)(22, 68)(23, 72)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48 ) }
Outer automorphisms :: reflexible
Dual of E6.246
Graph:: bipartite
	v = 13 e = 48 f = 25
	degree seq :: [ 4^12, 48 ]

E6.246 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 24, 24})
Quotient :: dipole
Aut^+ = C24 (small group id <24, 2>)
Aut   = D48 (small group id <48, 7>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^12 ]
Map::
	R = (1, 25, 2, 26, 5, 29, 9, 33, 13, 37, 17, 41, 21, 45, 23, 47, 19, 43, 15, 39, 11, 35, 7, 31, 3, 27, 6, 30, 10, 34, 14, 38, 18, 42, 22, 46, 24, 48, 20, 44, 16, 40, 12, 36, 8, 32, 4, 28)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(57, 81)(58, 82)(59, 83)(60, 84)(61, 85)(62, 86)(63, 87)(64, 88)(65, 89)(66, 90)(67, 91)(68, 92)(69, 93)(70, 94)(71, 95)(72, 96)
	L = (1, 51)(2, 54)(3, 49)(4, 55)(5, 58)(6, 50)(7, 52)(8, 59)(9, 62)(10, 53)(11, 56)(12, 63)(13, 66)(14, 57)(15, 60)(16, 67)(17, 70)(18, 61)(19, 64)(20, 71)(21, 72)(22, 65)(23, 68)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E6.245
Graph:: bipartite
	v = 25 e = 48 f = 13
	degree seq :: [ 2^24, 48 ]

E6.247 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 13, 26})
Quotient :: regular
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-13 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 24, 20, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 25)
	local type(s) :: { ( 13^26 ) }
Outer automorphisms :: reflexible
Dual of E6.248
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 13 f = 2
	degree seq :: [ 26 ]

E6.248 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 13, 26})
Quotient :: regular
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^13 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 25, 26, 23, 19, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 25)(24, 26)
	local type(s) :: { ( 26^13 ) }
Outer automorphisms :: reflexible
Dual of E6.247
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 13 f = 1
	degree seq :: [ 13^2 ]

E6.249 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 13, 26})
Quotient :: edge
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^13 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 26, 22, 18, 14, 10, 6)(27, 28)(29, 31)(30, 32)(33, 35)(34, 36)(37, 39)(38, 40)(41, 43)(42, 44)(45, 47)(46, 48)(49, 51)(50, 52)
	L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 52, 52 ), ( 52^13 ) }
Outer automorphisms :: reflexible
Dual of E6.253
Transitivity :: ET+
Graph:: simple bipartite
	v = 15 e = 26 f = 1
	degree seq :: [ 2^13, 13^2 ]

E6.250 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 13, 26})
Quotient :: edge
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^4 * T2^-1 * T1 * T2^-5, T2^-2 * T1^11, T2^3 * T1^2 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1 ]
Map:: non-degenerate
	R = (1, 3, 9, 13, 17, 21, 25, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 23, 20, 15, 12, 6, 5)(27, 28, 32, 37, 41, 45, 49, 51, 48, 43, 40, 35, 30)(29, 33, 31, 34, 38, 42, 46, 50, 52, 47, 44, 39, 36)
	L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 4^13 ), ( 4^26 ) }
Outer automorphisms :: reflexible
Dual of E6.254
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 26 f = 13
	degree seq :: [ 13^2, 26 ]

E6.251 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 13, 26})
Quotient :: edge
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-13 ]
Map::
	R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 25)(27, 28, 31, 35, 39, 43, 47, 51, 49, 45, 41, 37, 33, 29, 32, 36, 40, 44, 48, 52, 50, 46, 42, 38, 34, 30)
	L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)
	local type(s) :: { ( 26, 26 ), ( 26^26 ) }
Outer automorphisms :: reflexible
Dual of E6.252
Transitivity :: ET+
Graph:: bipartite
	v = 14 e = 26 f = 2
	degree seq :: [ 2^13, 26 ]

E6.252 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 13, 26})
Quotient :: loop
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^13 ]
Map::
	R = (1, 27, 3, 29, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 30)(2, 28, 5, 31, 9, 35, 13, 39, 17, 43, 21, 47, 25, 51, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 6, 32)
	L = (1, 28)(2, 27)(3, 31)(4, 32)(5, 29)(6, 30)(7, 35)(8, 36)(9, 33)(10, 34)(11, 39)(12, 40)(13, 37)(14, 38)(15, 43)(16, 44)(17, 41)(18, 42)(19, 47)(20, 48)(21, 45)(22, 46)(23, 51)(24, 52)(25, 49)(26, 50)
	local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.251
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 26 f = 14
	degree seq :: [ 26^2 ]

E6.253 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 13, 26})
Quotient :: loop
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^4 * T2^-1 * T1 * T2^-5, T2^-2 * T1^11, T2^3 * T1^2 * T2^-1 * T1^5 * T2^-1 * T1^5 * T2^-1 * T1 ]
Map::
	R = (1, 27, 3, 29, 9, 35, 13, 39, 17, 43, 21, 47, 25, 51, 24, 50, 19, 45, 16, 42, 11, 37, 8, 34, 2, 28, 7, 33, 4, 30, 10, 36, 14, 40, 18, 44, 22, 48, 26, 52, 23, 49, 20, 46, 15, 41, 12, 38, 6, 32, 5, 31)
	L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 37)(7, 31)(8, 38)(9, 30)(10, 29)(11, 41)(12, 42)(13, 36)(14, 35)(15, 45)(16, 46)(17, 40)(18, 39)(19, 49)(20, 50)(21, 44)(22, 43)(23, 51)(24, 52)(25, 48)(26, 47)
	local type(s) :: { ( 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13, 2, 13 ) }
Outer automorphisms :: reflexible
Dual of E6.249
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 26 f = 15
	degree seq :: [ 52 ]

E6.254 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 13, 26})
Quotient :: loop
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-13 ]
Map:: non-degenerate
	R = (1, 27, 3, 29)(2, 28, 6, 32)(4, 30, 7, 33)(5, 31, 10, 36)(8, 34, 11, 37)(9, 35, 14, 40)(12, 38, 15, 41)(13, 39, 18, 44)(16, 42, 19, 45)(17, 43, 22, 48)(20, 46, 23, 49)(21, 47, 26, 52)(24, 50, 25, 51)
	L = (1, 28)(2, 31)(3, 32)(4, 27)(5, 35)(6, 36)(7, 29)(8, 30)(9, 39)(10, 40)(11, 33)(12, 34)(13, 43)(14, 44)(15, 37)(16, 38)(17, 47)(18, 48)(19, 41)(20, 42)(21, 51)(22, 52)(23, 45)(24, 46)(25, 49)(26, 50)
	local type(s) :: { ( 13, 26, 13, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.250
Transitivity :: ET+ VT+ AT
Graph::
	v = 13 e = 26 f = 3
	degree seq :: [ 4^13 ]

E6.255 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^13, (Y3 * Y2^-1)^26 ]
Map::
	R = (1, 27, 2, 28)(3, 29, 5, 31)(4, 30, 6, 32)(7, 33, 9, 35)(8, 34, 10, 36)(11, 37, 13, 39)(12, 38, 14, 40)(15, 41, 17, 43)(16, 42, 18, 44)(19, 45, 21, 47)(20, 46, 22, 48)(23, 49, 25, 51)(24, 50, 26, 52)(53, 79, 55, 81, 59, 85, 63, 89, 67, 93, 71, 97, 75, 101, 76, 102, 72, 98, 68, 94, 64, 90, 60, 86, 56, 82)(54, 80, 57, 83, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 78, 104, 74, 100, 70, 96, 66, 92, 62, 88, 58, 84)
	L = (1, 54)(2, 53)(3, 57)(4, 58)(5, 55)(6, 56)(7, 61)(8, 62)(9, 59)(10, 60)(11, 65)(12, 66)(13, 63)(14, 64)(15, 69)(16, 70)(17, 67)(18, 68)(19, 73)(20, 74)(21, 71)(22, 72)(23, 77)(24, 78)(25, 75)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) }
Outer automorphisms :: reflexible
Dual of E6.258
Graph:: bipartite
	v = 15 e = 52 f = 27
	degree seq :: [ 4^13, 26^2 ]

E6.256 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y2^2 * Y1^2, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^12, Y1^13 ]
Map::
	R = (1, 27, 2, 28, 6, 32, 11, 37, 15, 41, 19, 45, 23, 49, 25, 51, 22, 48, 17, 43, 14, 40, 9, 35, 4, 30)(3, 29, 7, 33, 5, 31, 8, 34, 12, 38, 16, 42, 20, 46, 24, 50, 26, 52, 21, 47, 18, 44, 13, 39, 10, 36)(53, 79, 55, 81, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 76, 102, 71, 97, 68, 94, 63, 89, 60, 86, 54, 80, 59, 85, 56, 82, 62, 88, 66, 92, 70, 96, 74, 100, 78, 104, 75, 101, 72, 98, 67, 93, 64, 90, 58, 84, 57, 83)
	L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 57)(7, 56)(8, 54)(9, 65)(10, 66)(11, 60)(12, 58)(13, 69)(14, 70)(15, 64)(16, 63)(17, 73)(18, 74)(19, 68)(20, 67)(21, 77)(22, 78)(23, 72)(24, 71)(25, 76)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.257
Graph:: bipartite
	v = 3 e = 52 f = 39
	degree seq :: [ 26^2, 52 ]

E6.257 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^13 * Y2, (Y3^-1 * Y1^-1)^26 ]
Map::
	R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80)(55, 81, 57, 83)(56, 82, 58, 84)(59, 85, 61, 87)(60, 86, 62, 88)(63, 89, 65, 91)(64, 90, 66, 92)(67, 93, 69, 95)(68, 94, 70, 96)(71, 97, 73, 99)(72, 98, 74, 100)(75, 101, 77, 103)(76, 102, 78, 104)
	L = (1, 55)(2, 57)(3, 59)(4, 53)(5, 61)(6, 54)(7, 63)(8, 56)(9, 65)(10, 58)(11, 67)(12, 60)(13, 69)(14, 62)(15, 71)(16, 64)(17, 73)(18, 66)(19, 75)(20, 68)(21, 77)(22, 70)(23, 78)(24, 72)(25, 76)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52 ) }
Outer automorphisms :: reflexible
Dual of E6.256
Graph:: simple bipartite
	v = 39 e = 52 f = 3
	degree seq :: [ 2^26, 4^13 ]

E6.258 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-13 ]
Map::
	R = (1, 27, 2, 28, 5, 31, 9, 35, 13, 39, 17, 43, 21, 47, 25, 51, 23, 49, 19, 45, 15, 41, 11, 37, 7, 33, 3, 29, 6, 32, 10, 36, 14, 40, 18, 44, 22, 48, 26, 52, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104)
	L = (1, 55)(2, 58)(3, 53)(4, 59)(5, 62)(6, 54)(7, 56)(8, 63)(9, 66)(10, 57)(11, 60)(12, 67)(13, 70)(14, 61)(15, 64)(16, 71)(17, 74)(18, 65)(19, 68)(20, 75)(21, 78)(22, 69)(23, 72)(24, 77)(25, 76)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.255
Graph:: bipartite
	v = 27 e = 52 f = 15
	degree seq :: [ 2^26, 52 ]

E6.259 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^13 * Y1, (Y3 * Y2^-1)^13 ]
Map::
	R = (1, 27, 2, 28)(3, 29, 5, 31)(4, 30, 6, 32)(7, 33, 9, 35)(8, 34, 10, 36)(11, 37, 13, 39)(12, 38, 14, 40)(15, 41, 17, 43)(16, 42, 18, 44)(19, 45, 21, 47)(20, 46, 22, 48)(23, 49, 25, 51)(24, 50, 26, 52)(53, 79, 55, 81, 59, 85, 63, 89, 67, 93, 71, 97, 75, 101, 78, 104, 74, 100, 70, 96, 66, 92, 62, 88, 58, 84, 54, 80, 57, 83, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 76, 102, 72, 98, 68, 94, 64, 90, 60, 86, 56, 82)
	L = (1, 54)(2, 53)(3, 57)(4, 58)(5, 55)(6, 56)(7, 61)(8, 62)(9, 59)(10, 60)(11, 65)(12, 66)(13, 63)(14, 64)(15, 69)(16, 70)(17, 67)(18, 68)(19, 73)(20, 74)(21, 71)(22, 72)(23, 77)(24, 78)(25, 75)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 2, 26, 2, 26 ), ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.260
Graph:: bipartite
	v = 14 e = 52 f = 28
	degree seq :: [ 4^13, 52 ]

E6.260 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 13, 26})
Quotient :: dipole
Aut^+ = C26 (small group id <26, 2>)
Aut   = D52 (small group id <52, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^-2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^12, Y1^4 * Y3^-1 * Y1^2 * Y3^-5 * Y1, Y1^13, (Y3 * Y2^-1)^26 ]
Map::
	R = (1, 27, 2, 28, 6, 32, 11, 37, 15, 41, 19, 45, 23, 49, 25, 51, 22, 48, 17, 43, 14, 40, 9, 35, 4, 30)(3, 29, 7, 33, 5, 31, 8, 34, 12, 38, 16, 42, 20, 46, 24, 50, 26, 52, 21, 47, 18, 44, 13, 39, 10, 36)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104)
	L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 57)(7, 56)(8, 54)(9, 65)(10, 66)(11, 60)(12, 58)(13, 69)(14, 70)(15, 64)(16, 63)(17, 73)(18, 74)(19, 68)(20, 67)(21, 77)(22, 78)(23, 72)(24, 71)(25, 76)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)
	local type(s) :: { ( 4, 52 ), ( 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52 ) }
Outer automorphisms :: reflexible
Dual of E6.259
Graph:: simple bipartite
	v = 28 e = 52 f = 14
	degree seq :: [ 2^26, 26^2 ]

E6.261 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 7})
Quotient :: dipole
Aut^+ = D28 (small group id <28, 3>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (Y3 * Y1)^7 ]
Map:: polytopal non-degenerate
	R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 8, 36)(6, 34, 10, 38)(7, 35, 11, 39)(9, 37, 13, 41)(12, 40, 16, 44)(14, 42, 18, 46)(15, 43, 19, 47)(17, 45, 21, 49)(20, 48, 24, 52)(22, 50, 26, 54)(23, 51, 27, 55)(25, 53, 28, 56)(57, 85, 59, 87)(58, 86, 61, 89)(60, 88, 63, 91)(62, 90, 65, 93)(64, 92, 67, 95)(66, 94, 69, 97)(68, 96, 71, 99)(70, 98, 73, 101)(72, 100, 75, 103)(74, 102, 77, 105)(76, 104, 79, 107)(78, 106, 81, 109)(80, 108, 83, 111)(82, 110, 84, 112)
	L = (1, 60)(2, 62)(3, 63)(4, 57)(5, 65)(6, 58)(7, 59)(8, 68)(9, 61)(10, 70)(11, 71)(12, 64)(13, 73)(14, 66)(15, 67)(16, 76)(17, 69)(18, 78)(19, 79)(20, 72)(21, 81)(22, 74)(23, 75)(24, 82)(25, 77)(26, 80)(27, 84)(28, 83)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.262
Graph:: simple bipartite
	v = 28 e = 56 f = 18
	degree seq :: [ 4^28 ]

E6.262 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 7})
Quotient :: dipole
Aut^+ = D28 (small group id <28, 3>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, Y1^7 ]
Map:: polytopal non-degenerate
	R = (1, 29, 2, 30, 6, 34, 13, 41, 20, 48, 12, 40, 5, 33)(3, 31, 9, 37, 17, 45, 24, 52, 21, 49, 14, 42, 7, 35)(4, 32, 11, 39, 19, 47, 26, 54, 22, 50, 15, 43, 8, 36)(10, 38, 16, 44, 23, 51, 27, 55, 28, 56, 25, 53, 18, 46)(57, 85, 59, 87)(58, 86, 63, 91)(60, 88, 66, 94)(61, 89, 65, 93)(62, 90, 70, 98)(64, 92, 72, 100)(67, 95, 74, 102)(68, 96, 73, 101)(69, 97, 77, 105)(71, 99, 79, 107)(75, 103, 81, 109)(76, 104, 80, 108)(78, 106, 83, 111)(82, 110, 84, 112)
	L = (1, 60)(2, 64)(3, 66)(4, 57)(5, 67)(6, 71)(7, 72)(8, 58)(9, 74)(10, 59)(11, 61)(12, 75)(13, 78)(14, 79)(15, 62)(16, 63)(17, 81)(18, 65)(19, 68)(20, 82)(21, 83)(22, 69)(23, 70)(24, 84)(25, 73)(26, 76)(27, 77)(28, 80)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 4^4 ), ( 4^14 ) }
Outer automorphisms :: reflexible
Dual of E6.261
Graph:: simple bipartite
	v = 18 e = 56 f = 28
	degree seq :: [ 4^14, 14^4 ]

E6.263 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 7})
Quotient :: edge
Aut^+ = C7 : C4 (small group id <28, 1>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 17, 20, 12, 5)(2, 7, 15, 23, 24, 16, 8)(4, 11, 19, 26, 25, 18, 10)(6, 13, 21, 27, 28, 22, 14)(29, 30, 34, 32)(31, 36, 41, 38)(33, 35, 42, 39)(37, 44, 49, 46)(40, 43, 50, 47)(45, 52, 55, 53)(48, 51, 56, 54)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 8^4 ), ( 8^7 ) }
Outer automorphisms :: reflexible
Dual of E6.264
Transitivity :: ET+
Graph:: simple bipartite
	v = 11 e = 28 f = 7
	degree seq :: [ 4^7, 7^4 ]

E6.264 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 7})
Quotient :: loop
Aut^+ = C7 : C4 (small group id <28, 1>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^7 ]
Map:: non-degenerate
	R = (1, 29, 3, 31, 6, 34, 5, 33)(2, 30, 7, 35, 4, 32, 8, 36)(9, 37, 13, 41, 10, 38, 14, 42)(11, 39, 15, 43, 12, 40, 16, 44)(17, 45, 21, 49, 18, 46, 22, 50)(19, 47, 23, 51, 20, 48, 24, 52)(25, 53, 28, 56, 26, 54, 27, 55)
	L = (1, 30)(2, 34)(3, 37)(4, 29)(5, 38)(6, 32)(7, 39)(8, 40)(9, 33)(10, 31)(11, 36)(12, 35)(13, 45)(14, 46)(15, 47)(16, 48)(17, 42)(18, 41)(19, 44)(20, 43)(21, 53)(22, 54)(23, 55)(24, 56)(25, 50)(26, 49)(27, 52)(28, 51)
	local type(s) :: { ( 4, 7, 4, 7, 4, 7, 4, 7 ) }
Outer automorphisms :: reflexible
Dual of E6.263
Transitivity :: ET+ VT+ AT
Graph::
	v = 7 e = 28 f = 11
	degree seq :: [ 8^7 ]

E6.265 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 7})
Quotient :: dipole
Aut^+ = C7 : C4 (small group id <28, 1>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, Y2^7, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 29, 2, 30, 6, 34, 4, 32)(3, 31, 8, 36, 13, 41, 10, 38)(5, 33, 7, 35, 14, 42, 11, 39)(9, 37, 16, 44, 21, 49, 18, 46)(12, 40, 15, 43, 22, 50, 19, 47)(17, 45, 24, 52, 27, 55, 25, 53)(20, 48, 23, 51, 28, 56, 26, 54)(57, 85, 59, 87, 65, 93, 73, 101, 76, 104, 68, 96, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 80, 108, 72, 100, 64, 92)(60, 88, 67, 95, 75, 103, 82, 110, 81, 109, 74, 102, 66, 94)(62, 90, 69, 97, 77, 105, 83, 111, 84, 112, 78, 106, 70, 98)
	L = (1, 59)(2, 63)(3, 65)(4, 67)(5, 57)(6, 69)(7, 71)(8, 58)(9, 73)(10, 60)(11, 75)(12, 61)(13, 77)(14, 62)(15, 79)(16, 64)(17, 76)(18, 66)(19, 82)(20, 68)(21, 83)(22, 70)(23, 80)(24, 72)(25, 74)(26, 81)(27, 84)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.266
Graph:: bipartite
	v = 11 e = 56 f = 35
	degree seq :: [ 8^7, 14^4 ]

E6.266 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 7})
Quotient :: dipole
Aut^+ = C7 : C4 (small group id <28, 1>)
Aut   = (C14 x C2) : C2 (small group id <56, 7>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^7 ]
Map::
	R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 60, 88)(59, 87, 64, 92, 69, 97, 66, 94)(61, 89, 63, 91, 70, 98, 67, 95)(65, 93, 72, 100, 77, 105, 74, 102)(68, 96, 71, 99, 78, 106, 75, 103)(73, 101, 80, 108, 83, 111, 81, 109)(76, 104, 79, 107, 84, 112, 82, 110)
	L = (1, 59)(2, 63)(3, 65)(4, 67)(5, 57)(6, 69)(7, 71)(8, 58)(9, 73)(10, 60)(11, 75)(12, 61)(13, 77)(14, 62)(15, 79)(16, 64)(17, 76)(18, 66)(19, 82)(20, 68)(21, 83)(22, 70)(23, 80)(24, 72)(25, 74)(26, 81)(27, 84)(28, 78)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 8, 14 ), ( 8, 14, 8, 14, 8, 14, 8, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.265
Graph:: simple bipartite
	v = 35 e = 56 f = 11
	degree seq :: [ 2^28, 8^7 ]

E6.267 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 14, 14})
Quotient :: regular
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^14 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 21, 25, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 28, 27, 23, 19, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 28)
	local type(s) :: { ( 14^14 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 14 f = 2
	degree seq :: [ 14^2 ]

E6.268 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 14, 14})
Quotient :: edge
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^14 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 23, 27, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 28, 26, 22, 18, 14, 10, 6)(29, 30)(31, 33)(32, 34)(35, 37)(36, 38)(39, 41)(40, 42)(43, 45)(44, 46)(47, 49)(48, 50)(51, 53)(52, 54)(55, 56)
	L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)
	local type(s) :: { ( 28, 28 ), ( 28^14 ) }
Outer automorphisms :: reflexible
Dual of E6.269
Transitivity :: ET+
Graph:: simple bipartite
	v = 16 e = 28 f = 2
	degree seq :: [ 2^14, 14^2 ]

E6.269 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 14, 14})
Quotient :: loop
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^14 ]
Map::
	R = (1, 29, 3, 31, 7, 35, 11, 39, 15, 43, 19, 47, 23, 51, 27, 55, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 32)(2, 30, 5, 33, 9, 37, 13, 41, 17, 45, 21, 49, 25, 53, 28, 56, 26, 54, 22, 50, 18, 46, 14, 42, 10, 38, 6, 34)
	L = (1, 30)(2, 29)(3, 33)(4, 34)(5, 31)(6, 32)(7, 37)(8, 38)(9, 35)(10, 36)(11, 41)(12, 42)(13, 39)(14, 40)(15, 45)(16, 46)(17, 43)(18, 44)(19, 49)(20, 50)(21, 47)(22, 48)(23, 53)(24, 54)(25, 51)(26, 52)(27, 56)(28, 55)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.268
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 28 f = 16
	degree seq :: [ 28^2 ]

E6.270 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 14})
Quotient :: dipole
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^14, (Y3 * Y2^-1)^14 ]
Map::
	R = (1, 29, 2, 30)(3, 31, 5, 33)(4, 32, 6, 34)(7, 35, 9, 37)(8, 36, 10, 38)(11, 39, 13, 41)(12, 40, 14, 42)(15, 43, 17, 45)(16, 44, 18, 46)(19, 47, 21, 49)(20, 48, 22, 50)(23, 51, 25, 53)(24, 52, 26, 54)(27, 55, 28, 56)(57, 85, 59, 87, 63, 91, 67, 95, 71, 99, 75, 103, 79, 107, 83, 111, 80, 108, 76, 104, 72, 100, 68, 96, 64, 92, 60, 88)(58, 86, 61, 89, 65, 93, 69, 97, 73, 101, 77, 105, 81, 109, 84, 112, 82, 110, 78, 106, 74, 102, 70, 98, 66, 94, 62, 90)
	L = (1, 58)(2, 57)(3, 61)(4, 62)(5, 59)(6, 60)(7, 65)(8, 66)(9, 63)(10, 64)(11, 69)(12, 70)(13, 67)(14, 68)(15, 73)(16, 74)(17, 71)(18, 72)(19, 77)(20, 78)(21, 75)(22, 76)(23, 81)(24, 82)(25, 79)(26, 80)(27, 84)(28, 83)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.271
Graph:: bipartite
	v = 16 e = 56 f = 30
	degree seq :: [ 4^14, 28^2 ]

E6.271 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 14, 14})
Quotient :: dipole
Aut^+ = C14 x C2 (small group id <28, 4>)
Aut   = C2 x C2 x D14 (small group id <56, 12>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-14, Y1^14 ]
Map::
	R = (1, 29, 2, 30, 5, 33, 9, 37, 13, 41, 17, 45, 21, 49, 25, 53, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 32)(3, 31, 6, 34, 10, 38, 14, 42, 18, 46, 22, 50, 26, 54, 28, 56, 27, 55, 23, 51, 19, 47, 15, 43, 11, 39, 7, 35)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112)
	L = (1, 59)(2, 62)(3, 57)(4, 63)(5, 66)(6, 58)(7, 60)(8, 67)(9, 70)(10, 61)(11, 64)(12, 71)(13, 74)(14, 65)(15, 68)(16, 75)(17, 78)(18, 69)(19, 72)(20, 79)(21, 82)(22, 73)(23, 76)(24, 83)(25, 84)(26, 77)(27, 80)(28, 81)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.270
Graph:: simple bipartite
	v = 30 e = 56 f = 16
	degree seq :: [ 2^28, 28^2 ]

E6.272 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 10, 15})
Quotient :: regular
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4 * T2 * T1 * T2, T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2, (T1^-1 * T2)^10 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 17, 24, 29, 26, 28, 30, 27, 16, 22, 10, 4)(3, 7, 15, 20, 9, 19, 23, 12, 21, 25, 14, 6, 13, 18, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 20)(13, 22)(14, 24)(15, 26)(18, 28)(19, 27)(23, 29)(25, 30)
	local type(s) :: { ( 10^15 ) }
Outer automorphisms :: reflexible
Dual of E6.273
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 15 f = 3
	degree seq :: [ 15^2 ]

E6.273 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 10, 15})
Quotient :: regular
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^10 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 28, 27, 19, 10, 4)(3, 7, 12, 22, 29, 24, 30, 23, 17, 8)(6, 13, 21, 16, 26, 15, 25, 18, 9, 14)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 22)(19, 25)(20, 29)(26, 28)(27, 30)
	local type(s) :: { ( 15^10 ) }
Outer automorphisms :: reflexible
Dual of E6.272
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 3 e = 15 f = 2
	degree seq :: [ 10^3 ]

E6.274 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 10, 15})
Quotient :: edge
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^2 * T1, T2^3 * T1 * T2 * T1 * T2 * T1, T2^10 ]
Map::
	R = (1, 3, 8, 17, 26, 28, 27, 19, 10, 4)(2, 5, 12, 22, 29, 25, 30, 24, 14, 6)(7, 15, 23, 13, 21, 11, 20, 18, 9, 16)(31, 32)(33, 37)(34, 39)(35, 41)(36, 43)(38, 42)(40, 44)(45, 54)(46, 55)(47, 53)(48, 52)(49, 50)(51, 58)(56, 59)(57, 60)
	L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 30, 30 ), ( 30^10 ) }
Outer automorphisms :: reflexible
Dual of E6.278
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 30 f = 2
	degree seq :: [ 2^15, 10^3 ]

E6.275 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 10, 15})
Quotient :: edge
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2^3, T1^10 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 6, 17, 27, 26, 20, 24, 30, 28, 19, 13, 15, 5)(2, 7, 18, 16, 14, 25, 29, 22, 11, 23, 21, 9, 4, 12, 8)(31, 32, 36, 46, 56, 59, 60, 53, 43, 34)(33, 39, 47, 38, 50, 48, 58, 55, 45, 41)(35, 44, 40, 52, 57, 51, 54, 42, 49, 37)
	L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 4^10 ), ( 4^15 ) }
Outer automorphisms :: reflexible
Dual of E6.279
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 30 f = 15
	degree seq :: [ 10^3, 15^2 ]

E6.276 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 10, 15})
Quotient :: edge
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4 * T2 * T1 * T2, T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 20)(13, 22)(14, 24)(15, 26)(18, 28)(19, 27)(23, 29)(25, 30)(31, 32, 35, 41, 47, 54, 59, 56, 58, 60, 57, 46, 52, 40, 34)(33, 37, 45, 50, 39, 49, 53, 42, 51, 55, 44, 36, 43, 48, 38)
	L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)
	local type(s) :: { ( 20, 20 ), ( 20^15 ) }
Outer automorphisms :: reflexible
Dual of E6.277
Transitivity :: ET+
Graph:: simple bipartite
	v = 17 e = 30 f = 3
	degree seq :: [ 2^15, 15^2 ]

E6.277 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 10, 15})
Quotient :: loop
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-2 * T1 * T2^2 * T1, T2^3 * T1 * T2 * T1 * T2 * T1, T2^10 ]
Map::
	R = (1, 31, 3, 33, 8, 38, 17, 47, 26, 56, 28, 58, 27, 57, 19, 49, 10, 40, 4, 34)(2, 32, 5, 35, 12, 42, 22, 52, 29, 59, 25, 55, 30, 60, 24, 54, 14, 44, 6, 36)(7, 37, 15, 45, 23, 53, 13, 43, 21, 51, 11, 41, 20, 50, 18, 48, 9, 39, 16, 46)
	L = (1, 32)(2, 31)(3, 37)(4, 39)(5, 41)(6, 43)(7, 33)(8, 42)(9, 34)(10, 44)(11, 35)(12, 38)(13, 36)(14, 40)(15, 54)(16, 55)(17, 53)(18, 52)(19, 50)(20, 49)(21, 58)(22, 48)(23, 47)(24, 45)(25, 46)(26, 59)(27, 60)(28, 51)(29, 56)(30, 57)
	local type(s) :: { ( 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15 ) }
Outer automorphisms :: reflexible
Dual of E6.276
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 30 f = 17
	degree seq :: [ 20^3 ]

E6.278 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 10, 15})
Quotient :: loop
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-2 * T2^3, T1^10 ]
Map::
	R = (1, 31, 3, 33, 10, 40, 6, 36, 17, 47, 27, 57, 26, 56, 20, 50, 24, 54, 30, 60, 28, 58, 19, 49, 13, 43, 15, 45, 5, 35)(2, 32, 7, 37, 18, 48, 16, 46, 14, 44, 25, 55, 29, 59, 22, 52, 11, 41, 23, 53, 21, 51, 9, 39, 4, 34, 12, 42, 8, 38)
	L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 44)(6, 46)(7, 35)(8, 50)(9, 47)(10, 52)(11, 33)(12, 49)(13, 34)(14, 40)(15, 41)(16, 56)(17, 38)(18, 58)(19, 37)(20, 48)(21, 54)(22, 57)(23, 43)(24, 42)(25, 45)(26, 59)(27, 51)(28, 55)(29, 60)(30, 53)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.274
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 30 f = 18
	degree seq :: [ 30^2 ]

E6.279 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 10, 15})
Quotient :: loop
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4 * T2 * T1 * T2, T2 * T1^2 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 ]
Map:: polytopal non-degenerate
	R = (1, 31, 3, 33)(2, 32, 6, 36)(4, 34, 9, 39)(5, 35, 12, 42)(7, 37, 16, 46)(8, 38, 17, 47)(10, 40, 21, 51)(11, 41, 20, 50)(13, 43, 22, 52)(14, 44, 24, 54)(15, 45, 26, 56)(18, 48, 28, 58)(19, 49, 27, 57)(23, 53, 29, 59)(25, 55, 30, 60)
	L = (1, 32)(2, 35)(3, 37)(4, 31)(5, 41)(6, 43)(7, 45)(8, 33)(9, 49)(10, 34)(11, 47)(12, 51)(13, 48)(14, 36)(15, 50)(16, 52)(17, 54)(18, 38)(19, 53)(20, 39)(21, 55)(22, 40)(23, 42)(24, 59)(25, 44)(26, 58)(27, 46)(28, 60)(29, 56)(30, 57)
	local type(s) :: { ( 10, 15, 10, 15 ) }
Outer automorphisms :: reflexible
Dual of E6.275
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 15 e = 30 f = 5
	degree seq :: [ 4^15 ]

E6.280 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^2, Y2^10, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 9, 39)(5, 35, 11, 41)(6, 36, 13, 43)(8, 38, 12, 42)(10, 40, 14, 44)(15, 45, 24, 54)(16, 46, 25, 55)(17, 47, 23, 53)(18, 48, 22, 52)(19, 49, 20, 50)(21, 51, 28, 58)(26, 56, 29, 59)(27, 57, 30, 60)(61, 91, 63, 93, 68, 98, 77, 107, 86, 116, 88, 118, 87, 117, 79, 109, 70, 100, 64, 94)(62, 92, 65, 95, 72, 102, 82, 112, 89, 119, 85, 115, 90, 120, 84, 114, 74, 104, 66, 96)(67, 97, 75, 105, 83, 113, 73, 103, 81, 111, 71, 101, 80, 110, 78, 108, 69, 99, 76, 106)
	L = (1, 62)(2, 61)(3, 67)(4, 69)(5, 71)(6, 73)(7, 63)(8, 72)(9, 64)(10, 74)(11, 65)(12, 68)(13, 66)(14, 70)(15, 84)(16, 85)(17, 83)(18, 82)(19, 80)(20, 79)(21, 88)(22, 78)(23, 77)(24, 75)(25, 76)(26, 89)(27, 90)(28, 81)(29, 86)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 2, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30, 2, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.283
Graph:: bipartite
	v = 18 e = 60 f = 32
	degree seq :: [ 4^15, 20^3 ]

E6.281 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2^-3 * Y1, Y1^10 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 16, 46, 26, 56, 29, 59, 30, 60, 23, 53, 13, 43, 4, 34)(3, 33, 9, 39, 17, 47, 8, 38, 20, 50, 18, 48, 28, 58, 25, 55, 15, 45, 11, 41)(5, 35, 14, 44, 10, 40, 22, 52, 27, 57, 21, 51, 24, 54, 12, 42, 19, 49, 7, 37)(61, 91, 63, 93, 70, 100, 66, 96, 77, 107, 87, 117, 86, 116, 80, 110, 84, 114, 90, 120, 88, 118, 79, 109, 73, 103, 75, 105, 65, 95)(62, 92, 67, 97, 78, 108, 76, 106, 74, 104, 85, 115, 89, 119, 82, 112, 71, 101, 83, 113, 81, 111, 69, 99, 64, 94, 72, 102, 68, 98)
	L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 77)(7, 78)(8, 62)(9, 64)(10, 66)(11, 83)(12, 68)(13, 75)(14, 85)(15, 65)(16, 74)(17, 87)(18, 76)(19, 73)(20, 84)(21, 69)(22, 71)(23, 81)(24, 90)(25, 89)(26, 80)(27, 86)(28, 79)(29, 82)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.282
Graph:: bipartite
	v = 5 e = 60 f = 45
	degree seq :: [ 20^3, 30^2 ]

E6.282 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y3^-4, Y3 * Y2 * Y3^-2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^15 ]
Map:: polytopal
	R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92)(63, 93, 67, 97)(64, 94, 69, 99)(65, 95, 71, 101)(66, 96, 73, 103)(68, 98, 77, 107)(70, 100, 81, 111)(72, 102, 84, 114)(74, 104, 86, 116)(75, 105, 82, 112)(76, 106, 85, 115)(78, 108, 80, 110)(79, 109, 83, 113)(87, 117, 89, 119)(88, 118, 90, 120)
	L = (1, 63)(2, 65)(3, 68)(4, 61)(5, 72)(6, 62)(7, 75)(8, 78)(9, 79)(10, 64)(11, 82)(12, 80)(13, 85)(14, 66)(15, 74)(16, 67)(17, 81)(18, 73)(19, 88)(20, 69)(21, 87)(22, 70)(23, 71)(24, 86)(25, 90)(26, 89)(27, 76)(28, 77)(29, 83)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 20, 30 ), ( 20, 30, 20, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.281
Graph:: simple bipartite
	v = 45 e = 60 f = 5
	degree seq :: [ 2^30, 4^15 ]

E6.283 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^4 * Y3 * Y1 * Y3, Y3 * Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 ]
Map::
	R = (1, 31, 2, 32, 5, 35, 11, 41, 17, 47, 24, 54, 29, 59, 26, 56, 28, 58, 30, 60, 27, 57, 16, 46, 22, 52, 10, 40, 4, 34)(3, 33, 7, 37, 15, 45, 20, 50, 9, 39, 19, 49, 23, 53, 12, 42, 21, 51, 25, 55, 14, 44, 6, 36, 13, 43, 18, 48, 8, 38)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120)
	L = (1, 63)(2, 66)(3, 61)(4, 69)(5, 72)(6, 62)(7, 76)(8, 77)(9, 64)(10, 81)(11, 80)(12, 65)(13, 82)(14, 84)(15, 86)(16, 67)(17, 68)(18, 88)(19, 87)(20, 71)(21, 70)(22, 73)(23, 89)(24, 74)(25, 90)(26, 75)(27, 79)(28, 78)(29, 83)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.280
Graph:: simple bipartite
	v = 32 e = 60 f = 18
	degree seq :: [ 2^30, 30^2 ]

E6.284 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^4 * Y1 * Y2, (Y2^-1 * R * Y2^-2)^2, Y2 * Y1 * Y2^-2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 9, 39)(5, 35, 11, 41)(6, 36, 13, 43)(8, 38, 17, 47)(10, 40, 21, 51)(12, 42, 24, 54)(14, 44, 26, 56)(15, 45, 22, 52)(16, 46, 25, 55)(18, 48, 20, 50)(19, 49, 23, 53)(27, 57, 29, 59)(28, 58, 30, 60)(61, 91, 63, 93, 68, 98, 78, 108, 73, 103, 85, 115, 90, 120, 84, 114, 86, 116, 89, 119, 83, 113, 71, 101, 82, 112, 70, 100, 64, 94)(62, 92, 65, 95, 72, 102, 80, 110, 69, 99, 79, 109, 88, 118, 77, 107, 81, 111, 87, 117, 76, 106, 67, 97, 75, 105, 74, 104, 66, 96)
	L = (1, 62)(2, 61)(3, 67)(4, 69)(5, 71)(6, 73)(7, 63)(8, 77)(9, 64)(10, 81)(11, 65)(12, 84)(13, 66)(14, 86)(15, 82)(16, 85)(17, 68)(18, 80)(19, 83)(20, 78)(21, 70)(22, 75)(23, 79)(24, 72)(25, 76)(26, 74)(27, 89)(28, 90)(29, 87)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.285
Graph:: bipartite
	v = 17 e = 60 f = 33
	degree seq :: [ 4^15, 30^2 ]

E6.285 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 15})
Quotient :: dipole
Aut^+ = C5 x S3 (small group id <30, 1>)
Aut   = S3 x D10 (small group id <60, 8>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^2 * Y3^-3, (R * Y2 * Y3^-1)^2, Y1^10, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 31, 2, 32, 6, 36, 16, 46, 26, 56, 29, 59, 30, 60, 23, 53, 13, 43, 4, 34)(3, 33, 9, 39, 17, 47, 8, 38, 20, 50, 18, 48, 28, 58, 25, 55, 15, 45, 11, 41)(5, 35, 14, 44, 10, 40, 22, 52, 27, 57, 21, 51, 24, 54, 12, 42, 19, 49, 7, 37)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120)
	L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 77)(7, 78)(8, 62)(9, 64)(10, 66)(11, 83)(12, 68)(13, 75)(14, 85)(15, 65)(16, 74)(17, 87)(18, 76)(19, 73)(20, 84)(21, 69)(22, 71)(23, 81)(24, 90)(25, 89)(26, 80)(27, 86)(28, 79)(29, 82)(30, 88)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120)
	local type(s) :: { ( 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) }
Outer automorphisms :: reflexible
Dual of E6.284
Graph:: simple bipartite
	v = 33 e = 60 f = 17
	degree seq :: [ 2^30, 20^3 ]

E6.286 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 9, 9})
Quotient :: regular
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1^-2 * T2, T1^9 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 30, 22, 10, 4)(3, 7, 15, 24, 32, 34, 27, 18, 8)(6, 13, 26, 31, 36, 29, 21, 17, 14)(9, 19, 16, 12, 25, 33, 35, 28, 20)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 15)(14, 19)(18, 20)(22, 27)(23, 31)(25, 26)(28, 29)(30, 35)(32, 33)(34, 36)
	local type(s) :: { ( 9^9 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 4 e = 18 f = 4
	degree seq :: [ 9^4 ]

E6.287 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 9})
Quotient :: edge
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^9 ]
Map::
	R = (1, 3, 8, 18, 27, 30, 22, 10, 4)(2, 5, 12, 23, 31, 32, 24, 14, 6)(7, 15, 25, 33, 36, 29, 21, 13, 16)(9, 19, 11, 17, 26, 34, 35, 28, 20)(37, 38)(39, 43)(40, 45)(41, 47)(42, 49)(44, 53)(46, 57)(48, 51)(50, 56)(52, 55)(54, 59)(58, 60)(61, 62)(63, 69)(64, 65)(66, 71)(67, 70)(68, 72)
	L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)
	local type(s) :: { ( 18, 18 ), ( 18^9 ) }
Outer automorphisms :: reflexible
Dual of E6.288
Transitivity :: ET+
Graph:: simple bipartite
	v = 22 e = 36 f = 4
	degree seq :: [ 2^18, 9^4 ]

E6.288 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 9})
Quotient :: loop
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^9 ]
Map::
	R = (1, 37, 3, 39, 8, 44, 18, 54, 27, 63, 30, 66, 22, 58, 10, 46, 4, 40)(2, 38, 5, 41, 12, 48, 23, 59, 31, 67, 32, 68, 24, 60, 14, 50, 6, 42)(7, 43, 15, 51, 25, 61, 33, 69, 36, 72, 29, 65, 21, 57, 13, 49, 16, 52)(9, 45, 19, 55, 11, 47, 17, 53, 26, 62, 34, 70, 35, 71, 28, 64, 20, 56)
	L = (1, 38)(2, 37)(3, 43)(4, 45)(5, 47)(6, 49)(7, 39)(8, 53)(9, 40)(10, 57)(11, 41)(12, 51)(13, 42)(14, 56)(15, 48)(16, 55)(17, 44)(18, 59)(19, 52)(20, 50)(21, 46)(22, 60)(23, 54)(24, 58)(25, 62)(26, 61)(27, 69)(28, 65)(29, 64)(30, 71)(31, 70)(32, 72)(33, 63)(34, 67)(35, 66)(36, 68)
	local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) }
Outer automorphisms :: reflexible
Dual of E6.287
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 36 f = 22
	degree seq :: [ 18^4 ]

E6.289 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2, Y2^9, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 11, 47)(6, 42, 13, 49)(8, 44, 17, 53)(10, 46, 21, 57)(12, 48, 15, 51)(14, 50, 20, 56)(16, 52, 19, 55)(18, 54, 23, 59)(22, 58, 24, 60)(25, 61, 26, 62)(27, 63, 33, 69)(28, 64, 29, 65)(30, 66, 35, 71)(31, 67, 34, 70)(32, 68, 36, 72)(73, 109, 75, 111, 80, 116, 90, 126, 99, 135, 102, 138, 94, 130, 82, 118, 76, 112)(74, 110, 77, 113, 84, 120, 95, 131, 103, 139, 104, 140, 96, 132, 86, 122, 78, 114)(79, 115, 87, 123, 97, 133, 105, 141, 108, 144, 101, 137, 93, 129, 85, 121, 88, 124)(81, 117, 91, 127, 83, 119, 89, 125, 98, 134, 106, 142, 107, 143, 100, 136, 92, 128)
	L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 89)(9, 76)(10, 93)(11, 77)(12, 87)(13, 78)(14, 92)(15, 84)(16, 91)(17, 80)(18, 95)(19, 88)(20, 86)(21, 82)(22, 96)(23, 90)(24, 94)(25, 98)(26, 97)(27, 105)(28, 101)(29, 100)(30, 107)(31, 106)(32, 108)(33, 99)(34, 103)(35, 102)(36, 104)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.290
Graph:: bipartite
	v = 22 e = 72 f = 40
	degree seq :: [ 4^18, 18^4 ]

E6.290 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 9})
Quotient :: dipole
Aut^+ = (C2 x C2) : C9 (small group id <36, 3>)
Aut   = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^9 ]
Map::
	R = (1, 37, 2, 38, 5, 41, 11, 47, 23, 59, 30, 66, 22, 58, 10, 46, 4, 40)(3, 39, 7, 43, 15, 51, 24, 60, 32, 68, 34, 70, 27, 63, 18, 54, 8, 44)(6, 42, 13, 49, 26, 62, 31, 67, 36, 72, 29, 65, 21, 57, 17, 53, 14, 50)(9, 45, 19, 55, 16, 52, 12, 48, 25, 61, 33, 69, 35, 71, 28, 64, 20, 56)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144)
	L = (1, 75)(2, 78)(3, 73)(4, 81)(5, 84)(6, 74)(7, 88)(8, 89)(9, 76)(10, 93)(11, 96)(12, 77)(13, 87)(14, 91)(15, 85)(16, 79)(17, 80)(18, 92)(19, 86)(20, 90)(21, 82)(22, 99)(23, 103)(24, 83)(25, 98)(26, 97)(27, 94)(28, 101)(29, 100)(30, 107)(31, 95)(32, 105)(33, 104)(34, 108)(35, 102)(36, 106)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.289
Graph:: simple bipartite
	v = 40 e = 72 f = 22
	degree seq :: [ 2^36, 18^4 ]

E6.291 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {3, 3, 13})
Quotient :: edge
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = C13 : C3 (small group id <39, 1>)
|r| :: 1
Presentation :: [ X1^3, X2 * X1 * X2^-3 * X1^-1, (X2 * X1^-1)^3, (X2^-1 * X1^-1)^3, X1^-1 * X2^4 * X1 * X2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 23, 25)(11, 24, 28)(12, 29, 22)(15, 31, 26)(17, 32, 33)(21, 35, 34)(27, 37, 36)(30, 39, 38)(40, 42, 48, 63, 59, 72, 76, 78, 73, 57, 68, 54, 44)(41, 45, 56, 47, 61, 75, 62, 70, 77, 67, 52, 60, 46)(43, 50, 66, 55, 53, 64, 71, 74, 65, 49, 58, 69, 51)
	L = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78)
	local type(s) :: { ( 6^3 ), ( 6^13 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 16 e = 39 f = 13
	degree seq :: [ 3^13, 13^3 ]

E6.292 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {3, 3, 13})
Quotient :: loop
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = C13 : C3 (small group id <39, 1>)
|r| :: 1
Presentation :: [ X1^3, X2^3, (X1^-1 * X2)^3, X2 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 40, 2, 41, 4, 43)(3, 42, 8, 47, 9, 48)(5, 44, 12, 51, 13, 52)(6, 45, 14, 53, 15, 54)(7, 46, 16, 55, 17, 56)(10, 49, 21, 60, 22, 61)(11, 50, 23, 62, 24, 63)(18, 57, 33, 72, 34, 73)(19, 58, 26, 65, 28, 67)(20, 59, 35, 74, 36, 75)(25, 64, 32, 71, 38, 77)(27, 66, 39, 78, 30, 69)(29, 68, 31, 70, 37, 76)
	L = (1, 42)(2, 45)(3, 44)(4, 49)(5, 40)(6, 46)(7, 41)(8, 57)(9, 55)(10, 50)(11, 43)(12, 64)(13, 65)(14, 67)(15, 62)(16, 59)(17, 70)(18, 58)(19, 47)(20, 48)(21, 76)(22, 51)(23, 69)(24, 73)(25, 61)(26, 66)(27, 52)(28, 68)(29, 53)(30, 54)(31, 71)(32, 56)(33, 60)(34, 74)(35, 63)(36, 77)(37, 72)(38, 78)(39, 75)
	local type(s) :: { ( 3, 13, 3, 13, 3, 13 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph:: simple
	v = 13 e = 39 f = 16
	degree seq :: [ 6^13 ]

E6.293 :: Family: { 2*ex } :: Oriented family(ies): { E3c }
Signature :: (0; {3, 3, 13})
Quotient :: loop
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, T2^3, F * T1 * F * T2, (T1^-1 * T2)^3, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 5)(2, 6, 7)(4, 10, 11)(8, 18, 19)(9, 16, 20)(12, 25, 22)(13, 26, 27)(14, 28, 29)(15, 23, 30)(17, 31, 32)(21, 37, 33)(24, 34, 35)(36, 38, 39)(40, 41, 43)(42, 47, 48)(44, 51, 52)(45, 53, 54)(46, 55, 56)(49, 60, 61)(50, 62, 63)(57, 72, 73)(58, 65, 67)(59, 74, 75)(64, 71, 77)(66, 78, 69)(68, 70, 76)
	L = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78)
	local type(s) :: { ( 26^3 ) }
Outer automorphisms :: reflexible
Dual of E6.294
Transitivity :: ET+ VT AT
Graph:: simple bipartite
	v = 26 e = 39 f = 3
	degree seq :: [ 3^26 ]

E6.294 :: Family: { 2ex } :: Oriented family(ies): { E3*c }
Signature :: (0; {3, 3, 13})
Quotient :: edge
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, F * T1 * T2 * F * T1^-1, T2^-1 * T1 * T2^3 * T1^-1, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^3, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2^2 ]
Map:: polytopal non-degenerate
	R = (1, 40, 3, 42, 9, 48, 24, 63, 20, 59, 33, 72, 37, 76, 39, 78, 34, 73, 18, 57, 29, 68, 15, 54, 5, 44)(2, 41, 6, 45, 17, 56, 8, 47, 22, 61, 36, 75, 23, 62, 31, 70, 38, 77, 28, 67, 13, 52, 21, 60, 7, 46)(4, 43, 11, 50, 27, 66, 16, 55, 14, 53, 25, 64, 32, 71, 35, 74, 26, 65, 10, 49, 19, 58, 30, 69, 12, 51)
	L = (1, 41)(2, 43)(3, 47)(4, 40)(5, 52)(6, 55)(7, 58)(8, 49)(9, 62)(10, 42)(11, 63)(12, 68)(13, 53)(14, 44)(15, 70)(16, 57)(17, 71)(18, 45)(19, 59)(20, 46)(21, 74)(22, 51)(23, 64)(24, 67)(25, 48)(26, 54)(27, 76)(28, 50)(29, 61)(30, 78)(31, 65)(32, 72)(33, 56)(34, 60)(35, 73)(36, 66)(37, 75)(38, 69)(39, 77)
	local type(s) :: { ( 3^26 ) }
Outer automorphisms :: reflexible
Dual of E6.293
Transitivity :: ET+ VT+
Graph::
	v = 3 e = 39 f = 26
	degree seq :: [ 26^3 ]

E6.295 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 13})
Quotient :: edge^2
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 40, 4, 43, 15, 54, 19, 58, 29, 68, 39, 78, 38, 77, 33, 72, 24, 63, 25, 64, 11, 50, 23, 62, 7, 46)(2, 41, 8, 47, 20, 59, 6, 45, 12, 51, 32, 71, 17, 56, 31, 70, 34, 73, 37, 76, 21, 60, 30, 69, 10, 49)(3, 42, 5, 44, 18, 57, 27, 66, 9, 48, 22, 61, 36, 75, 26, 65, 35, 74, 14, 53, 16, 55, 28, 67, 13, 52)(79, 80, 83)(81, 89, 90)(82, 84, 94)(85, 99, 100)(86, 87, 103)(88, 106, 107)(91, 111, 112)(92, 101, 109)(93, 95, 114)(96, 97, 115)(98, 104, 117)(102, 108, 113)(105, 116, 110)(118, 120, 123)(119, 124, 126)(121, 131, 134)(122, 127, 136)(125, 141, 143)(128, 130, 148)(129, 142, 144)(132, 139, 154)(133, 137, 146)(135, 151, 155)(138, 140, 152)(145, 147, 150)(149, 156, 153)
	L = (1, 79)(2, 80)(3, 81)(4, 82)(5, 83)(6, 84)(7, 85)(8, 86)(9, 87)(10, 88)(11, 89)(12, 90)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 98)(21, 99)(22, 100)(23, 101)(24, 102)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 112)(35, 113)(36, 114)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156)
	local type(s) :: { ( 4^3 ), ( 4^26 ) }
Outer automorphisms :: reflexible
Dual of E6.298
Graph:: simple bipartite
	v = 29 e = 78 f = 39
	degree seq :: [ 3^26, 26^3 ]

E6.296 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {3, 3, 13})
Quotient :: edge^2
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2^-1)^3, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^13 ]
Map:: polytopal
	R = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78)(79, 80, 82)(81, 86, 87)(83, 90, 91)(84, 92, 93)(85, 94, 95)(88, 99, 100)(89, 101, 102)(96, 111, 112)(97, 104, 106)(98, 113, 114)(103, 110, 116)(105, 117, 108)(107, 109, 115)(118, 120, 122)(119, 123, 124)(121, 127, 128)(125, 135, 136)(126, 133, 137)(129, 142, 139)(130, 143, 144)(131, 145, 146)(132, 140, 147)(134, 148, 149)(138, 154, 150)(141, 151, 152)(153, 155, 156)
	L = (1, 79)(2, 80)(3, 81)(4, 82)(5, 83)(6, 84)(7, 85)(8, 86)(9, 87)(10, 88)(11, 89)(12, 90)(13, 91)(14, 92)(15, 93)(16, 94)(17, 95)(18, 96)(19, 97)(20, 98)(21, 99)(22, 100)(23, 101)(24, 102)(25, 103)(26, 104)(27, 105)(28, 106)(29, 107)(30, 108)(31, 109)(32, 110)(33, 111)(34, 112)(35, 113)(36, 114)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156)
	local type(s) :: { ( 52, 52 ), ( 52^3 ) }
Outer automorphisms :: reflexible
Dual of E6.297
Graph:: simple bipartite
	v = 65 e = 78 f = 3
	degree seq :: [ 2^39, 3^26 ]

E6.297 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 13})
Quotient :: loop^2
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y1 * Y3^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ]
Map::
	R = (1, 40, 79, 118, 4, 43, 82, 121, 15, 54, 93, 132, 19, 58, 97, 136, 29, 68, 107, 146, 39, 78, 117, 156, 38, 77, 116, 155, 33, 72, 111, 150, 24, 63, 102, 141, 25, 64, 103, 142, 11, 50, 89, 128, 23, 62, 101, 140, 7, 46, 85, 124)(2, 41, 80, 119, 8, 47, 86, 125, 20, 59, 98, 137, 6, 45, 84, 123, 12, 51, 90, 129, 32, 71, 110, 149, 17, 56, 95, 134, 31, 70, 109, 148, 34, 73, 112, 151, 37, 76, 115, 154, 21, 60, 99, 138, 30, 69, 108, 147, 10, 49, 88, 127)(3, 42, 81, 120, 5, 44, 83, 122, 18, 57, 96, 135, 27, 66, 105, 144, 9, 48, 87, 126, 22, 61, 100, 139, 36, 75, 114, 153, 26, 65, 104, 143, 35, 74, 113, 152, 14, 53, 92, 131, 16, 55, 94, 133, 28, 67, 106, 145, 13, 52, 91, 130)
	L = (1, 41)(2, 44)(3, 50)(4, 45)(5, 40)(6, 55)(7, 60)(8, 48)(9, 64)(10, 67)(11, 51)(12, 42)(13, 72)(14, 62)(15, 56)(16, 43)(17, 75)(18, 58)(19, 76)(20, 65)(21, 61)(22, 46)(23, 70)(24, 69)(25, 47)(26, 78)(27, 77)(28, 68)(29, 49)(30, 74)(31, 53)(32, 66)(33, 73)(34, 52)(35, 63)(36, 54)(37, 57)(38, 71)(39, 59)(79, 120)(80, 124)(81, 123)(82, 131)(83, 127)(84, 118)(85, 126)(86, 141)(87, 119)(88, 136)(89, 130)(90, 142)(91, 148)(92, 134)(93, 139)(94, 137)(95, 121)(96, 151)(97, 122)(98, 146)(99, 140)(100, 154)(101, 152)(102, 143)(103, 144)(104, 125)(105, 129)(106, 147)(107, 133)(108, 150)(109, 128)(110, 156)(111, 145)(112, 155)(113, 138)(114, 149)(115, 132)(116, 135)(117, 153)
	local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) }
Outer automorphisms :: reflexible
Dual of E6.296
Transitivity :: VT+
Graph::
	v = 3 e = 78 f = 65
	degree seq :: [ 52^3 ]

E6.298 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {3, 3, 13})
Quotient :: loop^2
Aut^+ = C13 : C3 (small group id <39, 1>)
Aut   = (C13 : C3) : C2 (small group id <78, 1>)
|r| :: 2
Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2^-1)^3, Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^13 ]
Map:: polytopal non-degenerate
	R = (1, 40, 79, 118)(2, 41, 80, 119)(3, 42, 81, 120)(4, 43, 82, 121)(5, 44, 83, 122)(6, 45, 84, 123)(7, 46, 85, 124)(8, 47, 86, 125)(9, 48, 87, 126)(10, 49, 88, 127)(11, 50, 89, 128)(12, 51, 90, 129)(13, 52, 91, 130)(14, 53, 92, 131)(15, 54, 93, 132)(16, 55, 94, 133)(17, 56, 95, 134)(18, 57, 96, 135)(19, 58, 97, 136)(20, 59, 98, 137)(21, 60, 99, 138)(22, 61, 100, 139)(23, 62, 101, 140)(24, 63, 102, 141)(25, 64, 103, 142)(26, 65, 104, 143)(27, 66, 105, 144)(28, 67, 106, 145)(29, 68, 107, 146)(30, 69, 108, 147)(31, 70, 109, 148)(32, 71, 110, 149)(33, 72, 111, 150)(34, 73, 112, 151)(35, 74, 113, 152)(36, 75, 114, 153)(37, 76, 115, 154)(38, 77, 116, 155)(39, 78, 117, 156)
	L = (1, 41)(2, 43)(3, 47)(4, 40)(5, 51)(6, 53)(7, 55)(8, 48)(9, 42)(10, 60)(11, 62)(12, 52)(13, 44)(14, 54)(15, 45)(16, 56)(17, 46)(18, 72)(19, 65)(20, 74)(21, 61)(22, 49)(23, 63)(24, 50)(25, 71)(26, 67)(27, 78)(28, 58)(29, 70)(30, 66)(31, 76)(32, 77)(33, 73)(34, 57)(35, 75)(36, 59)(37, 68)(38, 64)(39, 69)(79, 120)(80, 123)(81, 122)(82, 127)(83, 118)(84, 124)(85, 119)(86, 135)(87, 133)(88, 128)(89, 121)(90, 142)(91, 143)(92, 145)(93, 140)(94, 137)(95, 148)(96, 136)(97, 125)(98, 126)(99, 154)(100, 129)(101, 147)(102, 151)(103, 139)(104, 144)(105, 130)(106, 146)(107, 131)(108, 132)(109, 149)(110, 134)(111, 138)(112, 152)(113, 141)(114, 155)(115, 150)(116, 156)(117, 153)
	local type(s) :: { ( 3, 26, 3, 26 ) }
Outer automorphisms :: reflexible
Dual of E6.295
Transitivity :: VT+
Graph:: simple
	v = 39 e = 78 f = 29
	degree seq :: [ 4^39 ]

E6.299 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 8})
Quotient :: regular
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^8, (T1 * T2)^6 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 15, 25, 31, 22, 12, 8)(6, 13, 9, 18, 29, 32, 21, 14)(16, 26, 17, 28, 33, 43, 37, 27)(23, 34, 24, 36, 42, 41, 30, 35)(38, 45, 39, 47, 48, 46, 40, 44)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 47)(43, 48)
	local type(s) :: { ( 6^8 ) }
Outer automorphisms :: reflexible
Dual of E6.300
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 6 e = 24 f = 8
	degree seq :: [ 8^6 ]

E6.300 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 8})
Quotient :: regular
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 20, 12, 8)(6, 13, 9, 18, 19, 14)(16, 23, 17, 25, 27, 24)(21, 28, 22, 30, 26, 29)(31, 37, 32, 39, 33, 38)(34, 40, 35, 42, 36, 41)(43, 46, 44, 47, 45, 48)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)
	local type(s) :: { ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E6.299
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 24 f = 6
	degree seq :: [ 6^8 ]

E6.301 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^8 ]
Map:: polytopal
	R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 9, 18, 25, 16)(11, 19, 13, 22, 29, 20)(23, 31, 24, 33, 26, 32)(27, 34, 28, 36, 30, 35)(37, 43, 38, 45, 39, 44)(40, 46, 41, 48, 42, 47)(49, 50)(51, 55)(52, 57)(53, 59)(54, 61)(56, 62)(58, 60)(63, 71)(64, 72)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(79, 85)(80, 86)(81, 87)(82, 88)(83, 89)(84, 90)(91, 94)(92, 96)(93, 95)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 16, 16 ), ( 16^6 ) }
Outer automorphisms :: reflexible
Dual of E6.305
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 48 f = 6
	degree seq :: [ 2^24, 6^8 ]

E6.302 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^8 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 21, 33, 24, 13, 5)(2, 7, 17, 29, 40, 30, 18, 8)(4, 11, 23, 35, 42, 32, 20, 9)(6, 15, 27, 38, 46, 39, 28, 16)(12, 19, 31, 41, 47, 43, 34, 22)(14, 25, 36, 44, 48, 45, 37, 26)(49, 50, 54, 62, 60, 52)(51, 57, 67, 74, 63, 56)(53, 59, 70, 73, 64, 55)(58, 66, 75, 85, 79, 68)(61, 65, 76, 84, 82, 71)(69, 80, 89, 93, 86, 78)(72, 83, 91, 92, 87, 77)(81, 88, 94, 96, 95, 90)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^6 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.306
Transitivity :: ET+
Graph:: simple bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 6^8, 8^6 ]

E6.303 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^8, (T2 * T1)^6 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 47)(43, 48)(49, 50, 53, 59, 68, 67, 58, 52)(51, 55, 63, 73, 79, 70, 60, 56)(54, 61, 57, 66, 77, 80, 69, 62)(64, 74, 65, 76, 81, 91, 85, 75)(71, 82, 72, 84, 90, 89, 78, 83)(86, 93, 87, 95, 96, 94, 88, 92)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 12, 12 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E6.304
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 48 f = 8
	degree seq :: [ 2^24, 8^6 ]

E6.304 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^8 ]
Map::
	R = (1, 49, 3, 51, 8, 56, 17, 65, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 21, 69, 14, 62, 6, 54)(7, 55, 15, 63, 9, 57, 18, 66, 25, 73, 16, 64)(11, 59, 19, 67, 13, 61, 22, 70, 29, 77, 20, 68)(23, 71, 31, 79, 24, 72, 33, 81, 26, 74, 32, 80)(27, 75, 34, 82, 28, 76, 36, 84, 30, 78, 35, 83)(37, 85, 43, 91, 38, 86, 45, 93, 39, 87, 44, 92)(40, 88, 46, 94, 41, 89, 48, 96, 42, 90, 47, 95)
	L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 62)(9, 52)(10, 60)(11, 53)(12, 58)(13, 54)(14, 56)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 85)(32, 86)(33, 87)(34, 88)(35, 89)(36, 90)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(43, 94)(44, 96)(45, 95)(46, 91)(47, 93)(48, 92)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.303
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 48 f = 30
	degree seq :: [ 12^8 ]

E6.305 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^8 ]
Map::
	R = (1, 49, 3, 51, 10, 58, 21, 69, 33, 81, 24, 72, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 29, 77, 40, 88, 30, 78, 18, 66, 8, 56)(4, 52, 11, 59, 23, 71, 35, 83, 42, 90, 32, 80, 20, 68, 9, 57)(6, 54, 15, 63, 27, 75, 38, 86, 46, 94, 39, 87, 28, 76, 16, 64)(12, 60, 19, 67, 31, 79, 41, 89, 47, 95, 43, 91, 34, 82, 22, 70)(14, 62, 25, 73, 36, 84, 44, 92, 48, 96, 45, 93, 37, 85, 26, 74)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 62)(7, 53)(8, 51)(9, 67)(10, 66)(11, 70)(12, 52)(13, 65)(14, 60)(15, 56)(16, 55)(17, 76)(18, 75)(19, 74)(20, 58)(21, 80)(22, 73)(23, 61)(24, 83)(25, 64)(26, 63)(27, 85)(28, 84)(29, 72)(30, 69)(31, 68)(32, 89)(33, 88)(34, 71)(35, 91)(36, 82)(37, 79)(38, 78)(39, 77)(40, 94)(41, 93)(42, 81)(43, 92)(44, 87)(45, 86)(46, 96)(47, 90)(48, 95)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.301
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 48 f = 32
	degree seq :: [ 16^6 ]

E6.306 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^8, (T2 * T1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 15, 63)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(18, 66, 30, 78)(19, 67, 29, 77)(20, 68, 31, 79)(22, 70, 33, 81)(25, 73, 37, 85)(26, 74, 38, 86)(27, 75, 39, 87)(28, 76, 40, 88)(32, 80, 42, 90)(34, 82, 44, 92)(35, 83, 45, 93)(36, 84, 46, 94)(41, 89, 47, 95)(43, 91, 48, 96)
	L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 66)(10, 52)(11, 68)(12, 56)(13, 57)(14, 54)(15, 73)(16, 74)(17, 76)(18, 77)(19, 58)(20, 67)(21, 62)(22, 60)(23, 82)(24, 84)(25, 79)(26, 65)(27, 64)(28, 81)(29, 80)(30, 83)(31, 70)(32, 69)(33, 91)(34, 72)(35, 71)(36, 90)(37, 75)(38, 93)(39, 95)(40, 92)(41, 78)(42, 89)(43, 85)(44, 86)(45, 87)(46, 88)(47, 96)(48, 94)
	local type(s) :: { ( 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.302
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.307 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, Y2^6, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 14, 62)(10, 58, 12, 60)(15, 63, 23, 71)(16, 64, 24, 72)(17, 65, 25, 73)(18, 66, 26, 74)(19, 67, 27, 75)(20, 68, 28, 76)(21, 69, 29, 77)(22, 70, 30, 78)(31, 79, 37, 85)(32, 80, 38, 86)(33, 81, 39, 87)(34, 82, 40, 88)(35, 83, 41, 89)(36, 84, 42, 90)(43, 91, 46, 94)(44, 92, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 104, 152, 113, 161, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 117, 165, 110, 158, 102, 150)(103, 151, 111, 159, 105, 153, 114, 162, 121, 169, 112, 160)(107, 155, 115, 163, 109, 157, 118, 166, 125, 173, 116, 164)(119, 167, 127, 175, 120, 168, 129, 177, 122, 170, 128, 176)(123, 171, 130, 178, 124, 172, 132, 180, 126, 174, 131, 179)(133, 181, 139, 187, 134, 182, 141, 189, 135, 183, 140, 188)(136, 184, 142, 190, 137, 185, 144, 192, 138, 186, 143, 191)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 110)(9, 100)(10, 108)(11, 101)(12, 106)(13, 102)(14, 104)(15, 119)(16, 120)(17, 121)(18, 122)(19, 123)(20, 124)(21, 125)(22, 126)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 133)(32, 134)(33, 135)(34, 136)(35, 137)(36, 138)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 142)(44, 144)(45, 143)(46, 139)(47, 141)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.310
Graph:: bipartite
	v = 32 e = 96 f = 54
	degree seq :: [ 4^24, 12^8 ]

E6.308 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^6, Y2^8 ]
Map::
	R = (1, 49, 2, 50, 6, 54, 14, 62, 12, 60, 4, 52)(3, 51, 9, 57, 19, 67, 26, 74, 15, 63, 8, 56)(5, 53, 11, 59, 22, 70, 25, 73, 16, 64, 7, 55)(10, 58, 18, 66, 27, 75, 37, 85, 31, 79, 20, 68)(13, 61, 17, 65, 28, 76, 36, 84, 34, 82, 23, 71)(21, 69, 32, 80, 41, 89, 45, 93, 38, 86, 30, 78)(24, 72, 35, 83, 43, 91, 44, 92, 39, 87, 29, 77)(33, 81, 40, 88, 46, 94, 48, 96, 47, 95, 42, 90)(97, 145, 99, 147, 106, 154, 117, 165, 129, 177, 120, 168, 109, 157, 101, 149)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 126, 174, 114, 162, 104, 152)(100, 148, 107, 155, 119, 167, 131, 179, 138, 186, 128, 176, 116, 164, 105, 153)(102, 150, 111, 159, 123, 171, 134, 182, 142, 190, 135, 183, 124, 172, 112, 160)(108, 156, 115, 163, 127, 175, 137, 185, 143, 191, 139, 187, 130, 178, 118, 166)(110, 158, 121, 169, 132, 180, 140, 188, 144, 192, 141, 189, 133, 181, 122, 170)
	L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 111)(7, 113)(8, 98)(9, 100)(10, 117)(11, 119)(12, 115)(13, 101)(14, 121)(15, 123)(16, 102)(17, 125)(18, 104)(19, 127)(20, 105)(21, 129)(22, 108)(23, 131)(24, 109)(25, 132)(26, 110)(27, 134)(28, 112)(29, 136)(30, 114)(31, 137)(32, 116)(33, 120)(34, 118)(35, 138)(36, 140)(37, 122)(38, 142)(39, 124)(40, 126)(41, 143)(42, 128)(43, 130)(44, 144)(45, 133)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.309
Graph:: bipartite
	v = 14 e = 96 f = 72
	degree seq :: [ 12^8, 16^6 ]

E6.309 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^8, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^8 ]
Map:: polytopal
	R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 110, 158)(106, 154, 108, 156)(111, 159, 121, 169)(112, 160, 122, 170)(113, 161, 123, 171)(114, 162, 125, 173)(115, 163, 126, 174)(116, 164, 127, 175)(117, 165, 128, 176)(118, 166, 129, 177)(119, 167, 131, 179)(120, 168, 132, 180)(124, 172, 130, 178)(133, 181, 139, 187)(134, 182, 138, 186)(135, 183, 142, 190)(136, 184, 143, 191)(137, 185, 140, 188)(141, 189, 144, 192)
	L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 111)(8, 113)(9, 114)(10, 100)(11, 116)(12, 118)(13, 119)(14, 102)(15, 105)(16, 103)(17, 124)(18, 126)(19, 106)(20, 109)(21, 107)(22, 130)(23, 132)(24, 110)(25, 133)(26, 135)(27, 112)(28, 115)(29, 134)(30, 136)(31, 138)(32, 140)(33, 117)(34, 120)(35, 139)(36, 141)(37, 122)(38, 121)(39, 143)(40, 123)(41, 125)(42, 128)(43, 127)(44, 144)(45, 129)(46, 131)(47, 137)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.308
Graph:: simple bipartite
	v = 72 e = 96 f = 14
	degree seq :: [ 2^48, 4^24 ]

E6.310 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^8, (Y3^-1 * Y1)^6 ]
Map:: polytopal
	R = (1, 49, 2, 50, 5, 53, 11, 59, 20, 68, 19, 67, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 25, 73, 31, 79, 22, 70, 12, 60, 8, 56)(6, 54, 13, 61, 9, 57, 18, 66, 29, 77, 32, 80, 21, 69, 14, 62)(16, 64, 26, 74, 17, 65, 28, 76, 33, 81, 43, 91, 37, 85, 27, 75)(23, 71, 34, 82, 24, 72, 36, 84, 42, 90, 41, 89, 30, 78, 35, 83)(38, 86, 45, 93, 39, 87, 47, 95, 48, 96, 46, 94, 40, 88, 44, 92)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 113)(9, 100)(10, 111)(11, 117)(12, 101)(13, 119)(14, 120)(15, 106)(16, 103)(17, 104)(18, 126)(19, 125)(20, 127)(21, 107)(22, 129)(23, 109)(24, 110)(25, 133)(26, 134)(27, 135)(28, 136)(29, 115)(30, 114)(31, 116)(32, 138)(33, 118)(34, 140)(35, 141)(36, 142)(37, 121)(38, 122)(39, 123)(40, 124)(41, 143)(42, 128)(43, 144)(44, 130)(45, 131)(46, 132)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.307
Graph:: simple bipartite
	v = 54 e = 96 f = 32
	degree seq :: [ 2^48, 16^6 ]

E6.311 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, Y2^8, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 14, 62)(10, 58, 12, 60)(15, 63, 25, 73)(16, 64, 26, 74)(17, 65, 27, 75)(18, 66, 29, 77)(19, 67, 30, 78)(20, 68, 31, 79)(21, 69, 32, 80)(22, 70, 33, 81)(23, 71, 35, 83)(24, 72, 36, 84)(28, 76, 34, 82)(37, 85, 43, 91)(38, 86, 42, 90)(39, 87, 46, 94)(40, 88, 47, 95)(41, 89, 44, 92)(45, 93, 48, 96)(97, 145, 99, 147, 104, 152, 113, 161, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 130, 178, 120, 168, 110, 158, 102, 150)(103, 151, 111, 159, 105, 153, 114, 162, 126, 174, 136, 184, 123, 171, 112, 160)(107, 155, 116, 164, 109, 157, 119, 167, 132, 180, 141, 189, 129, 177, 117, 165)(121, 169, 133, 181, 122, 170, 135, 183, 143, 191, 137, 185, 125, 173, 134, 182)(127, 175, 138, 186, 128, 176, 140, 188, 144, 192, 142, 190, 131, 179, 139, 187)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 110)(9, 100)(10, 108)(11, 101)(12, 106)(13, 102)(14, 104)(15, 121)(16, 122)(17, 123)(18, 125)(19, 126)(20, 127)(21, 128)(22, 129)(23, 131)(24, 132)(25, 111)(26, 112)(27, 113)(28, 130)(29, 114)(30, 115)(31, 116)(32, 117)(33, 118)(34, 124)(35, 119)(36, 120)(37, 139)(38, 138)(39, 142)(40, 143)(41, 140)(42, 134)(43, 133)(44, 137)(45, 144)(46, 135)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.312
Graph:: bipartite
	v = 30 e = 96 f = 56
	degree seq :: [ 4^24, 16^6 ]

E6.312 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = (C3 x D8) : C2 (small group id <48, 15>)
Aut   = D16 x S3 (small group id <96, 117>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^8 ]
Map:: polytopal
	R = (1, 49, 2, 50, 6, 54, 14, 62, 12, 60, 4, 52)(3, 51, 9, 57, 19, 67, 26, 74, 15, 63, 8, 56)(5, 53, 11, 59, 22, 70, 25, 73, 16, 64, 7, 55)(10, 58, 18, 66, 27, 75, 37, 85, 31, 79, 20, 68)(13, 61, 17, 65, 28, 76, 36, 84, 34, 82, 23, 71)(21, 69, 32, 80, 41, 89, 45, 93, 38, 86, 30, 78)(24, 72, 35, 83, 43, 91, 44, 92, 39, 87, 29, 77)(33, 81, 40, 88, 46, 94, 48, 96, 47, 95, 42, 90)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 111)(7, 113)(8, 98)(9, 100)(10, 117)(11, 119)(12, 115)(13, 101)(14, 121)(15, 123)(16, 102)(17, 125)(18, 104)(19, 127)(20, 105)(21, 129)(22, 108)(23, 131)(24, 109)(25, 132)(26, 110)(27, 134)(28, 112)(29, 136)(30, 114)(31, 137)(32, 116)(33, 120)(34, 118)(35, 138)(36, 140)(37, 122)(38, 142)(39, 124)(40, 126)(41, 143)(42, 128)(43, 130)(44, 144)(45, 133)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.311
Graph:: simple bipartite
	v = 56 e = 96 f = 30
	degree seq :: [ 2^48, 12^8 ]

E6.313 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 8})
Quotient :: regular
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^8 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 23, 22, 10, 4)(3, 7, 15, 28, 38, 35, 18, 8)(6, 13, 27, 41, 33, 17, 30, 14)(9, 19, 32, 16, 24, 39, 36, 20)(12, 25, 40, 37, 21, 29, 42, 26)(31, 45, 48, 43, 34, 46, 47, 44)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 26)(20, 35)(22, 33)(23, 38)(25, 41)(27, 43)(30, 44)(32, 46)(36, 45)(37, 39)(40, 47)(42, 48)
	local type(s) :: { ( 6^8 ) }
Outer automorphisms :: reflexible
Dual of E6.314
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 6 e = 24 f = 8
	degree seq :: [ 8^6 ]

E6.314 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 8})
Quotient :: regular
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-1 * T2 * T1^3 * T2 * T1^-2, T1^-1 * T2 * T1^-1 * T2 * T1^2 * T2 * T1^-1 * T2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 22, 18, 8)(6, 13, 25, 21, 28, 14)(9, 19, 24, 12, 23, 20)(16, 30, 41, 34, 36, 31)(17, 32, 26, 29, 40, 33)(27, 39, 37, 38, 44, 35)(42, 48, 46, 47, 45, 43)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 29)(18, 34)(19, 35)(20, 36)(23, 37)(24, 30)(25, 38)(28, 33)(31, 42)(32, 43)(39, 45)(40, 46)(41, 47)(44, 48)
	local type(s) :: { ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E6.313
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 24 f = 6
	degree seq :: [ 6^8 ]

E6.315 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^3 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 25, 14, 6)(7, 15, 30, 21, 32, 16)(9, 19, 34, 17, 33, 20)(11, 22, 37, 28, 36, 23)(13, 26, 29, 24, 39, 27)(31, 42, 43, 41, 44, 35)(38, 46, 47, 45, 48, 40)(49, 50)(51, 55)(52, 57)(53, 59)(54, 61)(56, 65)(58, 69)(60, 72)(62, 76)(63, 77)(64, 79)(66, 73)(67, 83)(68, 84)(70, 82)(71, 86)(74, 88)(75, 80)(78, 89)(81, 91)(85, 93)(87, 95)(90, 96)(92, 94)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 16, 16 ), ( 16^6 ) }
Outer automorphisms :: reflexible
Dual of E6.319
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 48 f = 6
	degree seq :: [ 2^24, 6^8 ]

E6.316 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2^-1)^2, (T1^-2 * T2)^2, (T1 * T2^-1 * T1)^2, T1^6, T2 * T1^-3 * T2^3 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 26, 16, 35, 15, 5)(2, 7, 19, 29, 13, 31, 22, 8)(4, 12, 30, 18, 6, 17, 24, 9)(11, 28, 45, 34, 23, 41, 43, 25)(14, 32, 46, 37, 20, 27, 44, 33)(21, 39, 48, 42, 36, 38, 47, 40)(49, 50, 54, 64, 61, 52)(51, 57, 71, 83, 66, 59)(53, 62, 79, 74, 68, 55)(56, 69, 60, 77, 84, 65)(58, 73, 80, 63, 82, 75)(67, 85, 87, 70, 81, 86)(72, 90, 76, 78, 88, 89)(91, 95, 92, 93, 96, 94)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^6 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E6.320
Transitivity :: ET+
Graph:: bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 6^8, 8^6 ]

E6.317 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 8})
Quotient :: edge
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^8 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 34)(19, 26)(20, 35)(22, 33)(23, 38)(25, 41)(27, 43)(30, 44)(32, 46)(36, 45)(37, 39)(40, 47)(42, 48)(49, 50, 53, 59, 71, 70, 58, 52)(51, 55, 63, 76, 86, 83, 66, 56)(54, 61, 75, 89, 81, 65, 78, 62)(57, 67, 80, 64, 72, 87, 84, 68)(60, 73, 88, 85, 69, 77, 90, 74)(79, 93, 96, 91, 82, 94, 95, 92)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 12, 12 ), ( 12^8 ) }
Outer automorphisms :: reflexible
Dual of E6.318
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 48 f = 8
	degree seq :: [ 2^24, 8^6 ]

E6.318 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^3 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 49, 3, 51, 8, 56, 18, 66, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 25, 73, 14, 62, 6, 54)(7, 55, 15, 63, 30, 78, 21, 69, 32, 80, 16, 64)(9, 57, 19, 67, 34, 82, 17, 65, 33, 81, 20, 68)(11, 59, 22, 70, 37, 85, 28, 76, 36, 84, 23, 71)(13, 61, 26, 74, 29, 77, 24, 72, 39, 87, 27, 75)(31, 79, 42, 90, 43, 91, 41, 89, 44, 92, 35, 83)(38, 86, 46, 94, 47, 95, 45, 93, 48, 96, 40, 88)
	L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 72)(13, 54)(14, 76)(15, 77)(16, 79)(17, 56)(18, 73)(19, 83)(20, 84)(21, 58)(22, 82)(23, 86)(24, 60)(25, 66)(26, 88)(27, 80)(28, 62)(29, 63)(30, 89)(31, 64)(32, 75)(33, 91)(34, 70)(35, 67)(36, 68)(37, 93)(38, 71)(39, 95)(40, 74)(41, 78)(42, 96)(43, 81)(44, 94)(45, 85)(46, 92)(47, 87)(48, 90)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.317
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 48 f = 30
	degree seq :: [ 12^8 ]

E6.319 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2^-1)^2, (T1^-2 * T2)^2, (T1 * T2^-1 * T1)^2, T1^6, T2 * T1^-3 * T2^3 ]
Map::
	R = (1, 49, 3, 51, 10, 58, 26, 74, 16, 64, 35, 83, 15, 63, 5, 53)(2, 50, 7, 55, 19, 67, 29, 77, 13, 61, 31, 79, 22, 70, 8, 56)(4, 52, 12, 60, 30, 78, 18, 66, 6, 54, 17, 65, 24, 72, 9, 57)(11, 59, 28, 76, 45, 93, 34, 82, 23, 71, 41, 89, 43, 91, 25, 73)(14, 62, 32, 80, 46, 94, 37, 85, 20, 68, 27, 75, 44, 92, 33, 81)(21, 69, 39, 87, 48, 96, 42, 90, 36, 84, 38, 86, 47, 95, 40, 88)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 64)(7, 53)(8, 69)(9, 71)(10, 73)(11, 51)(12, 77)(13, 52)(14, 79)(15, 82)(16, 61)(17, 56)(18, 59)(19, 85)(20, 55)(21, 60)(22, 81)(23, 83)(24, 90)(25, 80)(26, 68)(27, 58)(28, 78)(29, 84)(30, 88)(31, 74)(32, 63)(33, 86)(34, 75)(35, 66)(36, 65)(37, 87)(38, 67)(39, 70)(40, 89)(41, 72)(42, 76)(43, 95)(44, 93)(45, 96)(46, 91)(47, 92)(48, 94)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.315
Transitivity :: ET+ VT+ AT
Graph::
	v = 6 e = 48 f = 32
	degree seq :: [ 16^6 ]

E6.320 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 8})
Quotient :: loop
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1 * T2 * T1 * T2 * T1^-1, T1^8 ]
Map:: polytopal non-degenerate
	R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 21, 69)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 29, 77)(15, 63, 31, 79)(18, 66, 34, 82)(19, 67, 26, 74)(20, 68, 35, 83)(22, 70, 33, 81)(23, 71, 38, 86)(25, 73, 41, 89)(27, 75, 43, 91)(30, 78, 44, 92)(32, 80, 46, 94)(36, 84, 45, 93)(37, 85, 39, 87)(40, 88, 47, 95)(42, 90, 48, 96)
	L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 76)(16, 72)(17, 78)(18, 56)(19, 80)(20, 57)(21, 77)(22, 58)(23, 70)(24, 87)(25, 88)(26, 60)(27, 89)(28, 86)(29, 90)(30, 62)(31, 93)(32, 64)(33, 65)(34, 94)(35, 66)(36, 68)(37, 69)(38, 83)(39, 84)(40, 85)(41, 81)(42, 74)(43, 82)(44, 79)(45, 96)(46, 95)(47, 92)(48, 91)
	local type(s) :: { ( 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.316
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.321 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (R * Y2^-2 * Y1)^2, Y2 * Y1 * Y2^-3 * Y1 * Y2^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 24, 72)(14, 62, 28, 76)(15, 63, 29, 77)(16, 64, 31, 79)(18, 66, 25, 73)(19, 67, 35, 83)(20, 68, 36, 84)(22, 70, 34, 82)(23, 71, 38, 86)(26, 74, 40, 88)(27, 75, 32, 80)(30, 78, 41, 89)(33, 81, 43, 91)(37, 85, 45, 93)(39, 87, 47, 95)(42, 90, 48, 96)(44, 92, 46, 94)(97, 145, 99, 147, 104, 152, 114, 162, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 121, 169, 110, 158, 102, 150)(103, 151, 111, 159, 126, 174, 117, 165, 128, 176, 112, 160)(105, 153, 115, 163, 130, 178, 113, 161, 129, 177, 116, 164)(107, 155, 118, 166, 133, 181, 124, 172, 132, 180, 119, 167)(109, 157, 122, 170, 125, 173, 120, 168, 135, 183, 123, 171)(127, 175, 138, 186, 139, 187, 137, 185, 140, 188, 131, 179)(134, 182, 142, 190, 143, 191, 141, 189, 144, 192, 136, 184)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 120)(13, 102)(14, 124)(15, 125)(16, 127)(17, 104)(18, 121)(19, 131)(20, 132)(21, 106)(22, 130)(23, 134)(24, 108)(25, 114)(26, 136)(27, 128)(28, 110)(29, 111)(30, 137)(31, 112)(32, 123)(33, 139)(34, 118)(35, 115)(36, 116)(37, 141)(38, 119)(39, 143)(40, 122)(41, 126)(42, 144)(43, 129)(44, 142)(45, 133)(46, 140)(47, 135)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.324
Graph:: bipartite
	v = 32 e = 96 f = 54
	degree seq :: [ 4^24, 12^8 ]

E6.322 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y1^6, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2, Y2^8 ]
Map::
	R = (1, 49, 2, 50, 6, 54, 16, 64, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 35, 83, 18, 66, 11, 59)(5, 53, 14, 62, 31, 79, 26, 74, 20, 68, 7, 55)(8, 56, 21, 69, 12, 60, 29, 77, 36, 84, 17, 65)(10, 58, 25, 73, 32, 80, 15, 63, 34, 82, 27, 75)(19, 67, 37, 85, 39, 87, 22, 70, 33, 81, 38, 86)(24, 72, 42, 90, 28, 76, 30, 78, 40, 88, 41, 89)(43, 91, 47, 95, 44, 92, 45, 93, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 122, 170, 112, 160, 131, 179, 111, 159, 101, 149)(98, 146, 103, 151, 115, 163, 125, 173, 109, 157, 127, 175, 118, 166, 104, 152)(100, 148, 108, 156, 126, 174, 114, 162, 102, 150, 113, 161, 120, 168, 105, 153)(107, 155, 124, 172, 141, 189, 130, 178, 119, 167, 137, 185, 139, 187, 121, 169)(110, 158, 128, 176, 142, 190, 133, 181, 116, 164, 123, 171, 140, 188, 129, 177)(117, 165, 135, 183, 144, 192, 138, 186, 132, 180, 134, 182, 143, 191, 136, 184)
	L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 115)(8, 98)(9, 100)(10, 122)(11, 124)(12, 126)(13, 127)(14, 128)(15, 101)(16, 131)(17, 120)(18, 102)(19, 125)(20, 123)(21, 135)(22, 104)(23, 137)(24, 105)(25, 107)(26, 112)(27, 140)(28, 141)(29, 109)(30, 114)(31, 118)(32, 142)(33, 110)(34, 119)(35, 111)(36, 134)(37, 116)(38, 143)(39, 144)(40, 117)(41, 139)(42, 132)(43, 121)(44, 129)(45, 130)(46, 133)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.323
Graph:: bipartite
	v = 14 e = 96 f = 72
	degree seq :: [ 12^8, 16^6 ]

E6.323 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-2, Y3^8, (Y3^-1 * Y1^-1)^8 ]
Map:: polytopal
	R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 113, 161)(106, 154, 117, 165)(108, 156, 121, 169)(110, 158, 125, 173)(111, 159, 122, 170)(112, 160, 128, 176)(114, 162, 119, 167)(115, 163, 130, 178)(116, 164, 126, 174)(118, 166, 124, 172)(120, 168, 135, 183)(123, 171, 137, 185)(127, 175, 140, 188)(129, 177, 139, 187)(131, 179, 138, 186)(132, 180, 136, 184)(133, 181, 134, 182)(141, 189, 144, 192)(142, 190, 143, 191)
	L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 111)(8, 114)(9, 115)(10, 100)(11, 119)(12, 122)(13, 123)(14, 102)(15, 127)(16, 103)(17, 129)(18, 131)(19, 120)(20, 105)(21, 128)(22, 106)(23, 134)(24, 107)(25, 136)(26, 138)(27, 112)(28, 109)(29, 135)(30, 110)(31, 139)(32, 141)(33, 142)(34, 113)(35, 118)(36, 116)(37, 117)(38, 132)(39, 143)(40, 144)(41, 121)(42, 126)(43, 124)(44, 125)(45, 130)(46, 133)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.322
Graph:: simple bipartite
	v = 72 e = 96 f = 14
	degree seq :: [ 2^48, 4^24 ]

E6.324 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-1 * Y3, Y1^8 ]
Map::
	R = (1, 49, 2, 50, 5, 53, 11, 59, 23, 71, 22, 70, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 28, 76, 38, 86, 35, 83, 18, 66, 8, 56)(6, 54, 13, 61, 27, 75, 41, 89, 33, 81, 17, 65, 30, 78, 14, 62)(9, 57, 19, 67, 32, 80, 16, 64, 24, 72, 39, 87, 36, 84, 20, 68)(12, 60, 25, 73, 40, 88, 37, 85, 21, 69, 29, 77, 42, 90, 26, 74)(31, 79, 45, 93, 48, 96, 43, 91, 34, 82, 46, 94, 47, 95, 44, 92)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 113)(9, 100)(10, 117)(11, 120)(12, 101)(13, 124)(14, 125)(15, 127)(16, 103)(17, 104)(18, 130)(19, 122)(20, 131)(21, 106)(22, 129)(23, 134)(24, 107)(25, 137)(26, 115)(27, 139)(28, 109)(29, 110)(30, 140)(31, 111)(32, 142)(33, 118)(34, 114)(35, 116)(36, 141)(37, 135)(38, 119)(39, 133)(40, 143)(41, 121)(42, 144)(43, 123)(44, 126)(45, 132)(46, 128)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.321
Graph:: simple bipartite
	v = 54 e = 96 f = 32
	degree seq :: [ 2^48, 16^6 ]

E6.325 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, Y2 * R * Y2^3 * R * Y2 * Y1, Y2^8, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 26, 74)(16, 64, 32, 80)(18, 66, 23, 71)(19, 67, 34, 82)(20, 68, 30, 78)(22, 70, 28, 76)(24, 72, 39, 87)(27, 75, 41, 89)(31, 79, 44, 92)(33, 81, 43, 91)(35, 83, 42, 90)(36, 84, 40, 88)(37, 85, 38, 86)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 104, 152, 114, 162, 131, 179, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 138, 186, 126, 174, 110, 158, 102, 150)(103, 151, 111, 159, 127, 175, 139, 187, 124, 172, 109, 157, 123, 171, 112, 160)(105, 153, 115, 163, 120, 168, 107, 155, 119, 167, 134, 182, 132, 180, 116, 164)(113, 161, 129, 177, 142, 190, 133, 181, 117, 165, 128, 176, 141, 189, 130, 178)(121, 169, 136, 184, 144, 192, 140, 188, 125, 173, 135, 183, 143, 191, 137, 185)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 121)(13, 102)(14, 125)(15, 122)(16, 128)(17, 104)(18, 119)(19, 130)(20, 126)(21, 106)(22, 124)(23, 114)(24, 135)(25, 108)(26, 111)(27, 137)(28, 118)(29, 110)(30, 116)(31, 140)(32, 112)(33, 139)(34, 115)(35, 138)(36, 136)(37, 134)(38, 133)(39, 120)(40, 132)(41, 123)(42, 131)(43, 129)(44, 127)(45, 144)(46, 143)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.326
Graph:: bipartite
	v = 30 e = 96 f = 56
	degree seq :: [ 4^24, 16^6 ]

E6.326 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 8})
Quotient :: dipole
Aut^+ = GL(2,3) (small group id <48, 29>)
Aut   = (SL(2,3) : C2) : C2 (small group id <96, 193>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1 * Y1)^2, Y1^6, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 49, 2, 50, 6, 54, 16, 64, 13, 61, 4, 52)(3, 51, 9, 57, 23, 71, 35, 83, 18, 66, 11, 59)(5, 53, 14, 62, 31, 79, 26, 74, 20, 68, 7, 55)(8, 56, 21, 69, 12, 60, 29, 77, 36, 84, 17, 65)(10, 58, 25, 73, 32, 80, 15, 63, 34, 82, 27, 75)(19, 67, 37, 85, 39, 87, 22, 70, 33, 81, 38, 86)(24, 72, 42, 90, 28, 76, 30, 78, 40, 88, 41, 89)(43, 91, 47, 95, 44, 92, 45, 93, 48, 96, 46, 94)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 115)(8, 98)(9, 100)(10, 122)(11, 124)(12, 126)(13, 127)(14, 128)(15, 101)(16, 131)(17, 120)(18, 102)(19, 125)(20, 123)(21, 135)(22, 104)(23, 137)(24, 105)(25, 107)(26, 112)(27, 140)(28, 141)(29, 109)(30, 114)(31, 118)(32, 142)(33, 110)(34, 119)(35, 111)(36, 134)(37, 116)(38, 143)(39, 144)(40, 117)(41, 139)(42, 132)(43, 121)(44, 129)(45, 130)(46, 133)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E6.325
Graph:: simple bipartite
	v = 56 e = 96 f = 30
	degree seq :: [ 2^48, 12^8 ]

E6.327 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 24})
Quotient :: regular
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, (T2 * T1^4)^2, T2 * T1^-1 * T2 * T1^11 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 29, 37, 45, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 46, 39, 30, 22, 12, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 45)(44, 47)
	local type(s) :: { ( 4^24 ) }
Outer automorphisms :: reflexible
Dual of E6.328
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 24 f = 12
	degree seq :: [ 24^2 ]

E6.328 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 24})
Quotient :: regular
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 41, 38, 42)(39, 43, 40, 44)(45, 48, 46, 47)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)
	local type(s) :: { ( 24^4 ) }
Outer automorphisms :: reflexible
Dual of E6.327
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 12 e = 24 f = 2
	degree seq :: [ 4^12 ]

E6.329 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 24})
Quotient :: edge
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 ]
Map::
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 39, 36, 40)(41, 45, 42, 46)(43, 47, 44, 48)(49, 50)(51, 55)(52, 57)(53, 58)(54, 60)(56, 59)(61, 65)(62, 66)(63, 67)(64, 68)(69, 73)(70, 74)(71, 75)(72, 76)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(93, 96)(94, 95)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 48, 48 ), ( 48^4 ) }
Outer automorphisms :: reflexible
Dual of E6.333
Transitivity :: ET+
Graph:: simple bipartite
	v = 36 e = 48 f = 2
	degree seq :: [ 2^24, 4^12 ]

E6.330 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 24})
Quotient :: edge
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^11 * T1 * T2^-1 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 34, 42, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 48, 40, 32, 24, 16, 8)(49, 50, 54, 52)(51, 57, 61, 56)(53, 59, 62, 55)(58, 64, 69, 65)(60, 63, 70, 67)(66, 73, 77, 72)(68, 75, 78, 71)(74, 80, 85, 81)(76, 79, 86, 83)(82, 89, 93, 88)(84, 91, 94, 87)(90, 96, 92, 95)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 4^4 ), ( 4^24 ) }
Outer automorphisms :: reflexible
Dual of E6.334
Transitivity :: ET+
Graph:: bipartite
	v = 14 e = 48 f = 24
	degree seq :: [ 4^12, 24^2 ]

E6.331 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 24})
Quotient :: edge
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, (T2 * T1^4)^2, T2 * T1^-1 * T2 * T1^11 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 45)(44, 47)(49, 50, 53, 59, 68, 77, 85, 93, 90, 82, 74, 64, 71, 65, 72, 80, 88, 96, 92, 84, 76, 67, 58, 52)(51, 55, 63, 73, 81, 89, 95, 86, 79, 69, 62, 54, 61, 57, 66, 75, 83, 91, 94, 87, 78, 70, 60, 56)
	L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)
	local type(s) :: { ( 8, 8 ), ( 8^24 ) }
Outer automorphisms :: reflexible
Dual of E6.332
Transitivity :: ET+
Graph:: simple bipartite
	v = 26 e = 48 f = 12
	degree seq :: [ 2^24, 24^2 ]

E6.332 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 24})
Quotient :: loop
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 ]
Map::
	R = (1, 49, 3, 51, 8, 56, 4, 52)(2, 50, 5, 53, 11, 59, 6, 54)(7, 55, 13, 61, 9, 57, 14, 62)(10, 58, 15, 63, 12, 60, 16, 64)(17, 65, 21, 69, 18, 66, 22, 70)(19, 67, 23, 71, 20, 68, 24, 72)(25, 73, 29, 77, 26, 74, 30, 78)(27, 75, 31, 79, 28, 76, 32, 80)(33, 81, 37, 85, 34, 82, 38, 86)(35, 83, 39, 87, 36, 84, 40, 88)(41, 89, 45, 93, 42, 90, 46, 94)(43, 91, 47, 95, 44, 92, 48, 96)
	L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 58)(6, 60)(7, 51)(8, 59)(9, 52)(10, 53)(11, 56)(12, 54)(13, 65)(14, 66)(15, 67)(16, 68)(17, 61)(18, 62)(19, 63)(20, 64)(21, 73)(22, 74)(23, 75)(24, 76)(25, 69)(26, 70)(27, 71)(28, 72)(29, 81)(30, 82)(31, 83)(32, 84)(33, 77)(34, 78)(35, 79)(36, 80)(37, 89)(38, 90)(39, 91)(40, 92)(41, 85)(42, 86)(43, 87)(44, 88)(45, 96)(46, 95)(47, 94)(48, 93)
	local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.331
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 48 f = 26
	degree seq :: [ 8^12 ]

E6.333 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 24})
Quotient :: loop
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^11 * T1 * T2^-1 * T1^-1 ]
Map::
	R = (1, 49, 3, 51, 10, 58, 18, 66, 26, 74, 34, 82, 42, 90, 46, 94, 38, 86, 30, 78, 22, 70, 14, 62, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 45, 93, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 47, 95, 41, 89, 33, 81, 25, 73, 17, 65, 9, 57, 4, 52, 11, 59, 19, 67, 27, 75, 35, 83, 43, 91, 48, 96, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)
	L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 52)(7, 53)(8, 51)(9, 61)(10, 64)(11, 62)(12, 63)(13, 56)(14, 55)(15, 70)(16, 69)(17, 58)(18, 73)(19, 60)(20, 75)(21, 65)(22, 67)(23, 68)(24, 66)(25, 77)(26, 80)(27, 78)(28, 79)(29, 72)(30, 71)(31, 86)(32, 85)(33, 74)(34, 89)(35, 76)(36, 91)(37, 81)(38, 83)(39, 84)(40, 82)(41, 93)(42, 96)(43, 94)(44, 95)(45, 88)(46, 87)(47, 90)(48, 92)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.329
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 48 f = 36
	degree seq :: [ 48^2 ]

E6.334 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 24})
Quotient :: loop
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, (T2 * T1^4)^2, T2 * T1^-1 * T2 * T1^11 ]
Map:: polytopal non-degenerate
	R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 15, 63)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(18, 66, 26, 74)(19, 67, 27, 75)(20, 68, 30, 78)(22, 70, 32, 80)(25, 73, 34, 82)(28, 76, 33, 81)(29, 77, 38, 86)(31, 79, 40, 88)(35, 83, 42, 90)(36, 84, 43, 91)(37, 85, 46, 94)(39, 87, 48, 96)(41, 89, 45, 93)(44, 92, 47, 95)
	L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 66)(10, 52)(11, 68)(12, 56)(13, 57)(14, 54)(15, 73)(16, 71)(17, 72)(18, 75)(19, 58)(20, 77)(21, 62)(22, 60)(23, 65)(24, 80)(25, 81)(26, 64)(27, 83)(28, 67)(29, 85)(30, 70)(31, 69)(32, 88)(33, 89)(34, 74)(35, 91)(36, 76)(37, 93)(38, 79)(39, 78)(40, 96)(41, 95)(42, 82)(43, 94)(44, 84)(45, 90)(46, 87)(47, 86)(48, 92)
	local type(s) :: { ( 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E6.330
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 24 e = 48 f = 14
	degree seq :: [ 4^24 ]

E6.335 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 11, 59)(13, 61, 17, 65)(14, 62, 18, 66)(15, 63, 19, 67)(16, 64, 20, 68)(21, 69, 25, 73)(22, 70, 26, 74)(23, 71, 27, 75)(24, 72, 28, 76)(29, 77, 33, 81)(30, 78, 34, 82)(31, 79, 35, 83)(32, 80, 36, 84)(37, 85, 41, 89)(38, 86, 42, 90)(39, 87, 43, 91)(40, 88, 44, 92)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 104, 152, 100, 148)(98, 146, 101, 149, 107, 155, 102, 150)(103, 151, 109, 157, 105, 153, 110, 158)(106, 154, 111, 159, 108, 156, 112, 160)(113, 161, 117, 165, 114, 162, 118, 166)(115, 163, 119, 167, 116, 164, 120, 168)(121, 169, 125, 173, 122, 170, 126, 174)(123, 171, 127, 175, 124, 172, 128, 176)(129, 177, 133, 181, 130, 178, 134, 182)(131, 179, 135, 183, 132, 180, 136, 184)(137, 185, 141, 189, 138, 186, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 106)(6, 108)(7, 99)(8, 107)(9, 100)(10, 101)(11, 104)(12, 102)(13, 113)(14, 114)(15, 115)(16, 116)(17, 109)(18, 110)(19, 111)(20, 112)(21, 121)(22, 122)(23, 123)(24, 124)(25, 117)(26, 118)(27, 119)(28, 120)(29, 129)(30, 130)(31, 131)(32, 132)(33, 125)(34, 126)(35, 127)(36, 128)(37, 137)(38, 138)(39, 139)(40, 140)(41, 133)(42, 134)(43, 135)(44, 136)(45, 144)(46, 143)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 48, 2, 48 ), ( 2, 48, 2, 48, 2, 48, 2, 48 ) }
Outer automorphisms :: reflexible
Dual of E6.338
Graph:: bipartite
	v = 36 e = 96 f = 50
	degree seq :: [ 4^24, 8^12 ]

E6.336 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y1^-1 * Y2^-12 * Y1^-1 ]
Map::
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 13, 61, 8, 56)(5, 53, 11, 59, 14, 62, 7, 55)(10, 58, 16, 64, 21, 69, 17, 65)(12, 60, 15, 63, 22, 70, 19, 67)(18, 66, 25, 73, 29, 77, 24, 72)(20, 68, 27, 75, 30, 78, 23, 71)(26, 74, 32, 80, 37, 85, 33, 81)(28, 76, 31, 79, 38, 86, 35, 83)(34, 82, 41, 89, 45, 93, 40, 88)(36, 84, 43, 91, 46, 94, 39, 87)(42, 90, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 142, 190, 134, 182, 126, 174, 118, 166, 110, 158, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 143, 191, 137, 185, 129, 177, 121, 169, 113, 161, 105, 153, 100, 148, 107, 155, 115, 163, 123, 171, 131, 179, 139, 187, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152)
	L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 109)(7, 111)(8, 98)(9, 100)(10, 114)(11, 115)(12, 101)(13, 117)(14, 102)(15, 119)(16, 104)(17, 105)(18, 122)(19, 123)(20, 108)(21, 125)(22, 110)(23, 127)(24, 112)(25, 113)(26, 130)(27, 131)(28, 116)(29, 133)(30, 118)(31, 135)(32, 120)(33, 121)(34, 138)(35, 139)(36, 124)(37, 141)(38, 126)(39, 143)(40, 128)(41, 129)(42, 142)(43, 144)(44, 132)(45, 140)(46, 134)(47, 137)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.337
Graph:: bipartite
	v = 14 e = 96 f = 72
	degree seq :: [ 8^12, 48^2 ]

E6.337 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, Y3^9 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^24 ]
Map:: polytopal
	R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 110, 158)(106, 154, 108, 156)(111, 159, 116, 164)(112, 160, 119, 167)(113, 161, 121, 169)(114, 162, 117, 165)(115, 163, 123, 171)(118, 166, 125, 173)(120, 168, 127, 175)(122, 170, 128, 176)(124, 172, 126, 174)(129, 177, 135, 183)(130, 178, 137, 185)(131, 179, 133, 181)(132, 180, 139, 187)(134, 182, 141, 189)(136, 184, 143, 191)(138, 186, 144, 192)(140, 188, 142, 190)
	L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 111)(8, 113)(9, 114)(10, 100)(11, 116)(12, 118)(13, 119)(14, 102)(15, 105)(16, 103)(17, 122)(18, 123)(19, 106)(20, 109)(21, 107)(22, 126)(23, 127)(24, 110)(25, 112)(26, 130)(27, 131)(28, 115)(29, 117)(30, 134)(31, 135)(32, 120)(33, 121)(34, 138)(35, 139)(36, 124)(37, 125)(38, 142)(39, 143)(40, 128)(41, 129)(42, 141)(43, 144)(44, 132)(45, 133)(46, 137)(47, 140)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48 ) }
Outer automorphisms :: reflexible
Dual of E6.336
Graph:: simple bipartite
	v = 72 e = 96 f = 14
	degree seq :: [ 2^48, 4^24 ]

E6.338 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, (Y3 * Y1^4)^2, Y3 * Y1^-1 * Y3 * Y1^11 ]
Map::
	R = (1, 49, 2, 50, 5, 53, 11, 59, 20, 68, 29, 77, 37, 85, 45, 93, 42, 90, 34, 82, 26, 74, 16, 64, 23, 71, 17, 65, 24, 72, 32, 80, 40, 88, 48, 96, 44, 92, 36, 84, 28, 76, 19, 67, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 25, 73, 33, 81, 41, 89, 47, 95, 38, 86, 31, 79, 21, 69, 14, 62, 6, 54, 13, 61, 9, 57, 18, 66, 27, 75, 35, 83, 43, 91, 46, 94, 39, 87, 30, 78, 22, 70, 12, 60, 8, 56)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 113)(9, 100)(10, 111)(11, 117)(12, 101)(13, 119)(14, 120)(15, 106)(16, 103)(17, 104)(18, 122)(19, 123)(20, 126)(21, 107)(22, 128)(23, 109)(24, 110)(25, 130)(26, 114)(27, 115)(28, 129)(29, 134)(30, 116)(31, 136)(32, 118)(33, 124)(34, 121)(35, 138)(36, 139)(37, 142)(38, 125)(39, 144)(40, 127)(41, 141)(42, 131)(43, 132)(44, 143)(45, 137)(46, 133)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.335
Graph:: simple bipartite
	v = 50 e = 96 f = 36
	degree seq :: [ 2^48, 48^2 ]

E6.339 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^3 * Y1 * Y2^-9 * Y1 ]
Map::
	R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 14, 62)(10, 58, 12, 60)(15, 63, 20, 68)(16, 64, 23, 71)(17, 65, 25, 73)(18, 66, 21, 69)(19, 67, 27, 75)(22, 70, 29, 77)(24, 72, 31, 79)(26, 74, 32, 80)(28, 76, 30, 78)(33, 81, 39, 87)(34, 82, 41, 89)(35, 83, 37, 85)(36, 84, 43, 91)(38, 86, 45, 93)(40, 88, 47, 95)(42, 90, 48, 96)(44, 92, 46, 94)(97, 145, 99, 147, 104, 152, 113, 161, 122, 170, 130, 178, 138, 186, 141, 189, 133, 181, 125, 173, 117, 165, 107, 155, 116, 164, 109, 157, 119, 167, 127, 175, 135, 183, 143, 191, 140, 188, 132, 180, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 126, 174, 134, 182, 142, 190, 137, 185, 129, 177, 121, 169, 112, 160, 103, 151, 111, 159, 105, 153, 114, 162, 123, 171, 131, 179, 139, 187, 144, 192, 136, 184, 128, 176, 120, 168, 110, 158, 102, 150)
	L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 110)(9, 100)(10, 108)(11, 101)(12, 106)(13, 102)(14, 104)(15, 116)(16, 119)(17, 121)(18, 117)(19, 123)(20, 111)(21, 114)(22, 125)(23, 112)(24, 127)(25, 113)(26, 128)(27, 115)(28, 126)(29, 118)(30, 124)(31, 120)(32, 122)(33, 135)(34, 137)(35, 133)(36, 139)(37, 131)(38, 141)(39, 129)(40, 143)(41, 130)(42, 144)(43, 132)(44, 142)(45, 134)(46, 140)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.340
Graph:: bipartite
	v = 26 e = 96 f = 60
	degree seq :: [ 4^24, 48^2 ]

E6.340 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 24})
Quotient :: dipole
Aut^+ = C24 : C2 (small group id <48, 6>)
Aut   = (C2 x D24) : C2 (small group id <96, 115>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-12 * Y1^-1, (Y3 * Y2^-1)^24 ]
Map::
	R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 13, 61, 8, 56)(5, 53, 11, 59, 14, 62, 7, 55)(10, 58, 16, 64, 21, 69, 17, 65)(12, 60, 15, 63, 22, 70, 19, 67)(18, 66, 25, 73, 29, 77, 24, 72)(20, 68, 27, 75, 30, 78, 23, 71)(26, 74, 32, 80, 37, 85, 33, 81)(28, 76, 31, 79, 38, 86, 35, 83)(34, 82, 41, 89, 45, 93, 40, 88)(36, 84, 43, 91, 46, 94, 39, 87)(42, 90, 48, 96, 44, 92, 47, 95)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192)
	L = (1, 99)(2, 103)(3, 106)(4, 107)(5, 97)(6, 109)(7, 111)(8, 98)(9, 100)(10, 114)(11, 115)(12, 101)(13, 117)(14, 102)(15, 119)(16, 104)(17, 105)(18, 122)(19, 123)(20, 108)(21, 125)(22, 110)(23, 127)(24, 112)(25, 113)(26, 130)(27, 131)(28, 116)(29, 133)(30, 118)(31, 135)(32, 120)(33, 121)(34, 138)(35, 139)(36, 124)(37, 141)(38, 126)(39, 143)(40, 128)(41, 129)(42, 142)(43, 144)(44, 132)(45, 140)(46, 134)(47, 137)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)
	local type(s) :: { ( 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48 ) }
Outer automorphisms :: reflexible
Dual of E6.339
Graph:: simple bipartite
	v = 60 e = 96 f = 26
	degree seq :: [ 2^48, 8^12 ]

E6.341 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 5, 10})
Quotient :: regular
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T1^-1 * T2)^5, T1^10 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 12, 22, 33, 45, 42, 28, 17, 8)(6, 13, 21, 34, 44, 43, 30, 18, 9, 14)(15, 25, 35, 47, 50, 48, 41, 27, 16, 26)(23, 36, 46, 40, 49, 39, 29, 38, 24, 37)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 36)(28, 41)(31, 42)(32, 44)(34, 46)(37, 48)(38, 47)(43, 49)(45, 50)
	local type(s) :: { ( 5^10 ) }
Outer automorphisms :: reflexible
Dual of E6.342
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 5 e = 25 f = 10
	degree seq :: [ 10^5 ]

E6.342 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 5, 10})
Quotient :: regular
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^5, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 * T1^-2 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 31, 32, 19)(11, 21, 35, 38, 22)(15, 24, 36, 42, 28)(16, 25, 37, 43, 29)(20, 33, 45, 46, 34)(27, 39, 47, 49, 41)(30, 40, 48, 50, 44)
	L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 30)(18, 28)(19, 29)(21, 36)(22, 37)(23, 39)(26, 40)(31, 41)(32, 44)(33, 42)(34, 43)(35, 47)(38, 48)(45, 49)(46, 50)
	local type(s) :: { ( 10^5 ) }
Outer automorphisms :: reflexible
Dual of E6.341
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 10 e = 25 f = 5
	degree seq :: [ 5^10 ]

E6.343 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 10})
Quotient :: edge
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 ]
Map:: polytopal
	R = (1, 3, 8, 10, 4)(2, 5, 12, 14, 6)(7, 15, 27, 28, 16)(9, 18, 31, 32, 19)(11, 21, 35, 36, 22)(13, 24, 39, 40, 25)(17, 29, 43, 44, 30)(20, 33, 45, 46, 34)(23, 37, 47, 48, 38)(26, 41, 49, 50, 42)(51, 52)(53, 57)(54, 59)(55, 61)(56, 63)(58, 67)(60, 70)(62, 73)(64, 76)(65, 71)(66, 74)(68, 72)(69, 75)(77, 87)(78, 91)(79, 85)(80, 89)(81, 88)(82, 92)(83, 86)(84, 90)(93, 97)(94, 99)(95, 98)(96, 100)
	L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)
	local type(s) :: { ( 20, 20 ), ( 20^5 ) }
Outer automorphisms :: reflexible
Dual of E6.347
Transitivity :: ET+
Graph:: simple bipartite
	v = 35 e = 50 f = 5
	degree seq :: [ 2^25, 5^10 ]

E6.344 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 10})
Quotient :: edge
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^5, T2 * T1^-1 * T2^-3 * T1^-1, T1^-1 * T2^-3 * T1^-1 * T2, T1^-1 * T2 * T1^-1 * T2^7 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 24, 41, 48, 38, 20, 15, 5)(2, 7, 18, 11, 26, 42, 49, 34, 21, 8)(4, 12, 25, 43, 50, 37, 31, 14, 23, 9)(6, 16, 32, 19, 36, 27, 45, 46, 35, 17)(13, 29, 44, 33, 47, 30, 40, 22, 39, 28)(51, 52, 56, 63, 54)(53, 59, 72, 77, 61)(55, 64, 80, 69, 57)(58, 70, 87, 83, 66)(60, 68, 82, 94, 75)(62, 78, 96, 92, 74)(65, 71, 85, 89, 73)(67, 84, 98, 93, 79)(76, 86, 97, 100, 91)(81, 88, 99, 95, 90)
	L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)
	local type(s) :: { ( 4^5 ), ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E6.348
Transitivity :: ET+
Graph:: simple bipartite
	v = 15 e = 50 f = 25
	degree seq :: [ 5^10, 10^5 ]

E6.345 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 10})
Quotient :: edge
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T2 * T1^-1)^5, T1^10 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 33)(22, 35)(25, 39)(26, 40)(27, 36)(28, 41)(31, 42)(32, 44)(34, 46)(37, 48)(38, 47)(43, 49)(45, 50)(51, 52, 55, 61, 70, 82, 81, 69, 60, 54)(53, 57, 62, 72, 83, 95, 92, 78, 67, 58)(56, 63, 71, 84, 94, 93, 80, 68, 59, 64)(65, 75, 85, 97, 100, 98, 91, 77, 66, 76)(73, 86, 96, 90, 99, 89, 79, 88, 74, 87)
	L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)
	local type(s) :: { ( 10, 10 ), ( 10^10 ) }
Outer automorphisms :: reflexible
Dual of E6.346
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 50 f = 10
	degree seq :: [ 2^25, 10^5 ]

E6.346 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 10})
Quotient :: loop
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1, T2^-2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^-2 * T1 ]
Map::
	R = (1, 51, 3, 53, 8, 58, 10, 60, 4, 54)(2, 52, 5, 55, 12, 62, 14, 64, 6, 56)(7, 57, 15, 65, 27, 77, 28, 78, 16, 66)(9, 59, 18, 68, 31, 81, 32, 82, 19, 69)(11, 61, 21, 71, 35, 85, 36, 86, 22, 72)(13, 63, 24, 74, 39, 89, 40, 90, 25, 75)(17, 67, 29, 79, 43, 93, 44, 94, 30, 80)(20, 70, 33, 83, 45, 95, 46, 96, 34, 84)(23, 73, 37, 87, 47, 97, 48, 98, 38, 88)(26, 76, 41, 91, 49, 99, 50, 100, 42, 92)
	L = (1, 52)(2, 51)(3, 57)(4, 59)(5, 61)(6, 63)(7, 53)(8, 67)(9, 54)(10, 70)(11, 55)(12, 73)(13, 56)(14, 76)(15, 71)(16, 74)(17, 58)(18, 72)(19, 75)(20, 60)(21, 65)(22, 68)(23, 62)(24, 66)(25, 69)(26, 64)(27, 87)(28, 91)(29, 85)(30, 89)(31, 88)(32, 92)(33, 86)(34, 90)(35, 79)(36, 83)(37, 77)(38, 81)(39, 80)(40, 84)(41, 78)(42, 82)(43, 97)(44, 99)(45, 98)(46, 100)(47, 93)(48, 95)(49, 94)(50, 96)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.345
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 10 e = 50 f = 30
	degree seq :: [ 10^10 ]

E6.347 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 10})
Quotient :: loop
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^5, T2 * T1^-1 * T2^-3 * T1^-1, T1^-1 * T2^-3 * T1^-1 * T2, T1^-1 * T2 * T1^-1 * T2^7 ]
Map::
	R = (1, 51, 3, 53, 10, 60, 24, 74, 41, 91, 48, 98, 38, 88, 20, 70, 15, 65, 5, 55)(2, 52, 7, 57, 18, 68, 11, 61, 26, 76, 42, 92, 49, 99, 34, 84, 21, 71, 8, 58)(4, 54, 12, 62, 25, 75, 43, 93, 50, 100, 37, 87, 31, 81, 14, 64, 23, 73, 9, 59)(6, 56, 16, 66, 32, 82, 19, 69, 36, 86, 27, 77, 45, 95, 46, 96, 35, 85, 17, 67)(13, 63, 29, 79, 44, 94, 33, 83, 47, 97, 30, 80, 40, 90, 22, 72, 39, 89, 28, 78)
	L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 64)(6, 63)(7, 55)(8, 70)(9, 72)(10, 68)(11, 53)(12, 78)(13, 54)(14, 80)(15, 71)(16, 58)(17, 84)(18, 82)(19, 57)(20, 87)(21, 85)(22, 77)(23, 65)(24, 62)(25, 60)(26, 86)(27, 61)(28, 96)(29, 67)(30, 69)(31, 88)(32, 94)(33, 66)(34, 98)(35, 89)(36, 97)(37, 83)(38, 99)(39, 73)(40, 81)(41, 76)(42, 74)(43, 79)(44, 75)(45, 90)(46, 92)(47, 100)(48, 93)(49, 95)(50, 91)
	local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) }
Outer automorphisms :: reflexible
Dual of E6.343
Transitivity :: ET+ VT+ AT
Graph::
	v = 5 e = 50 f = 35
	degree seq :: [ 20^5 ]

E6.348 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 10})
Quotient :: loop
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T2 * T1^-1)^5, T1^10 ]
Map:: polytopal non-degenerate
	R = (1, 51, 3, 53)(2, 52, 6, 56)(4, 54, 9, 59)(5, 55, 12, 62)(7, 57, 15, 65)(8, 58, 16, 66)(10, 60, 17, 67)(11, 61, 21, 71)(13, 63, 23, 73)(14, 64, 24, 74)(18, 68, 29, 79)(19, 69, 30, 80)(20, 70, 33, 83)(22, 72, 35, 85)(25, 75, 39, 89)(26, 76, 40, 90)(27, 77, 36, 86)(28, 78, 41, 91)(31, 81, 42, 92)(32, 82, 44, 94)(34, 84, 46, 96)(37, 87, 48, 98)(38, 88, 47, 97)(43, 93, 49, 99)(45, 95, 50, 100)
	L = (1, 52)(2, 55)(3, 57)(4, 51)(5, 61)(6, 63)(7, 62)(8, 53)(9, 64)(10, 54)(11, 70)(12, 72)(13, 71)(14, 56)(15, 75)(16, 76)(17, 58)(18, 59)(19, 60)(20, 82)(21, 84)(22, 83)(23, 86)(24, 87)(25, 85)(26, 65)(27, 66)(28, 67)(29, 88)(30, 68)(31, 69)(32, 81)(33, 95)(34, 94)(35, 97)(36, 96)(37, 73)(38, 74)(39, 79)(40, 99)(41, 77)(42, 78)(43, 80)(44, 93)(45, 92)(46, 90)(47, 100)(48, 91)(49, 89)(50, 98)
	local type(s) :: { ( 5, 10, 5, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.344
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 25 e = 50 f = 15
	degree seq :: [ 4^25 ]

E6.349 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 51, 2, 52)(3, 53, 7, 57)(4, 54, 9, 59)(5, 55, 11, 61)(6, 56, 13, 63)(8, 58, 17, 67)(10, 60, 20, 70)(12, 62, 23, 73)(14, 64, 26, 76)(15, 65, 21, 71)(16, 66, 24, 74)(18, 68, 22, 72)(19, 69, 25, 75)(27, 77, 37, 87)(28, 78, 41, 91)(29, 79, 35, 85)(30, 80, 39, 89)(31, 81, 38, 88)(32, 82, 42, 92)(33, 83, 36, 86)(34, 84, 40, 90)(43, 93, 47, 97)(44, 94, 49, 99)(45, 95, 48, 98)(46, 96, 50, 100)(101, 151, 103, 153, 108, 158, 110, 160, 104, 154)(102, 152, 105, 155, 112, 162, 114, 164, 106, 156)(107, 157, 115, 165, 127, 177, 128, 178, 116, 166)(109, 159, 118, 168, 131, 181, 132, 182, 119, 169)(111, 161, 121, 171, 135, 185, 136, 186, 122, 172)(113, 163, 124, 174, 139, 189, 140, 190, 125, 175)(117, 167, 129, 179, 143, 193, 144, 194, 130, 180)(120, 170, 133, 183, 145, 195, 146, 196, 134, 184)(123, 173, 137, 187, 147, 197, 148, 198, 138, 188)(126, 176, 141, 191, 149, 199, 150, 200, 142, 192)
	L = (1, 102)(2, 101)(3, 107)(4, 109)(5, 111)(6, 113)(7, 103)(8, 117)(9, 104)(10, 120)(11, 105)(12, 123)(13, 106)(14, 126)(15, 121)(16, 124)(17, 108)(18, 122)(19, 125)(20, 110)(21, 115)(22, 118)(23, 112)(24, 116)(25, 119)(26, 114)(27, 137)(28, 141)(29, 135)(30, 139)(31, 138)(32, 142)(33, 136)(34, 140)(35, 129)(36, 133)(37, 127)(38, 131)(39, 130)(40, 134)(41, 128)(42, 132)(43, 147)(44, 149)(45, 148)(46, 150)(47, 143)(48, 145)(49, 144)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.352
Graph:: bipartite
	v = 35 e = 100 f = 55
	degree seq :: [ 4^25, 10^10 ]

E6.350 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^5, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y1^-1 * Y2 * Y1^-1 * Y2^7 ]
Map::
	R = (1, 51, 2, 52, 6, 56, 13, 63, 4, 54)(3, 53, 9, 59, 22, 72, 27, 77, 11, 61)(5, 55, 14, 64, 30, 80, 19, 69, 7, 57)(8, 58, 20, 70, 37, 87, 33, 83, 16, 66)(10, 60, 18, 68, 32, 82, 44, 94, 25, 75)(12, 62, 28, 78, 46, 96, 42, 92, 24, 74)(15, 65, 21, 71, 35, 85, 39, 89, 23, 73)(17, 67, 34, 84, 48, 98, 43, 93, 29, 79)(26, 76, 36, 86, 47, 97, 50, 100, 41, 91)(31, 81, 38, 88, 49, 99, 45, 95, 40, 90)(101, 151, 103, 153, 110, 160, 124, 174, 141, 191, 148, 198, 138, 188, 120, 170, 115, 165, 105, 155)(102, 152, 107, 157, 118, 168, 111, 161, 126, 176, 142, 192, 149, 199, 134, 184, 121, 171, 108, 158)(104, 154, 112, 162, 125, 175, 143, 193, 150, 200, 137, 187, 131, 181, 114, 164, 123, 173, 109, 159)(106, 156, 116, 166, 132, 182, 119, 169, 136, 186, 127, 177, 145, 195, 146, 196, 135, 185, 117, 167)(113, 163, 129, 179, 144, 194, 133, 183, 147, 197, 130, 180, 140, 190, 122, 172, 139, 189, 128, 178)
	L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 116)(7, 118)(8, 102)(9, 104)(10, 124)(11, 126)(12, 125)(13, 129)(14, 123)(15, 105)(16, 132)(17, 106)(18, 111)(19, 136)(20, 115)(21, 108)(22, 139)(23, 109)(24, 141)(25, 143)(26, 142)(27, 145)(28, 113)(29, 144)(30, 140)(31, 114)(32, 119)(33, 147)(34, 121)(35, 117)(36, 127)(37, 131)(38, 120)(39, 128)(40, 122)(41, 148)(42, 149)(43, 150)(44, 133)(45, 146)(46, 135)(47, 130)(48, 138)(49, 134)(50, 137)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.351
Graph:: bipartite
	v = 15 e = 100 f = 75
	degree seq :: [ 10^10, 20^5 ]

E6.351 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^2 * Y2, (Y3 * Y2)^5, (Y3^-1 * Y1^-1)^10 ]
Map:: polytopal
	R = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)(101, 151, 102, 152)(103, 153, 107, 157)(104, 154, 109, 159)(105, 155, 111, 161)(106, 156, 113, 163)(108, 158, 112, 162)(110, 160, 114, 164)(115, 165, 125, 175)(116, 166, 127, 177)(117, 167, 126, 176)(118, 168, 129, 179)(119, 169, 130, 180)(120, 170, 132, 182)(121, 171, 134, 184)(122, 172, 133, 183)(123, 173, 136, 186)(124, 174, 137, 187)(128, 178, 135, 185)(131, 181, 138, 188)(139, 189, 148, 198)(140, 190, 146, 196)(141, 191, 145, 195)(142, 192, 149, 199)(143, 193, 144, 194)(147, 197, 150, 200)
	L = (1, 103)(2, 105)(3, 108)(4, 101)(5, 112)(6, 102)(7, 115)(8, 117)(9, 116)(10, 104)(11, 120)(12, 122)(13, 121)(14, 106)(15, 126)(16, 107)(17, 128)(18, 109)(19, 110)(20, 133)(21, 111)(22, 135)(23, 113)(24, 114)(25, 136)(26, 140)(27, 139)(28, 142)(29, 141)(30, 118)(31, 119)(32, 129)(33, 145)(34, 144)(35, 147)(36, 146)(37, 123)(38, 124)(39, 125)(40, 149)(41, 127)(42, 131)(43, 130)(44, 132)(45, 150)(46, 134)(47, 138)(48, 137)(49, 143)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.350
Graph:: simple bipartite
	v = 75 e = 100 f = 15
	degree seq :: [ 2^50, 4^25 ]

E6.352 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1^-1)^5, Y1^10 ]
Map:: polytopal
	R = (1, 51, 2, 52, 5, 55, 11, 61, 20, 70, 32, 82, 31, 81, 19, 69, 10, 60, 4, 54)(3, 53, 7, 57, 12, 62, 22, 72, 33, 83, 45, 95, 42, 92, 28, 78, 17, 67, 8, 58)(6, 56, 13, 63, 21, 71, 34, 84, 44, 94, 43, 93, 30, 80, 18, 68, 9, 59, 14, 64)(15, 65, 25, 75, 35, 85, 47, 97, 50, 100, 48, 98, 41, 91, 27, 77, 16, 66, 26, 76)(23, 73, 36, 86, 46, 96, 40, 90, 49, 99, 39, 89, 29, 79, 38, 88, 24, 74, 37, 87)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200)
	L = (1, 103)(2, 106)(3, 101)(4, 109)(5, 112)(6, 102)(7, 115)(8, 116)(9, 104)(10, 117)(11, 121)(12, 105)(13, 123)(14, 124)(15, 107)(16, 108)(17, 110)(18, 129)(19, 130)(20, 133)(21, 111)(22, 135)(23, 113)(24, 114)(25, 139)(26, 140)(27, 136)(28, 141)(29, 118)(30, 119)(31, 142)(32, 144)(33, 120)(34, 146)(35, 122)(36, 127)(37, 148)(38, 147)(39, 125)(40, 126)(41, 128)(42, 131)(43, 149)(44, 132)(45, 150)(46, 134)(47, 138)(48, 137)(49, 143)(50, 145)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.349
Graph:: simple bipartite
	v = 55 e = 100 f = 35
	degree seq :: [ 2^50, 20^5 ]

E6.353 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y3 * Y2^-1)^5, Y2^10 ]
Map::
	R = (1, 51, 2, 52)(3, 53, 7, 57)(4, 54, 9, 59)(5, 55, 11, 61)(6, 56, 13, 63)(8, 58, 12, 62)(10, 60, 14, 64)(15, 65, 25, 75)(16, 66, 27, 77)(17, 67, 26, 76)(18, 68, 29, 79)(19, 69, 30, 80)(20, 70, 32, 82)(21, 71, 34, 84)(22, 72, 33, 83)(23, 73, 36, 86)(24, 74, 37, 87)(28, 78, 35, 85)(31, 81, 38, 88)(39, 89, 48, 98)(40, 90, 46, 96)(41, 91, 45, 95)(42, 92, 49, 99)(43, 93, 44, 94)(47, 97, 50, 100)(101, 151, 103, 153, 108, 158, 117, 167, 128, 178, 142, 192, 131, 181, 119, 169, 110, 160, 104, 154)(102, 152, 105, 155, 112, 162, 122, 172, 135, 185, 147, 197, 138, 188, 124, 174, 114, 164, 106, 156)(107, 157, 115, 165, 126, 176, 140, 190, 149, 199, 143, 193, 130, 180, 118, 168, 109, 159, 116, 166)(111, 161, 120, 170, 133, 183, 145, 195, 150, 200, 148, 198, 137, 187, 123, 173, 113, 163, 121, 171)(125, 175, 136, 186, 146, 196, 134, 184, 144, 194, 132, 182, 129, 179, 141, 191, 127, 177, 139, 189)
	L = (1, 102)(2, 101)(3, 107)(4, 109)(5, 111)(6, 113)(7, 103)(8, 112)(9, 104)(10, 114)(11, 105)(12, 108)(13, 106)(14, 110)(15, 125)(16, 127)(17, 126)(18, 129)(19, 130)(20, 132)(21, 134)(22, 133)(23, 136)(24, 137)(25, 115)(26, 117)(27, 116)(28, 135)(29, 118)(30, 119)(31, 138)(32, 120)(33, 122)(34, 121)(35, 128)(36, 123)(37, 124)(38, 131)(39, 148)(40, 146)(41, 145)(42, 149)(43, 144)(44, 143)(45, 141)(46, 140)(47, 150)(48, 139)(49, 142)(50, 147)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.354
Graph:: bipartite
	v = 30 e = 100 f = 60
	degree seq :: [ 4^25, 20^5 ]

E6.354 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 10})
Quotient :: dipole
Aut^+ = C5 x D10 (small group id <50, 3>)
Aut   = D10 x D10 (small group id <100, 13>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^5, Y3 * Y1^-1 * Y3^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-3 * Y1^-1 * Y3, (Y3 * Y2^-1)^10 ]
Map:: polytopal
	R = (1, 51, 2, 52, 6, 56, 13, 63, 4, 54)(3, 53, 9, 59, 22, 72, 27, 77, 11, 61)(5, 55, 14, 64, 30, 80, 19, 69, 7, 57)(8, 58, 20, 70, 37, 87, 33, 83, 16, 66)(10, 60, 18, 68, 32, 82, 44, 94, 25, 75)(12, 62, 28, 78, 46, 96, 42, 92, 24, 74)(15, 65, 21, 71, 35, 85, 39, 89, 23, 73)(17, 67, 34, 84, 48, 98, 43, 93, 29, 79)(26, 76, 36, 86, 47, 97, 50, 100, 41, 91)(31, 81, 38, 88, 49, 99, 45, 95, 40, 90)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200)
	L = (1, 103)(2, 107)(3, 110)(4, 112)(5, 101)(6, 116)(7, 118)(8, 102)(9, 104)(10, 124)(11, 126)(12, 125)(13, 129)(14, 123)(15, 105)(16, 132)(17, 106)(18, 111)(19, 136)(20, 115)(21, 108)(22, 139)(23, 109)(24, 141)(25, 143)(26, 142)(27, 145)(28, 113)(29, 144)(30, 140)(31, 114)(32, 119)(33, 147)(34, 121)(35, 117)(36, 127)(37, 131)(38, 120)(39, 128)(40, 122)(41, 148)(42, 149)(43, 150)(44, 133)(45, 146)(46, 135)(47, 130)(48, 138)(49, 134)(50, 137)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200)
	local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.353
Graph:: simple bipartite
	v = 60 e = 100 f = 30
	degree seq :: [ 2^50, 10^10 ]

E6.355 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 14})
Quotient :: regular
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^14 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 29, 37, 45, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 53, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 52, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 54, 56, 55, 50, 42, 34, 26)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 52)(47, 54)(51, 55)(53, 56)
	local type(s) :: { ( 4^14 ) }
Outer automorphisms :: reflexible
Dual of E6.356
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 4 e = 28 f = 14
	degree seq :: [ 14^4 ]

E6.356 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 14})
Quotient :: regular
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^14 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 41, 38, 42)(39, 43, 40, 44)(45, 49, 46, 50)(47, 51, 48, 52)(53, 56, 54, 55)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 39)(36, 40)(41, 45)(42, 46)(43, 47)(44, 48)(49, 53)(50, 54)(51, 55)(52, 56)
	local type(s) :: { ( 14^4 ) }
Outer automorphisms :: reflexible
Dual of E6.355
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 14 e = 28 f = 4
	degree seq :: [ 4^14 ]

E6.357 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 14})
Quotient :: edge
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^14 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 39, 36, 40)(41, 45, 42, 46)(43, 47, 44, 48)(49, 53, 50, 54)(51, 55, 52, 56)(57, 58)(59, 63)(60, 65)(61, 66)(62, 68)(64, 67)(69, 73)(70, 74)(71, 75)(72, 76)(77, 81)(78, 82)(79, 83)(80, 84)(85, 89)(86, 90)(87, 91)(88, 92)(93, 97)(94, 98)(95, 99)(96, 100)(101, 105)(102, 106)(103, 107)(104, 108)(109, 112)(110, 111)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 28, 28 ), ( 28^4 ) }
Outer automorphisms :: reflexible
Dual of E6.361
Transitivity :: ET+
Graph:: simple bipartite
	v = 42 e = 56 f = 4
	degree seq :: [ 2^28, 4^14 ]

E6.358 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 14})
Quotient :: edge
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^14 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 34, 42, 50, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 54, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 55, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 52, 56, 53, 46, 38, 30, 22, 14)(57, 58, 62, 60)(59, 65, 69, 64)(61, 67, 70, 63)(66, 72, 77, 73)(68, 71, 78, 75)(74, 81, 85, 80)(76, 83, 86, 79)(82, 88, 93, 89)(84, 87, 94, 91)(90, 97, 101, 96)(92, 99, 102, 95)(98, 104, 108, 105)(100, 103, 109, 107)(106, 111, 112, 110)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 4^4 ), ( 4^14 ) }
Outer automorphisms :: reflexible
Dual of E6.362
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 56 f = 28
	degree seq :: [ 4^14, 14^4 ]

E6.359 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 14})
Quotient :: edge
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^14 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 26)(19, 27)(20, 30)(22, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 50)(44, 49)(45, 52)(47, 54)(51, 55)(53, 56)(57, 58, 61, 67, 76, 85, 93, 101, 100, 92, 84, 75, 66, 60)(59, 63, 71, 81, 89, 97, 105, 109, 102, 95, 86, 78, 68, 64)(62, 69, 65, 74, 83, 91, 99, 107, 108, 103, 94, 87, 77, 70)(72, 79, 73, 80, 88, 96, 104, 110, 112, 111, 106, 98, 90, 82)
	L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)
	local type(s) :: { ( 8, 8 ), ( 8^14 ) }
Outer automorphisms :: reflexible
Dual of E6.360
Transitivity :: ET+
Graph:: simple bipartite
	v = 32 e = 56 f = 14
	degree seq :: [ 2^28, 14^4 ]

E6.360 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 14})
Quotient :: loop
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^14 ]
Map::
	R = (1, 57, 3, 59, 8, 64, 4, 60)(2, 58, 5, 61, 11, 67, 6, 62)(7, 63, 13, 69, 9, 65, 14, 70)(10, 66, 15, 71, 12, 68, 16, 72)(17, 73, 21, 77, 18, 74, 22, 78)(19, 75, 23, 79, 20, 76, 24, 80)(25, 81, 29, 85, 26, 82, 30, 86)(27, 83, 31, 87, 28, 84, 32, 88)(33, 89, 37, 93, 34, 90, 38, 94)(35, 91, 39, 95, 36, 92, 40, 96)(41, 97, 45, 101, 42, 98, 46, 102)(43, 99, 47, 103, 44, 100, 48, 104)(49, 105, 53, 109, 50, 106, 54, 110)(51, 107, 55, 111, 52, 108, 56, 112)
	L = (1, 58)(2, 57)(3, 63)(4, 65)(5, 66)(6, 68)(7, 59)(8, 67)(9, 60)(10, 61)(11, 64)(12, 62)(13, 73)(14, 74)(15, 75)(16, 76)(17, 69)(18, 70)(19, 71)(20, 72)(21, 81)(22, 82)(23, 83)(24, 84)(25, 77)(26, 78)(27, 79)(28, 80)(29, 89)(30, 90)(31, 91)(32, 92)(33, 85)(34, 86)(35, 87)(36, 88)(37, 97)(38, 98)(39, 99)(40, 100)(41, 93)(42, 94)(43, 95)(44, 96)(45, 105)(46, 106)(47, 107)(48, 108)(49, 101)(50, 102)(51, 103)(52, 104)(53, 112)(54, 111)(55, 110)(56, 109)
	local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.359
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 14 e = 56 f = 32
	degree seq :: [ 8^14 ]

E6.361 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 14})
Quotient :: loop
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^14 ]
Map::
	R = (1, 57, 3, 59, 10, 66, 18, 74, 26, 82, 34, 90, 42, 98, 50, 106, 44, 100, 36, 92, 28, 84, 20, 76, 12, 68, 5, 61)(2, 58, 7, 63, 15, 71, 23, 79, 31, 87, 39, 95, 47, 103, 54, 110, 48, 104, 40, 96, 32, 88, 24, 80, 16, 72, 8, 64)(4, 60, 11, 67, 19, 75, 27, 83, 35, 91, 43, 99, 51, 107, 55, 111, 49, 105, 41, 97, 33, 89, 25, 81, 17, 73, 9, 65)(6, 62, 13, 69, 21, 77, 29, 85, 37, 93, 45, 101, 52, 108, 56, 112, 53, 109, 46, 102, 38, 94, 30, 86, 22, 78, 14, 70)
	L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 67)(6, 60)(7, 61)(8, 59)(9, 69)(10, 72)(11, 70)(12, 71)(13, 64)(14, 63)(15, 78)(16, 77)(17, 66)(18, 81)(19, 68)(20, 83)(21, 73)(22, 75)(23, 76)(24, 74)(25, 85)(26, 88)(27, 86)(28, 87)(29, 80)(30, 79)(31, 94)(32, 93)(33, 82)(34, 97)(35, 84)(36, 99)(37, 89)(38, 91)(39, 92)(40, 90)(41, 101)(42, 104)(43, 102)(44, 103)(45, 96)(46, 95)(47, 109)(48, 108)(49, 98)(50, 111)(51, 100)(52, 105)(53, 107)(54, 106)(55, 112)(56, 110)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.357
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 56 f = 42
	degree seq :: [ 28^4 ]

E6.362 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 14})
Quotient :: loop
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^14 ]
Map:: polytopal non-degenerate
	R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 12, 68)(7, 63, 16, 72)(8, 64, 17, 73)(10, 66, 15, 71)(11, 67, 21, 77)(13, 69, 23, 79)(14, 70, 24, 80)(18, 74, 26, 82)(19, 75, 27, 83)(20, 76, 30, 86)(22, 78, 32, 88)(25, 81, 34, 90)(28, 84, 33, 89)(29, 85, 38, 94)(31, 87, 40, 96)(35, 91, 42, 98)(36, 92, 43, 99)(37, 93, 46, 102)(39, 95, 48, 104)(41, 97, 50, 106)(44, 100, 49, 105)(45, 101, 52, 108)(47, 103, 54, 110)(51, 107, 55, 111)(53, 109, 56, 112)
	L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 67)(6, 69)(7, 71)(8, 59)(9, 74)(10, 60)(11, 76)(12, 64)(13, 65)(14, 62)(15, 81)(16, 79)(17, 80)(18, 83)(19, 66)(20, 85)(21, 70)(22, 68)(23, 73)(24, 88)(25, 89)(26, 72)(27, 91)(28, 75)(29, 93)(30, 78)(31, 77)(32, 96)(33, 97)(34, 82)(35, 99)(36, 84)(37, 101)(38, 87)(39, 86)(40, 104)(41, 105)(42, 90)(43, 107)(44, 92)(45, 100)(46, 95)(47, 94)(48, 110)(49, 109)(50, 98)(51, 108)(52, 103)(53, 102)(54, 112)(55, 106)(56, 111)
	local type(s) :: { ( 4, 14, 4, 14 ) }
Outer automorphisms :: reflexible
Dual of E6.358
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 28 e = 56 f = 18
	degree seq :: [ 4^28 ]

E6.363 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^14 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 10, 66)(6, 62, 12, 68)(8, 64, 11, 67)(13, 69, 17, 73)(14, 70, 18, 74)(15, 71, 19, 75)(16, 72, 20, 76)(21, 77, 25, 81)(22, 78, 26, 82)(23, 79, 27, 83)(24, 80, 28, 84)(29, 85, 33, 89)(30, 86, 34, 90)(31, 87, 35, 91)(32, 88, 36, 92)(37, 93, 41, 97)(38, 94, 42, 98)(39, 95, 43, 99)(40, 96, 44, 100)(45, 101, 49, 105)(46, 102, 50, 106)(47, 103, 51, 107)(48, 104, 52, 108)(53, 109, 56, 112)(54, 110, 55, 111)(113, 169, 115, 171, 120, 176, 116, 172)(114, 170, 117, 173, 123, 179, 118, 174)(119, 175, 125, 181, 121, 177, 126, 182)(122, 178, 127, 183, 124, 180, 128, 184)(129, 185, 133, 189, 130, 186, 134, 190)(131, 187, 135, 191, 132, 188, 136, 192)(137, 193, 141, 197, 138, 194, 142, 198)(139, 195, 143, 199, 140, 196, 144, 200)(145, 201, 149, 205, 146, 202, 150, 206)(147, 203, 151, 207, 148, 204, 152, 208)(153, 209, 157, 213, 154, 210, 158, 214)(155, 211, 159, 215, 156, 212, 160, 216)(161, 217, 165, 221, 162, 218, 166, 222)(163, 219, 167, 223, 164, 220, 168, 224)
	L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 122)(6, 124)(7, 115)(8, 123)(9, 116)(10, 117)(11, 120)(12, 118)(13, 129)(14, 130)(15, 131)(16, 132)(17, 125)(18, 126)(19, 127)(20, 128)(21, 137)(22, 138)(23, 139)(24, 140)(25, 133)(26, 134)(27, 135)(28, 136)(29, 145)(30, 146)(31, 147)(32, 148)(33, 141)(34, 142)(35, 143)(36, 144)(37, 153)(38, 154)(39, 155)(40, 156)(41, 149)(42, 150)(43, 151)(44, 152)(45, 161)(46, 162)(47, 163)(48, 164)(49, 157)(50, 158)(51, 159)(52, 160)(53, 168)(54, 167)(55, 166)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.366
Graph:: bipartite
	v = 42 e = 112 f = 60
	degree seq :: [ 4^28, 8^14 ]

E6.364 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^14 ]
Map::
	R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 8, 64)(5, 61, 11, 67, 14, 70, 7, 63)(10, 66, 16, 72, 21, 77, 17, 73)(12, 68, 15, 71, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 24, 80)(20, 76, 27, 83, 30, 86, 23, 79)(26, 82, 32, 88, 37, 93, 33, 89)(28, 84, 31, 87, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 40, 96)(36, 92, 43, 99, 46, 102, 39, 95)(42, 98, 48, 104, 52, 108, 49, 105)(44, 100, 47, 103, 53, 109, 51, 107)(50, 106, 55, 111, 56, 112, 54, 110)(113, 169, 115, 171, 122, 178, 130, 186, 138, 194, 146, 202, 154, 210, 162, 218, 156, 212, 148, 204, 140, 196, 132, 188, 124, 180, 117, 173)(114, 170, 119, 175, 127, 183, 135, 191, 143, 199, 151, 207, 159, 215, 166, 222, 160, 216, 152, 208, 144, 200, 136, 192, 128, 184, 120, 176)(116, 172, 123, 179, 131, 187, 139, 195, 147, 203, 155, 211, 163, 219, 167, 223, 161, 217, 153, 209, 145, 201, 137, 193, 129, 185, 121, 177)(118, 174, 125, 181, 133, 189, 141, 197, 149, 205, 157, 213, 164, 220, 168, 224, 165, 221, 158, 214, 150, 206, 142, 198, 134, 190, 126, 182)
	L = (1, 115)(2, 119)(3, 122)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 116)(10, 130)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 121)(18, 138)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 129)(26, 146)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 164)(46, 150)(47, 166)(48, 152)(49, 153)(50, 156)(51, 167)(52, 168)(53, 158)(54, 160)(55, 161)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.365
Graph:: bipartite
	v = 18 e = 112 f = 84
	degree seq :: [ 8^14, 28^4 ]

E6.365 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^14 ]
Map:: polytopal
	R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170)(115, 171, 119, 175)(116, 172, 121, 177)(117, 173, 123, 179)(118, 174, 125, 181)(120, 176, 126, 182)(122, 178, 124, 180)(127, 183, 132, 188)(128, 184, 135, 191)(129, 185, 137, 193)(130, 186, 133, 189)(131, 187, 139, 195)(134, 190, 141, 197)(136, 192, 143, 199)(138, 194, 144, 200)(140, 196, 142, 198)(145, 201, 151, 207)(146, 202, 153, 209)(147, 203, 149, 205)(148, 204, 155, 211)(150, 206, 157, 213)(152, 208, 159, 215)(154, 210, 160, 216)(156, 212, 158, 214)(161, 217, 166, 222)(162, 218, 167, 223)(163, 219, 164, 220)(165, 221, 168, 224)
	L = (1, 115)(2, 117)(3, 120)(4, 113)(5, 124)(6, 114)(7, 127)(8, 129)(9, 130)(10, 116)(11, 132)(12, 134)(13, 135)(14, 118)(15, 121)(16, 119)(17, 138)(18, 139)(19, 122)(20, 125)(21, 123)(22, 142)(23, 143)(24, 126)(25, 128)(26, 146)(27, 147)(28, 131)(29, 133)(30, 150)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 141)(38, 158)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 149)(46, 165)(47, 166)(48, 152)(49, 153)(50, 156)(51, 167)(52, 157)(53, 160)(54, 168)(55, 161)(56, 164)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 8, 28 ), ( 8, 28, 8, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.364
Graph:: simple bipartite
	v = 84 e = 112 f = 18
	degree seq :: [ 2^56, 4^28 ]

E6.366 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^14 ]
Map:: polytopal
	R = (1, 57, 2, 58, 5, 61, 11, 67, 20, 76, 29, 85, 37, 93, 45, 101, 44, 100, 36, 92, 28, 84, 19, 75, 10, 66, 4, 60)(3, 59, 7, 63, 15, 71, 25, 81, 33, 89, 41, 97, 49, 105, 53, 109, 46, 102, 39, 95, 30, 86, 22, 78, 12, 68, 8, 64)(6, 62, 13, 69, 9, 65, 18, 74, 27, 83, 35, 91, 43, 99, 51, 107, 52, 108, 47, 103, 38, 94, 31, 87, 21, 77, 14, 70)(16, 72, 23, 79, 17, 73, 24, 80, 32, 88, 40, 96, 48, 104, 54, 110, 56, 112, 55, 111, 50, 106, 42, 98, 34, 90, 26, 82)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 118)(3, 113)(4, 121)(5, 124)(6, 114)(7, 128)(8, 129)(9, 116)(10, 127)(11, 133)(12, 117)(13, 135)(14, 136)(15, 122)(16, 119)(17, 120)(18, 138)(19, 139)(20, 142)(21, 123)(22, 144)(23, 125)(24, 126)(25, 146)(26, 130)(27, 131)(28, 145)(29, 150)(30, 132)(31, 152)(32, 134)(33, 140)(34, 137)(35, 154)(36, 155)(37, 158)(38, 141)(39, 160)(40, 143)(41, 162)(42, 147)(43, 148)(44, 161)(45, 164)(46, 149)(47, 166)(48, 151)(49, 156)(50, 153)(51, 167)(52, 157)(53, 168)(54, 159)(55, 163)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.363
Graph:: simple bipartite
	v = 60 e = 112 f = 42
	degree seq :: [ 2^56, 28^4 ]

E6.367 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^14 ]
Map::
	R = (1, 57, 2, 58)(3, 59, 7, 63)(4, 60, 9, 65)(5, 61, 11, 67)(6, 62, 13, 69)(8, 64, 14, 70)(10, 66, 12, 68)(15, 71, 20, 76)(16, 72, 23, 79)(17, 73, 25, 81)(18, 74, 21, 77)(19, 75, 27, 83)(22, 78, 29, 85)(24, 80, 31, 87)(26, 82, 32, 88)(28, 84, 30, 86)(33, 89, 39, 95)(34, 90, 41, 97)(35, 91, 37, 93)(36, 92, 43, 99)(38, 94, 45, 101)(40, 96, 47, 103)(42, 98, 48, 104)(44, 100, 46, 102)(49, 105, 54, 110)(50, 106, 55, 111)(51, 107, 52, 108)(53, 109, 56, 112)(113, 169, 115, 171, 120, 176, 129, 185, 138, 194, 146, 202, 154, 210, 162, 218, 156, 212, 148, 204, 140, 196, 131, 187, 122, 178, 116, 172)(114, 170, 117, 173, 124, 180, 134, 190, 142, 198, 150, 206, 158, 214, 165, 221, 160, 216, 152, 208, 144, 200, 136, 192, 126, 182, 118, 174)(119, 175, 127, 183, 121, 177, 130, 186, 139, 195, 147, 203, 155, 211, 163, 219, 167, 223, 161, 217, 153, 209, 145, 201, 137, 193, 128, 184)(123, 179, 132, 188, 125, 181, 135, 191, 143, 199, 151, 207, 159, 215, 166, 222, 168, 224, 164, 220, 157, 213, 149, 205, 141, 197, 133, 189)
	L = (1, 114)(2, 113)(3, 119)(4, 121)(5, 123)(6, 125)(7, 115)(8, 126)(9, 116)(10, 124)(11, 117)(12, 122)(13, 118)(14, 120)(15, 132)(16, 135)(17, 137)(18, 133)(19, 139)(20, 127)(21, 130)(22, 141)(23, 128)(24, 143)(25, 129)(26, 144)(27, 131)(28, 142)(29, 134)(30, 140)(31, 136)(32, 138)(33, 151)(34, 153)(35, 149)(36, 155)(37, 147)(38, 157)(39, 145)(40, 159)(41, 146)(42, 160)(43, 148)(44, 158)(45, 150)(46, 156)(47, 152)(48, 154)(49, 166)(50, 167)(51, 164)(52, 163)(53, 168)(54, 161)(55, 162)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.368
Graph:: bipartite
	v = 32 e = 112 f = 70
	degree seq :: [ 4^28, 28^4 ]

E6.368 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 14})
Quotient :: dipole
Aut^+ = (C14 x C2) : C2 (small group id <56, 7>)
Aut   = D8 x D14 (small group id <112, 31>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^14 ]
Map:: polytopal
	R = (1, 57, 2, 58, 6, 62, 4, 60)(3, 59, 9, 65, 13, 69, 8, 64)(5, 61, 11, 67, 14, 70, 7, 63)(10, 66, 16, 72, 21, 77, 17, 73)(12, 68, 15, 71, 22, 78, 19, 75)(18, 74, 25, 81, 29, 85, 24, 80)(20, 76, 27, 83, 30, 86, 23, 79)(26, 82, 32, 88, 37, 93, 33, 89)(28, 84, 31, 87, 38, 94, 35, 91)(34, 90, 41, 97, 45, 101, 40, 96)(36, 92, 43, 99, 46, 102, 39, 95)(42, 98, 48, 104, 52, 108, 49, 105)(44, 100, 47, 103, 53, 109, 51, 107)(50, 106, 55, 111, 56, 112, 54, 110)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224)
	L = (1, 115)(2, 119)(3, 122)(4, 123)(5, 113)(6, 125)(7, 127)(8, 114)(9, 116)(10, 130)(11, 131)(12, 117)(13, 133)(14, 118)(15, 135)(16, 120)(17, 121)(18, 138)(19, 139)(20, 124)(21, 141)(22, 126)(23, 143)(24, 128)(25, 129)(26, 146)(27, 147)(28, 132)(29, 149)(30, 134)(31, 151)(32, 136)(33, 137)(34, 154)(35, 155)(36, 140)(37, 157)(38, 142)(39, 159)(40, 144)(41, 145)(42, 162)(43, 163)(44, 148)(45, 164)(46, 150)(47, 166)(48, 152)(49, 153)(50, 156)(51, 167)(52, 168)(53, 158)(54, 160)(55, 161)(56, 165)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224)
	local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28 ) }
Outer automorphisms :: reflexible
Dual of E6.367
Graph:: simple bipartite
	v = 70 e = 112 f = 32
	degree seq :: [ 2^56, 8^14 ]

E6.369 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 3})
Quotient :: halfedge^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y2)^2, (Y1 * Y3 * Y2)^3, (Y1 * Y2)^5, (Y3 * Y1)^5, (Y2 * Y1 * Y3 * Y1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 62, 2, 61)(3, 67, 7, 63)(4, 69, 9, 64)(5, 70, 10, 65)(6, 72, 12, 66)(8, 75, 15, 68)(11, 80, 20, 71)(13, 83, 23, 73)(14, 85, 25, 74)(16, 88, 28, 76)(17, 90, 30, 77)(18, 91, 31, 78)(19, 93, 33, 79)(21, 94, 34, 81)(22, 96, 36, 82)(24, 89, 29, 84)(26, 100, 40, 86)(27, 101, 41, 87)(32, 95, 35, 92)(37, 111, 51, 97)(38, 109, 49, 98)(39, 113, 53, 99)(42, 114, 54, 102)(43, 106, 46, 103)(44, 118, 58, 104)(45, 112, 52, 105)(47, 115, 55, 107)(48, 116, 56, 108)(50, 117, 57, 110)(59, 120, 60, 119)
	L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 13)(9, 16)(10, 18)(12, 21)(14, 24)(15, 26)(17, 29)(19, 32)(20, 27)(22, 35)(23, 31)(25, 38)(28, 42)(30, 44)(33, 46)(34, 48)(36, 50)(37, 45)(39, 52)(40, 54)(41, 56)(43, 57)(47, 51)(49, 58)(53, 59)(55, 60)(61, 64)(62, 66)(63, 68)(65, 71)(67, 74)(69, 77)(70, 79)(72, 82)(73, 84)(75, 87)(76, 89)(78, 92)(80, 86)(81, 95)(83, 97)(85, 99)(88, 103)(90, 96)(91, 105)(93, 107)(94, 109)(98, 112)(100, 115)(101, 113)(102, 117)(104, 110)(106, 111)(108, 118)(114, 120)(116, 119)
	local type(s) :: { ( 6^4 ) }
Outer automorphisms :: reflexible
Dual of E6.370
Transitivity :: VT+ AT
Graph:: simple
	v = 30 e = 60 f = 20
	degree seq :: [ 4^30 ]

E6.370 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 3})
Quotient :: halfedge^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y2)^3, (Y3 * Y2 * Y1)^2, (Y2 * Y1^-1 * Y3 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 62, 2, 65, 5, 61)(3, 68, 8, 70, 10, 63)(4, 71, 11, 73, 13, 64)(6, 76, 16, 78, 18, 66)(7, 79, 19, 81, 21, 67)(9, 84, 24, 80, 20, 69)(12, 90, 30, 91, 31, 72)(14, 93, 33, 94, 34, 74)(15, 95, 35, 97, 37, 75)(17, 100, 40, 96, 36, 77)(22, 106, 46, 108, 48, 82)(23, 109, 49, 99, 39, 83)(25, 112, 52, 103, 43, 85)(26, 105, 45, 113, 53, 86)(27, 114, 54, 104, 44, 87)(28, 116, 56, 101, 41, 88)(29, 117, 57, 118, 58, 89)(32, 110, 50, 119, 59, 92)(38, 120, 60, 111, 51, 98)(42, 115, 55, 107, 47, 102)
	L = (1, 3)(2, 6)(4, 12)(5, 14)(7, 20)(8, 22)(9, 25)(10, 26)(11, 28)(13, 23)(15, 36)(16, 38)(17, 41)(18, 42)(19, 44)(21, 39)(24, 50)(27, 55)(29, 43)(30, 54)(31, 51)(32, 47)(33, 59)(34, 58)(35, 52)(37, 49)(40, 48)(45, 56)(46, 57)(53, 60)(61, 64)(62, 67)(63, 69)(65, 75)(66, 77)(68, 83)(70, 87)(71, 89)(72, 85)(73, 92)(74, 90)(76, 99)(78, 103)(79, 105)(80, 101)(81, 106)(82, 107)(84, 111)(86, 112)(88, 102)(91, 108)(93, 109)(94, 116)(95, 115)(96, 114)(97, 120)(98, 117)(100, 110)(104, 118)(113, 119)
	local type(s) :: { ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E6.369
Transitivity :: VT+ AT
Graph:: simple
	v = 20 e = 60 f = 30
	degree seq :: [ 6^20 ]

E6.371 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 3})
Quotient :: edge^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2, (Y3 * Y2)^5, (Y3 * Y1)^5, (Y3 * Y1 * Y3 * Y2)^3 ]
Map:: polytopal
	R = (1, 61, 4, 64)(2, 62, 6, 66)(3, 63, 7, 67)(5, 65, 10, 70)(8, 68, 16, 76)(9, 69, 17, 77)(11, 71, 21, 81)(12, 72, 22, 82)(13, 73, 24, 84)(14, 74, 25, 85)(15, 75, 26, 86)(18, 78, 31, 91)(19, 79, 32, 92)(20, 80, 23, 83)(27, 87, 33, 93)(28, 88, 42, 102)(29, 89, 44, 104)(30, 90, 40, 100)(34, 94, 50, 110)(35, 95, 52, 112)(36, 96, 48, 108)(37, 97, 45, 105)(38, 98, 54, 114)(39, 99, 56, 116)(41, 101, 43, 103)(46, 106, 57, 117)(47, 107, 58, 118)(49, 109, 51, 111)(53, 113, 55, 115)(59, 119, 60, 120)(121, 122)(123, 125)(124, 128)(126, 131)(127, 133)(129, 135)(130, 138)(132, 140)(134, 143)(136, 147)(137, 149)(139, 146)(141, 153)(142, 155)(144, 157)(145, 159)(148, 161)(150, 163)(151, 165)(152, 167)(154, 169)(156, 171)(158, 173)(160, 175)(162, 174)(164, 178)(166, 179)(168, 180)(170, 177)(172, 176)(181, 183)(182, 185)(184, 189)(186, 192)(187, 194)(188, 195)(190, 199)(191, 200)(193, 203)(196, 208)(197, 210)(198, 206)(201, 214)(202, 216)(204, 218)(205, 220)(207, 221)(209, 223)(211, 226)(212, 228)(213, 229)(215, 231)(217, 233)(219, 235)(222, 237)(224, 232)(225, 239)(227, 240)(230, 234)(236, 238)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 12, 12 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E6.374
Graph:: simple bipartite
	v = 90 e = 120 f = 20
	degree seq :: [ 2^60, 4^30 ]

E6.372 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 3})
Quotient :: edge^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y3 * Y1)^2, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1, (Y1 * Y3^-1)^5 ]
Map:: polytopal
	R = (1, 61, 4, 64, 5, 65)(2, 62, 7, 67, 8, 68)(3, 63, 9, 69, 10, 70)(6, 66, 15, 75, 16, 76)(11, 71, 21, 81, 22, 82)(12, 72, 23, 83, 24, 84)(13, 73, 25, 85, 26, 86)(14, 74, 27, 87, 28, 88)(17, 77, 29, 89, 30, 90)(18, 78, 31, 91, 32, 92)(19, 79, 33, 93, 34, 94)(20, 80, 35, 95, 36, 96)(37, 97, 51, 111, 53, 113)(38, 98, 54, 114, 52, 112)(39, 99, 48, 108, 55, 115)(40, 100, 56, 116, 47, 107)(41, 101, 57, 117, 50, 110)(42, 102, 49, 109, 58, 118)(43, 103, 59, 119, 45, 105)(44, 104, 46, 106, 60, 120)(121, 122)(123, 126)(124, 131)(125, 133)(127, 137)(128, 139)(129, 140)(130, 138)(132, 136)(134, 135)(141, 157)(142, 159)(143, 160)(144, 158)(145, 161)(146, 163)(147, 164)(148, 162)(149, 165)(150, 167)(151, 168)(152, 166)(153, 169)(154, 171)(155, 172)(156, 170)(173, 180)(174, 179)(175, 177)(176, 178)(181, 183)(182, 186)(184, 192)(185, 194)(187, 198)(188, 200)(189, 199)(190, 197)(191, 196)(193, 195)(201, 218)(202, 220)(203, 219)(204, 217)(205, 222)(206, 224)(207, 223)(208, 221)(209, 226)(210, 228)(211, 227)(212, 225)(213, 230)(214, 232)(215, 231)(216, 229)(233, 239)(234, 240)(235, 238)(236, 237)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 8, 8 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E6.373
Graph:: simple bipartite
	v = 80 e = 120 f = 30
	degree seq :: [ 2^60, 6^20 ]

E6.373 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 3})
Quotient :: loop^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y2 * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y2, (Y3 * Y2)^5, (Y3 * Y1)^5, (Y3 * Y1 * Y3 * Y2)^3 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184)(2, 62, 122, 182, 6, 66, 126, 186)(3, 63, 123, 183, 7, 67, 127, 187)(5, 65, 125, 185, 10, 70, 130, 190)(8, 68, 128, 188, 16, 76, 136, 196)(9, 69, 129, 189, 17, 77, 137, 197)(11, 71, 131, 191, 21, 81, 141, 201)(12, 72, 132, 192, 22, 82, 142, 202)(13, 73, 133, 193, 24, 84, 144, 204)(14, 74, 134, 194, 25, 85, 145, 205)(15, 75, 135, 195, 26, 86, 146, 206)(18, 78, 138, 198, 31, 91, 151, 211)(19, 79, 139, 199, 32, 92, 152, 212)(20, 80, 140, 200, 23, 83, 143, 203)(27, 87, 147, 207, 33, 93, 153, 213)(28, 88, 148, 208, 42, 102, 162, 222)(29, 89, 149, 209, 44, 104, 164, 224)(30, 90, 150, 210, 40, 100, 160, 220)(34, 94, 154, 214, 50, 110, 170, 230)(35, 95, 155, 215, 52, 112, 172, 232)(36, 96, 156, 216, 48, 108, 168, 228)(37, 97, 157, 217, 45, 105, 165, 225)(38, 98, 158, 218, 54, 114, 174, 234)(39, 99, 159, 219, 56, 116, 176, 236)(41, 101, 161, 221, 43, 103, 163, 223)(46, 106, 166, 226, 57, 117, 177, 237)(47, 107, 167, 227, 58, 118, 178, 238)(49, 109, 169, 229, 51, 111, 171, 231)(53, 113, 173, 233, 55, 115, 175, 235)(59, 119, 179, 239, 60, 120, 180, 240)
	L = (1, 62)(2, 61)(3, 65)(4, 68)(5, 63)(6, 71)(7, 73)(8, 64)(9, 75)(10, 78)(11, 66)(12, 80)(13, 67)(14, 83)(15, 69)(16, 87)(17, 89)(18, 70)(19, 86)(20, 72)(21, 93)(22, 95)(23, 74)(24, 97)(25, 99)(26, 79)(27, 76)(28, 101)(29, 77)(30, 103)(31, 105)(32, 107)(33, 81)(34, 109)(35, 82)(36, 111)(37, 84)(38, 113)(39, 85)(40, 115)(41, 88)(42, 114)(43, 90)(44, 118)(45, 91)(46, 119)(47, 92)(48, 120)(49, 94)(50, 117)(51, 96)(52, 116)(53, 98)(54, 102)(55, 100)(56, 112)(57, 110)(58, 104)(59, 106)(60, 108)(121, 183)(122, 185)(123, 181)(124, 189)(125, 182)(126, 192)(127, 194)(128, 195)(129, 184)(130, 199)(131, 200)(132, 186)(133, 203)(134, 187)(135, 188)(136, 208)(137, 210)(138, 206)(139, 190)(140, 191)(141, 214)(142, 216)(143, 193)(144, 218)(145, 220)(146, 198)(147, 221)(148, 196)(149, 223)(150, 197)(151, 226)(152, 228)(153, 229)(154, 201)(155, 231)(156, 202)(157, 233)(158, 204)(159, 235)(160, 205)(161, 207)(162, 237)(163, 209)(164, 232)(165, 239)(166, 211)(167, 240)(168, 212)(169, 213)(170, 234)(171, 215)(172, 224)(173, 217)(174, 230)(175, 219)(176, 238)(177, 222)(178, 236)(179, 225)(180, 227)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.372
Transitivity :: VT+
Graph::
	v = 30 e = 120 f = 80
	degree seq :: [ 8^30 ]

E6.374 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 3})
Quotient :: loop^2
Aut^+ = A5 (small group id <60, 5>)
Aut   = S5 (small group id <120, 34>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y3 * Y1)^2, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1, (Y1 * Y3^-1)^5 ]
Map::
	R = (1, 61, 121, 181, 4, 64, 124, 184, 5, 65, 125, 185)(2, 62, 122, 182, 7, 67, 127, 187, 8, 68, 128, 188)(3, 63, 123, 183, 9, 69, 129, 189, 10, 70, 130, 190)(6, 66, 126, 186, 15, 75, 135, 195, 16, 76, 136, 196)(11, 71, 131, 191, 21, 81, 141, 201, 22, 82, 142, 202)(12, 72, 132, 192, 23, 83, 143, 203, 24, 84, 144, 204)(13, 73, 133, 193, 25, 85, 145, 205, 26, 86, 146, 206)(14, 74, 134, 194, 27, 87, 147, 207, 28, 88, 148, 208)(17, 77, 137, 197, 29, 89, 149, 209, 30, 90, 150, 210)(18, 78, 138, 198, 31, 91, 151, 211, 32, 92, 152, 212)(19, 79, 139, 199, 33, 93, 153, 213, 34, 94, 154, 214)(20, 80, 140, 200, 35, 95, 155, 215, 36, 96, 156, 216)(37, 97, 157, 217, 51, 111, 171, 231, 53, 113, 173, 233)(38, 98, 158, 218, 54, 114, 174, 234, 52, 112, 172, 232)(39, 99, 159, 219, 48, 108, 168, 228, 55, 115, 175, 235)(40, 100, 160, 220, 56, 116, 176, 236, 47, 107, 167, 227)(41, 101, 161, 221, 57, 117, 177, 237, 50, 110, 170, 230)(42, 102, 162, 222, 49, 109, 169, 229, 58, 118, 178, 238)(43, 103, 163, 223, 59, 119, 179, 239, 45, 105, 165, 225)(44, 104, 164, 224, 46, 106, 166, 226, 60, 120, 180, 240)
	L = (1, 62)(2, 61)(3, 66)(4, 71)(5, 73)(6, 63)(7, 77)(8, 79)(9, 80)(10, 78)(11, 64)(12, 76)(13, 65)(14, 75)(15, 74)(16, 72)(17, 67)(18, 70)(19, 68)(20, 69)(21, 97)(22, 99)(23, 100)(24, 98)(25, 101)(26, 103)(27, 104)(28, 102)(29, 105)(30, 107)(31, 108)(32, 106)(33, 109)(34, 111)(35, 112)(36, 110)(37, 81)(38, 84)(39, 82)(40, 83)(41, 85)(42, 88)(43, 86)(44, 87)(45, 89)(46, 92)(47, 90)(48, 91)(49, 93)(50, 96)(51, 94)(52, 95)(53, 120)(54, 119)(55, 117)(56, 118)(57, 115)(58, 116)(59, 114)(60, 113)(121, 183)(122, 186)(123, 181)(124, 192)(125, 194)(126, 182)(127, 198)(128, 200)(129, 199)(130, 197)(131, 196)(132, 184)(133, 195)(134, 185)(135, 193)(136, 191)(137, 190)(138, 187)(139, 189)(140, 188)(141, 218)(142, 220)(143, 219)(144, 217)(145, 222)(146, 224)(147, 223)(148, 221)(149, 226)(150, 228)(151, 227)(152, 225)(153, 230)(154, 232)(155, 231)(156, 229)(157, 204)(158, 201)(159, 203)(160, 202)(161, 208)(162, 205)(163, 207)(164, 206)(165, 212)(166, 209)(167, 211)(168, 210)(169, 216)(170, 213)(171, 215)(172, 214)(173, 239)(174, 240)(175, 238)(176, 237)(177, 236)(178, 235)(179, 233)(180, 234)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.371
Transitivity :: VT+
Graph::
	v = 20 e = 120 f = 90
	degree seq :: [ 12^20 ]

E6.375 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 3})
Quotient :: dipole
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^3, (Y1 * Y2)^5, Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 10, 70)(6, 66, 12, 72)(8, 68, 15, 75)(11, 71, 19, 79)(13, 73, 21, 81)(14, 74, 23, 83)(16, 76, 25, 85)(17, 77, 26, 86)(18, 78, 28, 88)(20, 80, 30, 90)(22, 82, 32, 92)(24, 84, 34, 94)(27, 87, 38, 98)(29, 89, 40, 100)(31, 91, 43, 103)(33, 93, 45, 105)(35, 95, 46, 106)(36, 96, 42, 102)(37, 97, 49, 109)(39, 99, 51, 111)(41, 101, 52, 112)(44, 104, 56, 116)(47, 107, 58, 118)(48, 108, 60, 120)(50, 110, 59, 119)(53, 113, 57, 117)(54, 114, 55, 115)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 128, 188)(126, 186, 131, 191)(127, 187, 133, 193)(129, 189, 136, 196)(130, 190, 137, 197)(132, 192, 140, 200)(134, 194, 142, 202)(135, 195, 144, 204)(138, 198, 147, 207)(139, 199, 149, 209)(141, 201, 146, 206)(143, 203, 153, 213)(145, 205, 155, 215)(148, 208, 159, 219)(150, 210, 161, 221)(151, 211, 157, 217)(152, 212, 164, 224)(154, 214, 166, 226)(156, 216, 168, 228)(158, 218, 170, 230)(160, 220, 172, 232)(162, 222, 174, 234)(163, 223, 175, 235)(165, 225, 177, 237)(167, 227, 179, 239)(169, 229, 180, 240)(171, 231, 178, 238)(173, 233, 176, 236)
	L = (1, 124)(2, 126)(3, 128)(4, 121)(5, 131)(6, 122)(7, 134)(8, 123)(9, 132)(10, 138)(11, 125)(12, 129)(13, 142)(14, 127)(15, 143)(16, 140)(17, 147)(18, 130)(19, 148)(20, 136)(21, 151)(22, 133)(23, 135)(24, 153)(25, 156)(26, 157)(27, 137)(28, 139)(29, 159)(30, 162)(31, 141)(32, 163)(33, 144)(34, 167)(35, 168)(36, 145)(37, 146)(38, 169)(39, 149)(40, 173)(41, 174)(42, 150)(43, 152)(44, 175)(45, 178)(46, 179)(47, 154)(48, 155)(49, 158)(50, 180)(51, 177)(52, 176)(53, 160)(54, 161)(55, 164)(56, 172)(57, 171)(58, 165)(59, 166)(60, 170)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.376
Graph:: simple bipartite
	v = 60 e = 120 f = 50
	degree seq :: [ 4^60 ]

E6.376 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 3})
Quotient :: dipole
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^5, Y1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 61, 2, 62, 5, 65)(3, 63, 8, 68, 10, 70)(4, 64, 11, 71, 7, 67)(6, 66, 13, 73, 15, 75)(9, 69, 18, 78, 17, 77)(12, 72, 21, 81, 22, 82)(14, 74, 25, 85, 24, 84)(16, 76, 27, 87, 29, 89)(19, 79, 31, 91, 32, 92)(20, 80, 33, 93, 34, 94)(23, 83, 37, 97, 39, 99)(26, 86, 41, 101, 42, 102)(28, 88, 45, 105, 44, 104)(30, 90, 47, 107, 48, 108)(35, 95, 52, 112, 53, 113)(36, 96, 54, 114, 43, 103)(38, 98, 56, 116, 55, 115)(40, 100, 58, 118, 46, 106)(49, 109, 60, 120, 51, 111)(50, 110, 59, 119, 57, 117)(121, 181, 123, 183)(122, 182, 126, 186)(124, 184, 129, 189)(125, 185, 132, 192)(127, 187, 134, 194)(128, 188, 136, 196)(130, 190, 139, 199)(131, 191, 140, 200)(133, 193, 143, 203)(135, 195, 146, 206)(137, 197, 148, 208)(138, 198, 150, 210)(141, 201, 155, 215)(142, 202, 156, 216)(144, 204, 158, 218)(145, 205, 160, 220)(147, 207, 163, 223)(149, 209, 166, 226)(151, 211, 169, 229)(152, 212, 157, 217)(153, 213, 170, 230)(154, 214, 171, 231)(159, 219, 177, 237)(161, 221, 165, 225)(162, 222, 172, 232)(164, 224, 179, 239)(167, 227, 175, 235)(168, 228, 173, 233)(174, 234, 176, 236)(178, 238, 180, 240)
	L = (1, 124)(2, 127)(3, 129)(4, 121)(5, 131)(6, 134)(7, 122)(8, 137)(9, 123)(10, 138)(11, 125)(12, 140)(13, 144)(14, 126)(15, 145)(16, 148)(17, 128)(18, 130)(19, 150)(20, 132)(21, 154)(22, 153)(23, 158)(24, 133)(25, 135)(26, 160)(27, 164)(28, 136)(29, 165)(30, 139)(31, 168)(32, 167)(33, 142)(34, 141)(35, 171)(36, 170)(37, 175)(38, 143)(39, 176)(40, 146)(41, 166)(42, 178)(43, 179)(44, 147)(45, 149)(46, 161)(47, 152)(48, 151)(49, 173)(50, 156)(51, 155)(52, 180)(53, 169)(54, 177)(55, 157)(56, 159)(57, 174)(58, 162)(59, 163)(60, 172)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4^4 ), ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E6.375
Graph:: simple bipartite
	v = 50 e = 120 f = 60
	degree seq :: [ 4^30, 6^20 ]

E6.377 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 9})
Quotient :: regular
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2 * T1^-1)^2, (T1^-1 * T2)^4, T1^9 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 23, 40, 22, 10, 4)(3, 7, 15, 31, 50, 42, 24, 18, 8)(6, 13, 27, 21, 39, 58, 41, 30, 14)(9, 19, 37, 56, 45, 26, 12, 25, 20)(16, 33, 52, 36, 44, 61, 65, 54, 34)(17, 35, 49, 59, 66, 51, 32, 47, 28)(29, 48, 62, 69, 57, 38, 46, 60, 43)(53, 68, 72, 71, 64, 55, 67, 70, 63)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 41)(25, 43)(26, 44)(27, 46)(30, 49)(34, 53)(35, 55)(37, 54)(39, 51)(40, 56)(42, 59)(45, 62)(47, 63)(48, 64)(50, 65)(52, 67)(57, 68)(58, 69)(60, 70)(61, 71)(66, 72)
	local type(s) :: { ( 4^9 ) }
Outer automorphisms :: reflexible
Dual of E6.378
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 36 f = 18
	degree seq :: [ 9^8 ]

E6.378 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 9})
Quotient :: regular
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1 * T2 * T1^-1)^2, (T1^-1 * T2)^9 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 33, 25)(15, 26, 32, 27)(21, 35, 30, 36)(22, 37, 29, 38)(23, 39, 44, 34)(40, 49, 43, 50)(41, 51, 42, 52)(45, 53, 48, 54)(46, 55, 47, 56)(57, 65, 60, 66)(58, 67, 59, 68)(61, 69, 64, 70)(62, 71, 63, 72)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48)(49, 57)(50, 58)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 72)(66, 69)(67, 70)(68, 71)
	local type(s) :: { ( 9^4 ) }
Outer automorphisms :: reflexible
Dual of E6.377
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 18 e = 36 f = 8
	degree seq :: [ 4^18 ]

E6.379 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 9})
Quotient :: edge
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^9 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 30, 40)(25, 41, 28, 42)(31, 44, 38, 45)(33, 46, 36, 47)(49, 57, 52, 58)(50, 59, 51, 60)(53, 61, 56, 62)(54, 63, 55, 64)(65, 70, 68, 71)(66, 72, 67, 69)(73, 74)(75, 79)(76, 81)(77, 82)(78, 84)(80, 87)(83, 92)(85, 95)(86, 97)(88, 100)(89, 102)(90, 103)(91, 105)(93, 108)(94, 110)(96, 107)(98, 109)(99, 104)(101, 106)(111, 121)(112, 122)(113, 123)(114, 124)(115, 120)(116, 125)(117, 126)(118, 127)(119, 128)(129, 137)(130, 138)(131, 139)(132, 140)(133, 141)(134, 142)(135, 143)(136, 144)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 18, 18 ), ( 18^4 ) }
Outer automorphisms :: reflexible
Dual of E6.383
Transitivity :: ET+
Graph:: simple bipartite
	v = 54 e = 72 f = 8
	degree seq :: [ 2^36, 4^18 ]

E6.380 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 9})
Quotient :: edge
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2^-2 * T1)^2, T2^9 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 24, 43, 47, 29, 14, 5)(2, 7, 17, 35, 54, 56, 38, 20, 8)(4, 12, 26, 45, 61, 58, 41, 22, 9)(6, 15, 30, 49, 64, 66, 52, 33, 16)(11, 25, 13, 28, 46, 62, 59, 42, 23)(18, 36, 19, 37, 55, 68, 67, 53, 34)(21, 39, 57, 69, 70, 60, 44, 27, 40)(31, 50, 32, 51, 65, 72, 71, 63, 48)(73, 74, 78, 76)(75, 81, 93, 83)(77, 85, 90, 79)(80, 91, 103, 87)(82, 95, 109, 92)(84, 88, 104, 99)(86, 98, 116, 100)(89, 106, 123, 105)(94, 102, 120, 111)(96, 110, 121, 113)(97, 112, 122, 108)(101, 107, 124, 117)(114, 129, 135, 127)(115, 130, 141, 131)(118, 132, 137, 125)(119, 134, 139, 126)(128, 140, 143, 136)(133, 138, 144, 142)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 4^4 ), ( 4^9 ) }
Outer automorphisms :: reflexible
Dual of E6.384
Transitivity :: ET+
Graph:: simple bipartite
	v = 26 e = 72 f = 36
	degree seq :: [ 4^18, 9^8 ]

E6.381 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 9})
Quotient :: edge
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T1^-2 * T2 * T1^-1)^2, T1^9 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 38)(20, 33)(22, 31)(23, 41)(25, 43)(26, 44)(27, 46)(30, 49)(34, 53)(35, 55)(37, 54)(39, 51)(40, 56)(42, 59)(45, 62)(47, 63)(48, 64)(50, 65)(52, 67)(57, 68)(58, 69)(60, 70)(61, 71)(66, 72)(73, 74, 77, 83, 95, 112, 94, 82, 76)(75, 79, 87, 103, 122, 114, 96, 90, 80)(78, 85, 99, 93, 111, 130, 113, 102, 86)(81, 91, 109, 128, 117, 98, 84, 97, 92)(88, 105, 124, 108, 116, 133, 137, 126, 106)(89, 107, 121, 131, 138, 123, 104, 119, 100)(101, 120, 134, 141, 129, 110, 118, 132, 115)(125, 140, 144, 143, 136, 127, 139, 142, 135)
	L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)
	local type(s) :: { ( 8, 8 ), ( 8^9 ) }
Outer automorphisms :: reflexible
Dual of E6.382
Transitivity :: ET+
Graph:: simple bipartite
	v = 44 e = 72 f = 18
	degree seq :: [ 2^36, 9^8 ]

E6.382 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 9})
Quotient :: loop
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^9 ]
Map::
	R = (1, 73, 3, 75, 8, 80, 4, 76)(2, 74, 5, 77, 11, 83, 6, 78)(7, 79, 13, 85, 24, 96, 14, 86)(9, 81, 16, 88, 29, 101, 17, 89)(10, 82, 18, 90, 32, 104, 19, 91)(12, 84, 21, 93, 37, 109, 22, 94)(15, 87, 26, 98, 43, 115, 27, 99)(20, 92, 34, 106, 48, 120, 35, 107)(23, 95, 39, 111, 30, 102, 40, 112)(25, 97, 41, 113, 28, 100, 42, 114)(31, 103, 44, 116, 38, 110, 45, 117)(33, 105, 46, 118, 36, 108, 47, 119)(49, 121, 57, 129, 52, 124, 58, 130)(50, 122, 59, 131, 51, 123, 60, 132)(53, 125, 61, 133, 56, 128, 62, 134)(54, 126, 63, 135, 55, 127, 64, 136)(65, 137, 70, 142, 68, 140, 71, 143)(66, 138, 72, 144, 67, 139, 69, 141)
	L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 82)(6, 84)(7, 75)(8, 87)(9, 76)(10, 77)(11, 92)(12, 78)(13, 95)(14, 97)(15, 80)(16, 100)(17, 102)(18, 103)(19, 105)(20, 83)(21, 108)(22, 110)(23, 85)(24, 107)(25, 86)(26, 109)(27, 104)(28, 88)(29, 106)(30, 89)(31, 90)(32, 99)(33, 91)(34, 101)(35, 96)(36, 93)(37, 98)(38, 94)(39, 121)(40, 122)(41, 123)(42, 124)(43, 120)(44, 125)(45, 126)(46, 127)(47, 128)(48, 115)(49, 111)(50, 112)(51, 113)(52, 114)(53, 116)(54, 117)(55, 118)(56, 119)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 129)(66, 130)(67, 131)(68, 132)(69, 133)(70, 134)(71, 135)(72, 136)
	local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9 ) }
Outer automorphisms :: reflexible
Dual of E6.381
Transitivity :: ET+ VT+ AT
Graph::
	v = 18 e = 72 f = 44
	degree seq :: [ 8^18 ]

E6.383 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 9})
Quotient :: loop
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2^-2 * T1)^2, T2^9 ]
Map::
	R = (1, 73, 3, 75, 10, 82, 24, 96, 43, 115, 47, 119, 29, 101, 14, 86, 5, 77)(2, 74, 7, 79, 17, 89, 35, 107, 54, 126, 56, 128, 38, 110, 20, 92, 8, 80)(4, 76, 12, 84, 26, 98, 45, 117, 61, 133, 58, 130, 41, 113, 22, 94, 9, 81)(6, 78, 15, 87, 30, 102, 49, 121, 64, 136, 66, 138, 52, 124, 33, 105, 16, 88)(11, 83, 25, 97, 13, 85, 28, 100, 46, 118, 62, 134, 59, 131, 42, 114, 23, 95)(18, 90, 36, 108, 19, 91, 37, 109, 55, 127, 68, 140, 67, 139, 53, 125, 34, 106)(21, 93, 39, 111, 57, 129, 69, 141, 70, 142, 60, 132, 44, 116, 27, 99, 40, 112)(31, 103, 50, 122, 32, 104, 51, 123, 65, 137, 72, 144, 71, 143, 63, 135, 48, 120)
	L = (1, 74)(2, 78)(3, 81)(4, 73)(5, 85)(6, 76)(7, 77)(8, 91)(9, 93)(10, 95)(11, 75)(12, 88)(13, 90)(14, 98)(15, 80)(16, 104)(17, 106)(18, 79)(19, 103)(20, 82)(21, 83)(22, 102)(23, 109)(24, 110)(25, 112)(26, 116)(27, 84)(28, 86)(29, 107)(30, 120)(31, 87)(32, 99)(33, 89)(34, 123)(35, 124)(36, 97)(37, 92)(38, 121)(39, 94)(40, 122)(41, 96)(42, 129)(43, 130)(44, 100)(45, 101)(46, 132)(47, 134)(48, 111)(49, 113)(50, 108)(51, 105)(52, 117)(53, 118)(54, 119)(55, 114)(56, 140)(57, 135)(58, 141)(59, 115)(60, 137)(61, 138)(62, 139)(63, 127)(64, 128)(65, 125)(66, 144)(67, 126)(68, 143)(69, 131)(70, 133)(71, 136)(72, 142)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.379
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 72 f = 54
	degree seq :: [ 18^8 ]

E6.384 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 9})
Quotient :: loop
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T1^-2 * T2 * T1^-1)^2, T1^9 ]
Map:: polytopal non-degenerate
	R = (1, 73, 3, 75)(2, 74, 6, 78)(4, 76, 9, 81)(5, 77, 12, 84)(7, 79, 16, 88)(8, 80, 17, 89)(10, 82, 21, 93)(11, 83, 24, 96)(13, 85, 28, 100)(14, 86, 29, 101)(15, 87, 32, 104)(18, 90, 36, 108)(19, 91, 38, 110)(20, 92, 33, 105)(22, 94, 31, 103)(23, 95, 41, 113)(25, 97, 43, 115)(26, 98, 44, 116)(27, 99, 46, 118)(30, 102, 49, 121)(34, 106, 53, 125)(35, 107, 55, 127)(37, 109, 54, 126)(39, 111, 51, 123)(40, 112, 56, 128)(42, 114, 59, 131)(45, 117, 62, 134)(47, 119, 63, 135)(48, 120, 64, 136)(50, 122, 65, 137)(52, 124, 67, 139)(57, 129, 68, 140)(58, 130, 69, 141)(60, 132, 70, 142)(61, 133, 71, 143)(66, 138, 72, 144)
	L = (1, 74)(2, 77)(3, 79)(4, 73)(5, 83)(6, 85)(7, 87)(8, 75)(9, 91)(10, 76)(11, 95)(12, 97)(13, 99)(14, 78)(15, 103)(16, 105)(17, 107)(18, 80)(19, 109)(20, 81)(21, 111)(22, 82)(23, 112)(24, 90)(25, 92)(26, 84)(27, 93)(28, 89)(29, 120)(30, 86)(31, 122)(32, 119)(33, 124)(34, 88)(35, 121)(36, 116)(37, 128)(38, 118)(39, 130)(40, 94)(41, 102)(42, 96)(43, 101)(44, 133)(45, 98)(46, 132)(47, 100)(48, 134)(49, 131)(50, 114)(51, 104)(52, 108)(53, 140)(54, 106)(55, 139)(56, 117)(57, 110)(58, 113)(59, 138)(60, 115)(61, 137)(62, 141)(63, 125)(64, 127)(65, 126)(66, 123)(67, 142)(68, 144)(69, 129)(70, 135)(71, 136)(72, 143)
	local type(s) :: { ( 4, 9, 4, 9 ) }
Outer automorphisms :: reflexible
Dual of E6.380
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 36 e = 72 f = 26
	degree seq :: [ 4^36 ]

E6.385 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 10, 82)(6, 78, 12, 84)(8, 80, 15, 87)(11, 83, 20, 92)(13, 85, 23, 95)(14, 86, 25, 97)(16, 88, 28, 100)(17, 89, 30, 102)(18, 90, 31, 103)(19, 91, 33, 105)(21, 93, 36, 108)(22, 94, 38, 110)(24, 96, 35, 107)(26, 98, 37, 109)(27, 99, 32, 104)(29, 101, 34, 106)(39, 111, 49, 121)(40, 112, 50, 122)(41, 113, 51, 123)(42, 114, 52, 124)(43, 115, 48, 120)(44, 116, 53, 125)(45, 117, 54, 126)(46, 118, 55, 127)(47, 119, 56, 128)(57, 129, 65, 137)(58, 130, 66, 138)(59, 131, 67, 139)(60, 132, 68, 140)(61, 133, 69, 141)(62, 134, 70, 142)(63, 135, 71, 143)(64, 136, 72, 144)(145, 217, 147, 219, 152, 224, 148, 220)(146, 218, 149, 221, 155, 227, 150, 222)(151, 223, 157, 229, 168, 240, 158, 230)(153, 225, 160, 232, 173, 245, 161, 233)(154, 226, 162, 234, 176, 248, 163, 235)(156, 228, 165, 237, 181, 253, 166, 238)(159, 231, 170, 242, 187, 259, 171, 243)(164, 236, 178, 250, 192, 264, 179, 251)(167, 239, 183, 255, 174, 246, 184, 256)(169, 241, 185, 257, 172, 244, 186, 258)(175, 247, 188, 260, 182, 254, 189, 261)(177, 249, 190, 262, 180, 252, 191, 263)(193, 265, 201, 273, 196, 268, 202, 274)(194, 266, 203, 275, 195, 267, 204, 276)(197, 269, 205, 277, 200, 272, 206, 278)(198, 270, 207, 279, 199, 271, 208, 280)(209, 281, 214, 286, 212, 284, 215, 287)(210, 282, 216, 288, 211, 283, 213, 285)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 154)(6, 156)(7, 147)(8, 159)(9, 148)(10, 149)(11, 164)(12, 150)(13, 167)(14, 169)(15, 152)(16, 172)(17, 174)(18, 175)(19, 177)(20, 155)(21, 180)(22, 182)(23, 157)(24, 179)(25, 158)(26, 181)(27, 176)(28, 160)(29, 178)(30, 161)(31, 162)(32, 171)(33, 163)(34, 173)(35, 168)(36, 165)(37, 170)(38, 166)(39, 193)(40, 194)(41, 195)(42, 196)(43, 192)(44, 197)(45, 198)(46, 199)(47, 200)(48, 187)(49, 183)(50, 184)(51, 185)(52, 186)(53, 188)(54, 189)(55, 190)(56, 191)(57, 209)(58, 210)(59, 211)(60, 212)(61, 213)(62, 214)(63, 215)(64, 216)(65, 201)(66, 202)(67, 203)(68, 204)(69, 205)(70, 206)(71, 207)(72, 208)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.388
Graph:: bipartite
	v = 54 e = 144 f = 80
	degree seq :: [ 4^36, 8^18 ]

E6.386 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^9 ]
Map::
	R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 21, 93, 11, 83)(5, 77, 13, 85, 18, 90, 7, 79)(8, 80, 19, 91, 31, 103, 15, 87)(10, 82, 23, 95, 37, 109, 20, 92)(12, 84, 16, 88, 32, 104, 27, 99)(14, 86, 26, 98, 44, 116, 28, 100)(17, 89, 34, 106, 51, 123, 33, 105)(22, 94, 30, 102, 48, 120, 39, 111)(24, 96, 38, 110, 49, 121, 41, 113)(25, 97, 40, 112, 50, 122, 36, 108)(29, 101, 35, 107, 52, 124, 45, 117)(42, 114, 57, 129, 63, 135, 55, 127)(43, 115, 58, 130, 69, 141, 59, 131)(46, 118, 60, 132, 65, 137, 53, 125)(47, 119, 62, 134, 67, 139, 54, 126)(56, 128, 68, 140, 71, 143, 64, 136)(61, 133, 66, 138, 72, 144, 70, 142)(145, 217, 147, 219, 154, 226, 168, 240, 187, 259, 191, 263, 173, 245, 158, 230, 149, 221)(146, 218, 151, 223, 161, 233, 179, 251, 198, 270, 200, 272, 182, 254, 164, 236, 152, 224)(148, 220, 156, 228, 170, 242, 189, 261, 205, 277, 202, 274, 185, 257, 166, 238, 153, 225)(150, 222, 159, 231, 174, 246, 193, 265, 208, 280, 210, 282, 196, 268, 177, 249, 160, 232)(155, 227, 169, 241, 157, 229, 172, 244, 190, 262, 206, 278, 203, 275, 186, 258, 167, 239)(162, 234, 180, 252, 163, 235, 181, 253, 199, 271, 212, 284, 211, 283, 197, 269, 178, 250)(165, 237, 183, 255, 201, 273, 213, 285, 214, 286, 204, 276, 188, 260, 171, 243, 184, 256)(175, 247, 194, 266, 176, 248, 195, 267, 209, 281, 216, 288, 215, 287, 207, 279, 192, 264)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 159)(7, 161)(8, 146)(9, 148)(10, 168)(11, 169)(12, 170)(13, 172)(14, 149)(15, 174)(16, 150)(17, 179)(18, 180)(19, 181)(20, 152)(21, 183)(22, 153)(23, 155)(24, 187)(25, 157)(26, 189)(27, 184)(28, 190)(29, 158)(30, 193)(31, 194)(32, 195)(33, 160)(34, 162)(35, 198)(36, 163)(37, 199)(38, 164)(39, 201)(40, 165)(41, 166)(42, 167)(43, 191)(44, 171)(45, 205)(46, 206)(47, 173)(48, 175)(49, 208)(50, 176)(51, 209)(52, 177)(53, 178)(54, 200)(55, 212)(56, 182)(57, 213)(58, 185)(59, 186)(60, 188)(61, 202)(62, 203)(63, 192)(64, 210)(65, 216)(66, 196)(67, 197)(68, 211)(69, 214)(70, 204)(71, 207)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.387
Graph:: bipartite
	v = 26 e = 144 f = 108
	degree seq :: [ 8^18, 18^8 ]

E6.387 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3^-1 * Y2 * Y3^-2)^2, (Y3^-1 * Y1^-1)^9 ]
Map:: polytopal
	R = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(145, 217, 146, 218)(147, 219, 151, 223)(148, 220, 153, 225)(149, 221, 155, 227)(150, 222, 157, 229)(152, 224, 161, 233)(154, 226, 165, 237)(156, 228, 169, 241)(158, 230, 173, 245)(159, 231, 172, 244)(160, 232, 176, 248)(162, 234, 174, 246)(163, 235, 181, 253)(164, 236, 167, 239)(166, 238, 170, 242)(168, 240, 186, 258)(171, 243, 191, 263)(175, 247, 195, 267)(177, 249, 192, 264)(178, 250, 197, 269)(179, 251, 193, 265)(180, 252, 198, 270)(182, 254, 187, 259)(183, 255, 189, 261)(184, 256, 201, 273)(185, 257, 203, 275)(188, 260, 205, 277)(190, 262, 206, 278)(194, 266, 209, 281)(196, 268, 208, 280)(199, 271, 212, 284)(200, 272, 204, 276)(202, 274, 213, 285)(207, 279, 215, 287)(210, 282, 216, 288)(211, 283, 214, 286)
	L = (1, 147)(2, 149)(3, 152)(4, 145)(5, 156)(6, 146)(7, 159)(8, 162)(9, 163)(10, 148)(11, 167)(12, 170)(13, 171)(14, 150)(15, 175)(16, 151)(17, 178)(18, 180)(19, 182)(20, 153)(21, 183)(22, 154)(23, 185)(24, 155)(25, 188)(26, 190)(27, 192)(28, 157)(29, 193)(30, 158)(31, 165)(32, 196)(33, 160)(34, 164)(35, 161)(36, 184)(37, 195)(38, 201)(39, 202)(40, 166)(41, 173)(42, 204)(43, 168)(44, 172)(45, 169)(46, 194)(47, 203)(48, 209)(49, 210)(50, 174)(51, 211)(52, 212)(53, 176)(54, 177)(55, 179)(56, 181)(57, 199)(58, 198)(59, 214)(60, 215)(61, 186)(62, 187)(63, 189)(64, 191)(65, 207)(66, 206)(67, 197)(68, 213)(69, 200)(70, 205)(71, 216)(72, 208)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 8, 18 ), ( 8, 18, 8, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.386
Graph:: simple bipartite
	v = 108 e = 144 f = 26
	degree seq :: [ 2^72, 4^36 ]

E6.388 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y1^9 ]
Map:: polytopal
	R = (1, 73, 2, 74, 5, 77, 11, 83, 23, 95, 40, 112, 22, 94, 10, 82, 4, 76)(3, 75, 7, 79, 15, 87, 31, 103, 50, 122, 42, 114, 24, 96, 18, 90, 8, 80)(6, 78, 13, 85, 27, 99, 21, 93, 39, 111, 58, 130, 41, 113, 30, 102, 14, 86)(9, 81, 19, 91, 37, 109, 56, 128, 45, 117, 26, 98, 12, 84, 25, 97, 20, 92)(16, 88, 33, 105, 52, 124, 36, 108, 44, 116, 61, 133, 65, 137, 54, 126, 34, 106)(17, 89, 35, 107, 49, 121, 59, 131, 66, 138, 51, 123, 32, 104, 47, 119, 28, 100)(29, 101, 48, 120, 62, 134, 69, 141, 57, 129, 38, 110, 46, 118, 60, 132, 43, 115)(53, 125, 68, 140, 72, 144, 71, 143, 64, 136, 55, 127, 67, 139, 70, 142, 63, 135)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 150)(3, 145)(4, 153)(5, 156)(6, 146)(7, 160)(8, 161)(9, 148)(10, 165)(11, 168)(12, 149)(13, 172)(14, 173)(15, 176)(16, 151)(17, 152)(18, 180)(19, 182)(20, 177)(21, 154)(22, 175)(23, 185)(24, 155)(25, 187)(26, 188)(27, 190)(28, 157)(29, 158)(30, 193)(31, 166)(32, 159)(33, 164)(34, 197)(35, 199)(36, 162)(37, 198)(38, 163)(39, 195)(40, 200)(41, 167)(42, 203)(43, 169)(44, 170)(45, 206)(46, 171)(47, 207)(48, 208)(49, 174)(50, 209)(51, 183)(52, 211)(53, 178)(54, 181)(55, 179)(56, 184)(57, 212)(58, 213)(59, 186)(60, 214)(61, 215)(62, 189)(63, 191)(64, 192)(65, 194)(66, 216)(67, 196)(68, 201)(69, 202)(70, 204)(71, 205)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.385
Graph:: simple bipartite
	v = 80 e = 144 f = 54
	degree seq :: [ 2^72, 18^8 ]

E6.389 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-2)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, Y2^9 ]
Map::
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 17, 89)(10, 82, 21, 93)(12, 84, 25, 97)(14, 86, 29, 101)(15, 87, 28, 100)(16, 88, 32, 104)(18, 90, 30, 102)(19, 91, 37, 109)(20, 92, 23, 95)(22, 94, 26, 98)(24, 96, 42, 114)(27, 99, 47, 119)(31, 103, 51, 123)(33, 105, 48, 120)(34, 106, 53, 125)(35, 107, 49, 121)(36, 108, 54, 126)(38, 110, 43, 115)(39, 111, 45, 117)(40, 112, 57, 129)(41, 113, 59, 131)(44, 116, 61, 133)(46, 118, 62, 134)(50, 122, 65, 137)(52, 124, 64, 136)(55, 127, 68, 140)(56, 128, 60, 132)(58, 130, 69, 141)(63, 135, 71, 143)(66, 138, 72, 144)(67, 139, 70, 142)(145, 217, 147, 219, 152, 224, 162, 234, 180, 252, 184, 256, 166, 238, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 170, 242, 190, 262, 194, 266, 174, 246, 158, 230, 150, 222)(151, 223, 159, 231, 175, 247, 165, 237, 183, 255, 202, 274, 198, 270, 177, 249, 160, 232)(153, 225, 163, 235, 182, 254, 201, 273, 199, 271, 179, 251, 161, 233, 178, 250, 164, 236)(155, 227, 167, 239, 185, 257, 173, 245, 193, 265, 210, 282, 206, 278, 187, 259, 168, 240)(157, 229, 171, 243, 192, 264, 209, 281, 207, 279, 189, 261, 169, 241, 188, 260, 172, 244)(176, 248, 196, 268, 212, 284, 213, 285, 200, 272, 181, 253, 195, 267, 211, 283, 197, 269)(186, 258, 204, 276, 215, 287, 216, 288, 208, 280, 191, 263, 203, 275, 214, 286, 205, 277)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 169)(13, 150)(14, 173)(15, 172)(16, 176)(17, 152)(18, 174)(19, 181)(20, 167)(21, 154)(22, 170)(23, 164)(24, 186)(25, 156)(26, 166)(27, 191)(28, 159)(29, 158)(30, 162)(31, 195)(32, 160)(33, 192)(34, 197)(35, 193)(36, 198)(37, 163)(38, 187)(39, 189)(40, 201)(41, 203)(42, 168)(43, 182)(44, 205)(45, 183)(46, 206)(47, 171)(48, 177)(49, 179)(50, 209)(51, 175)(52, 208)(53, 178)(54, 180)(55, 212)(56, 204)(57, 184)(58, 213)(59, 185)(60, 200)(61, 188)(62, 190)(63, 215)(64, 196)(65, 194)(66, 216)(67, 214)(68, 199)(69, 202)(70, 211)(71, 207)(72, 210)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.390
Graph:: bipartite
	v = 44 e = 144 f = 90
	degree seq :: [ 4^36, 18^8 ]

E6.390 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 9})
Quotient :: dipole
Aut^+ = ((C2 x C2) : C9) : C2 (small group id <72, 15>)
Aut   = C2 x (((C2 x C2) : C9) : C2) (small group id <144, 109>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1 * Y3)^2, (Y3 * Y2^-1)^9 ]
Map:: polytopal
	R = (1, 73, 2, 74, 6, 78, 4, 76)(3, 75, 9, 81, 21, 93, 11, 83)(5, 77, 13, 85, 18, 90, 7, 79)(8, 80, 19, 91, 31, 103, 15, 87)(10, 82, 23, 95, 37, 109, 20, 92)(12, 84, 16, 88, 32, 104, 27, 99)(14, 86, 26, 98, 44, 116, 28, 100)(17, 89, 34, 106, 51, 123, 33, 105)(22, 94, 30, 102, 48, 120, 39, 111)(24, 96, 38, 110, 49, 121, 41, 113)(25, 97, 40, 112, 50, 122, 36, 108)(29, 101, 35, 107, 52, 124, 45, 117)(42, 114, 57, 129, 63, 135, 55, 127)(43, 115, 58, 130, 69, 141, 59, 131)(46, 118, 60, 132, 65, 137, 53, 125)(47, 119, 62, 134, 67, 139, 54, 126)(56, 128, 68, 140, 71, 143, 64, 136)(61, 133, 66, 138, 72, 144, 70, 142)(145, 217)(146, 218)(147, 219)(148, 220)(149, 221)(150, 222)(151, 223)(152, 224)(153, 225)(154, 226)(155, 227)(156, 228)(157, 229)(158, 230)(159, 231)(160, 232)(161, 233)(162, 234)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 241)(170, 242)(171, 243)(172, 244)(173, 245)(174, 246)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 253)(182, 254)(183, 255)(184, 256)(185, 257)(186, 258)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 265)(194, 266)(195, 267)(196, 268)(197, 269)(198, 270)(199, 271)(200, 272)(201, 273)(202, 274)(203, 275)(204, 276)(205, 277)(206, 278)(207, 279)(208, 280)(209, 281)(210, 282)(211, 283)(212, 284)(213, 285)(214, 286)(215, 287)(216, 288)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 159)(7, 161)(8, 146)(9, 148)(10, 168)(11, 169)(12, 170)(13, 172)(14, 149)(15, 174)(16, 150)(17, 179)(18, 180)(19, 181)(20, 152)(21, 183)(22, 153)(23, 155)(24, 187)(25, 157)(26, 189)(27, 184)(28, 190)(29, 158)(30, 193)(31, 194)(32, 195)(33, 160)(34, 162)(35, 198)(36, 163)(37, 199)(38, 164)(39, 201)(40, 165)(41, 166)(42, 167)(43, 191)(44, 171)(45, 205)(46, 206)(47, 173)(48, 175)(49, 208)(50, 176)(51, 209)(52, 177)(53, 178)(54, 200)(55, 212)(56, 182)(57, 213)(58, 185)(59, 186)(60, 188)(61, 202)(62, 203)(63, 192)(64, 210)(65, 216)(66, 196)(67, 197)(68, 211)(69, 214)(70, 204)(71, 207)(72, 215)(73, 217)(74, 218)(75, 219)(76, 220)(77, 221)(78, 222)(79, 223)(80, 224)(81, 225)(82, 226)(83, 227)(84, 228)(85, 229)(86, 230)(87, 231)(88, 232)(89, 233)(90, 234)(91, 235)(92, 236)(93, 237)(94, 238)(95, 239)(96, 240)(97, 241)(98, 242)(99, 243)(100, 244)(101, 245)(102, 246)(103, 247)(104, 248)(105, 249)(106, 250)(107, 251)(108, 252)(109, 253)(110, 254)(111, 255)(112, 256)(113, 257)(114, 258)(115, 259)(116, 260)(117, 261)(118, 262)(119, 263)(120, 264)(121, 265)(122, 266)(123, 267)(124, 268)(125, 269)(126, 270)(127, 271)(128, 272)(129, 273)(130, 274)(131, 275)(132, 276)(133, 277)(134, 278)(135, 279)(136, 280)(137, 281)(138, 282)(139, 283)(140, 284)(141, 285)(142, 286)(143, 287)(144, 288)
	local type(s) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18 ) }
Outer automorphisms :: reflexible
Dual of E6.389
Graph:: simple bipartite
	v = 90 e = 144 f = 44
	degree seq :: [ 2^72, 8^18 ]

E6.391 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 3, 5})
Quotient :: edge
Aut^+ = (C5 x C5) : C3 (small group id <75, 2>)
Aut   = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^5, (T2^-1 * T1^-1)^3, (T1^-1 * T2)^3, (T2^-1 * T1^-1)^3, T2^2 * T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-1 ]
Map:: polyhedral non-degenerate
	R = (1, 3, 9, 15, 5)(2, 6, 17, 21, 7)(4, 11, 28, 31, 12)(8, 22, 44, 46, 23)(10, 19, 40, 51, 26)(13, 32, 59, 55, 29)(14, 33, 60, 36, 16)(18, 30, 50, 67, 39)(20, 41, 69, 52, 27)(24, 47, 57, 72, 48)(25, 45, 42, 70, 49)(34, 62, 74, 54, 61)(35, 63, 65, 37, 58)(38, 64, 56, 73, 66)(43, 71, 75, 53, 68)(76, 77, 79)(78, 83, 85)(80, 88, 89)(81, 91, 93)(82, 94, 95)(84, 99, 100)(86, 102, 104)(87, 105, 97)(90, 109, 110)(92, 112, 113)(96, 117, 118)(98, 120, 116)(101, 125, 122)(103, 128, 129)(106, 131, 132)(107, 133, 114)(108, 127, 136)(111, 139, 119)(115, 143, 130)(121, 140, 146)(123, 138, 144)(124, 142, 137)(126, 148, 149)(134, 145, 141)(135, 150, 147)
	L = (1, 76)(2, 77)(3, 78)(4, 79)(5, 80)(6, 81)(7, 82)(8, 83)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 95)(21, 96)(22, 97)(23, 98)(24, 99)(25, 100)(26, 101)(27, 102)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 108)(34, 109)(35, 110)(36, 111)(37, 112)(38, 113)(39, 114)(40, 115)(41, 116)(42, 117)(43, 118)(44, 119)(45, 120)(46, 121)(47, 122)(48, 123)(49, 124)(50, 125)(51, 126)(52, 127)(53, 128)(54, 129)(55, 130)(56, 131)(57, 132)(58, 133)(59, 134)(60, 135)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 141)(67, 142)(68, 143)(69, 144)(70, 145)(71, 146)(72, 147)(73, 148)(74, 149)(75, 150)
	local type(s) :: { ( 6^3 ), ( 6^5 ) }
Outer automorphisms :: reflexible
Dual of E6.392
Transitivity :: ET+
Graph:: simple bipartite
	v = 40 e = 75 f = 25
	degree seq :: [ 3^25, 5^15 ]

E6.392 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 3, 5})
Quotient :: loop
Aut^+ = (C5 x C5) : C3 (small group id <75, 2>)
Aut   = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
|r| :: 2
Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2^-1)^3, (T2^-1 * T1^-1)^5 ]
Map:: polyhedral non-degenerate
	R = (1, 76, 3, 78, 5, 80)(2, 77, 6, 81, 7, 82)(4, 79, 10, 85, 11, 86)(8, 83, 18, 93, 19, 94)(9, 84, 16, 91, 20, 95)(12, 87, 25, 100, 22, 97)(13, 88, 26, 101, 27, 102)(14, 89, 28, 103, 29, 104)(15, 90, 23, 98, 30, 105)(17, 92, 31, 106, 32, 107)(21, 96, 38, 113, 39, 114)(24, 99, 40, 115, 41, 116)(33, 108, 53, 128, 54, 129)(34, 109, 36, 111, 55, 130)(35, 110, 56, 131, 57, 132)(37, 112, 51, 126, 58, 133)(42, 117, 63, 138, 60, 135)(43, 118, 44, 119, 64, 139)(45, 120, 65, 140, 46, 121)(47, 122, 49, 124, 66, 141)(48, 123, 67, 142, 68, 143)(50, 125, 62, 137, 69, 144)(52, 127, 70, 145, 59, 134)(61, 136, 74, 149, 71, 146)(72, 147, 73, 148, 75, 150)
	L = (1, 77)(2, 79)(3, 83)(4, 76)(5, 87)(6, 89)(7, 91)(8, 84)(9, 78)(10, 96)(11, 98)(12, 88)(13, 80)(14, 90)(15, 81)(16, 92)(17, 82)(18, 108)(19, 101)(20, 111)(21, 97)(22, 85)(23, 99)(24, 86)(25, 117)(26, 110)(27, 119)(28, 121)(29, 106)(30, 124)(31, 123)(32, 126)(33, 109)(34, 93)(35, 94)(36, 112)(37, 95)(38, 134)(39, 115)(40, 136)(41, 137)(42, 118)(43, 100)(44, 120)(45, 102)(46, 122)(47, 103)(48, 104)(49, 125)(50, 105)(51, 127)(52, 107)(53, 116)(54, 131)(55, 144)(56, 146)(57, 140)(58, 148)(59, 135)(60, 113)(61, 114)(62, 128)(63, 133)(64, 150)(65, 142)(66, 139)(67, 132)(68, 145)(69, 147)(70, 149)(71, 129)(72, 130)(73, 138)(74, 143)(75, 141)
	local type(s) :: { ( 3, 5, 3, 5, 3, 5 ) }
Outer automorphisms :: reflexible
Dual of E6.391
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 25 e = 75 f = 40
	degree seq :: [ 6^25 ]

E6.393 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 5})
Quotient :: dipole
Aut^+ = (C5 x C5) : C3 (small group id <75, 2>)
Aut   = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^5, (Y2^-1 * Y1^-1)^3, (Y1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, Y2^2 * Y1^-1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1^-1 ]
Map::
	R = (1, 76, 2, 77, 4, 79)(3, 78, 8, 83, 10, 85)(5, 80, 13, 88, 14, 89)(6, 81, 16, 91, 18, 93)(7, 82, 19, 94, 20, 95)(9, 84, 24, 99, 25, 100)(11, 86, 27, 102, 29, 104)(12, 87, 30, 105, 22, 97)(15, 90, 34, 109, 35, 110)(17, 92, 37, 112, 38, 113)(21, 96, 42, 117, 43, 118)(23, 98, 45, 120, 41, 116)(26, 101, 50, 125, 47, 122)(28, 103, 53, 128, 54, 129)(31, 106, 56, 131, 57, 132)(32, 107, 58, 133, 39, 114)(33, 108, 52, 127, 61, 136)(36, 111, 64, 139, 44, 119)(40, 115, 68, 143, 55, 130)(46, 121, 65, 140, 71, 146)(48, 123, 63, 138, 69, 144)(49, 124, 67, 142, 62, 137)(51, 126, 73, 148, 74, 149)(59, 134, 70, 145, 66, 141)(60, 135, 75, 150, 72, 147)(151, 226, 153, 228, 159, 234, 165, 240, 155, 230)(152, 227, 156, 231, 167, 242, 171, 246, 157, 232)(154, 229, 161, 236, 178, 253, 181, 256, 162, 237)(158, 233, 172, 247, 194, 269, 196, 271, 173, 248)(160, 235, 169, 244, 190, 265, 201, 276, 176, 251)(163, 238, 182, 257, 209, 284, 205, 280, 179, 254)(164, 239, 183, 258, 210, 285, 186, 261, 166, 241)(168, 243, 180, 255, 200, 275, 217, 292, 189, 264)(170, 245, 191, 266, 219, 294, 202, 277, 177, 252)(174, 249, 197, 272, 207, 282, 222, 297, 198, 273)(175, 250, 195, 270, 192, 267, 220, 295, 199, 274)(184, 259, 212, 287, 224, 299, 204, 279, 211, 286)(185, 260, 213, 288, 215, 290, 187, 262, 208, 283)(188, 263, 214, 289, 206, 281, 223, 298, 216, 291)(193, 268, 221, 296, 225, 300, 203, 278, 218, 293)
	L = (1, 153)(2, 156)(3, 159)(4, 161)(5, 151)(6, 167)(7, 152)(8, 172)(9, 165)(10, 169)(11, 178)(12, 154)(13, 182)(14, 183)(15, 155)(16, 164)(17, 171)(18, 180)(19, 190)(20, 191)(21, 157)(22, 194)(23, 158)(24, 197)(25, 195)(26, 160)(27, 170)(28, 181)(29, 163)(30, 200)(31, 162)(32, 209)(33, 210)(34, 212)(35, 213)(36, 166)(37, 208)(38, 214)(39, 168)(40, 201)(41, 219)(42, 220)(43, 221)(44, 196)(45, 192)(46, 173)(47, 207)(48, 174)(49, 175)(50, 217)(51, 176)(52, 177)(53, 218)(54, 211)(55, 179)(56, 223)(57, 222)(58, 185)(59, 205)(60, 186)(61, 184)(62, 224)(63, 215)(64, 206)(65, 187)(66, 188)(67, 189)(68, 193)(69, 202)(70, 199)(71, 225)(72, 198)(73, 216)(74, 204)(75, 203)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.394
Graph:: bipartite
	v = 40 e = 150 f = 100
	degree seq :: [ 6^25, 10^15 ]

E6.394 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 5})
Quotient :: dipole
Aut^+ = (C5 x C5) : C3 (small group id <75, 2>)
Aut   = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1)^3, (Y3 * Y2^-1)^3, Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2 * Y3^2 * Y2, Y3 * Y2 * Y3^-2 * Y2 * Y3 * Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y1^-1)^5 ]
Map:: polytopal
	R = (1, 76)(2, 77)(3, 78)(4, 79)(5, 80)(6, 81)(7, 82)(8, 83)(9, 84)(10, 85)(11, 86)(12, 87)(13, 88)(14, 89)(15, 90)(16, 91)(17, 92)(18, 93)(19, 94)(20, 95)(21, 96)(22, 97)(23, 98)(24, 99)(25, 100)(26, 101)(27, 102)(28, 103)(29, 104)(30, 105)(31, 106)(32, 107)(33, 108)(34, 109)(35, 110)(36, 111)(37, 112)(38, 113)(39, 114)(40, 115)(41, 116)(42, 117)(43, 118)(44, 119)(45, 120)(46, 121)(47, 122)(48, 123)(49, 124)(50, 125)(51, 126)(52, 127)(53, 128)(54, 129)(55, 130)(56, 131)(57, 132)(58, 133)(59, 134)(60, 135)(61, 136)(62, 137)(63, 138)(64, 139)(65, 140)(66, 141)(67, 142)(68, 143)(69, 144)(70, 145)(71, 146)(72, 147)(73, 148)(74, 149)(75, 150)(151, 226, 152, 227, 154, 229)(153, 228, 158, 233, 160, 235)(155, 230, 163, 238, 164, 239)(156, 231, 166, 241, 168, 243)(157, 232, 169, 244, 170, 245)(159, 234, 174, 249, 175, 250)(161, 236, 177, 252, 179, 254)(162, 237, 180, 255, 172, 247)(165, 240, 184, 259, 185, 260)(167, 242, 187, 262, 188, 263)(171, 246, 192, 267, 193, 268)(173, 248, 195, 270, 191, 266)(176, 251, 200, 275, 197, 272)(178, 253, 203, 278, 204, 279)(181, 256, 206, 281, 207, 282)(182, 257, 208, 283, 189, 264)(183, 258, 202, 277, 211, 286)(186, 261, 214, 289, 194, 269)(190, 265, 218, 293, 205, 280)(196, 271, 215, 290, 221, 296)(198, 273, 213, 288, 219, 294)(199, 274, 217, 292, 212, 287)(201, 276, 223, 298, 224, 299)(209, 284, 220, 295, 216, 291)(210, 285, 225, 300, 222, 297)
	L = (1, 153)(2, 156)(3, 159)(4, 161)(5, 151)(6, 167)(7, 152)(8, 172)(9, 165)(10, 169)(11, 178)(12, 154)(13, 182)(14, 183)(15, 155)(16, 164)(17, 171)(18, 180)(19, 190)(20, 191)(21, 157)(22, 194)(23, 158)(24, 197)(25, 195)(26, 160)(27, 170)(28, 181)(29, 163)(30, 200)(31, 162)(32, 209)(33, 210)(34, 212)(35, 213)(36, 166)(37, 208)(38, 214)(39, 168)(40, 201)(41, 219)(42, 220)(43, 221)(44, 196)(45, 192)(46, 173)(47, 207)(48, 174)(49, 175)(50, 217)(51, 176)(52, 177)(53, 218)(54, 211)(55, 179)(56, 223)(57, 222)(58, 185)(59, 205)(60, 186)(61, 184)(62, 224)(63, 215)(64, 206)(65, 187)(66, 188)(67, 189)(68, 193)(69, 202)(70, 199)(71, 225)(72, 198)(73, 216)(74, 204)(75, 203)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)
	local type(s) :: { ( 6, 10 ), ( 6, 10, 6, 10, 6, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.393
Graph:: simple bipartite
	v = 100 e = 150 f = 40
	degree seq :: [ 2^75, 6^25 ]

E6.395 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 6})
Quotient :: regular
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T1^-1 * T2)^4, (T2 * T1^-2)^3 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 45, 28, 14)(9, 19, 35, 57, 37, 20)(12, 23, 34, 56, 44, 24)(16, 31, 51, 74, 53, 32)(17, 33, 54, 67, 46, 26)(21, 38, 61, 50, 30, 39)(22, 40, 48, 70, 58, 41)(27, 47, 68, 78, 55, 42)(36, 59, 52, 75, 82, 60)(43, 65, 84, 89, 69, 63)(49, 71, 76, 96, 77, 72)(62, 64, 81, 101, 103, 83)(66, 85, 87, 106, 88, 86)(73, 93, 109, 111, 95, 91)(79, 92, 97, 113, 104, 98)(80, 99, 102, 110, 94, 100)(90, 105, 107, 116, 114, 108)(112, 117, 118, 120, 119, 115)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 34)(19, 36)(20, 31)(23, 42)(24, 43)(25, 37)(28, 48)(29, 49)(32, 52)(33, 55)(35, 58)(38, 62)(39, 59)(40, 63)(41, 64)(44, 61)(45, 66)(46, 51)(47, 69)(50, 73)(53, 76)(54, 77)(56, 79)(57, 80)(60, 81)(65, 83)(67, 87)(68, 88)(70, 90)(71, 91)(72, 92)(74, 94)(75, 95)(78, 97)(82, 102)(84, 104)(85, 100)(86, 105)(89, 107)(93, 98)(96, 112)(99, 108)(101, 114)(103, 109)(106, 115)(110, 117)(111, 118)(113, 119)(116, 120)
	local type(s) :: { ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E6.396
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 20 e = 60 f = 30
	degree seq :: [ 6^20 ]

E6.396 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 6})
Quotient :: regular
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, T1 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1, (T1 * T2)^6 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 23, 19)(14, 24, 37, 25)(15, 26, 40, 27)(21, 33, 51, 34)(22, 35, 54, 36)(29, 43, 64, 44)(30, 45, 67, 46)(31, 47, 69, 48)(32, 49, 72, 50)(38, 57, 81, 58)(39, 59, 83, 60)(41, 61, 86, 62)(42, 63, 75, 52)(53, 76, 89, 77)(55, 78, 100, 79)(56, 80, 95, 70)(65, 74, 98, 90)(66, 91, 108, 92)(68, 93, 82, 94)(71, 96, 102, 87)(73, 85, 105, 97)(84, 103, 112, 104)(88, 106, 111, 107)(99, 113, 110, 114)(101, 115, 109, 116)(117, 120, 118, 119)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 31)(19, 32)(20, 28)(24, 38)(25, 39)(26, 41)(27, 42)(33, 52)(34, 53)(35, 55)(36, 56)(37, 40)(43, 65)(44, 66)(45, 68)(46, 57)(47, 70)(48, 71)(49, 73)(50, 74)(51, 54)(58, 82)(59, 84)(60, 85)(61, 87)(62, 88)(63, 89)(64, 67)(69, 72)(75, 86)(76, 99)(77, 93)(78, 92)(79, 101)(80, 102)(81, 83)(90, 105)(91, 109)(94, 110)(95, 100)(96, 111)(97, 112)(98, 108)(103, 107)(104, 117)(106, 118)(113, 116)(114, 119)(115, 120)
	local type(s) :: { ( 6^4 ) }
Outer automorphisms :: reflexible
Dual of E6.395
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 30 e = 60 f = 20
	degree seq :: [ 4^30 ]

E6.397 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2, (T1 * T2)^6 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 35, 22)(15, 26, 20, 27)(23, 37, 55, 38)(25, 39, 58, 40)(28, 43, 65, 44)(30, 45, 68, 46)(31, 47, 69, 48)(33, 49, 72, 50)(34, 51, 75, 52)(36, 53, 78, 54)(41, 60, 85, 61)(42, 62, 88, 63)(56, 79, 77, 80)(57, 81, 102, 82)(59, 83, 104, 84)(64, 89, 107, 90)(66, 91, 109, 92)(67, 93, 70, 94)(71, 95, 111, 96)(73, 97, 106, 87)(74, 86, 105, 98)(76, 99, 114, 100)(101, 115, 110, 116)(103, 117, 108, 118)(112, 119, 113, 120)(121, 122)(123, 127)(124, 129)(125, 130)(126, 132)(128, 135)(131, 140)(133, 143)(134, 145)(136, 148)(137, 150)(138, 151)(139, 153)(141, 154)(142, 156)(144, 149)(146, 161)(147, 162)(152, 155)(157, 174)(158, 176)(159, 177)(160, 179)(163, 184)(164, 186)(165, 187)(166, 167)(168, 190)(169, 191)(170, 193)(171, 194)(172, 196)(173, 197)(175, 178)(180, 204)(181, 206)(182, 207)(183, 209)(185, 188)(189, 192)(195, 198)(199, 221)(200, 213)(201, 212)(202, 223)(203, 218)(205, 208)(210, 217)(211, 228)(214, 230)(215, 220)(216, 232)(219, 233)(222, 224)(225, 234)(226, 231)(227, 229)(235, 238)(236, 240)(237, 239)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 12, 12 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E6.401
Transitivity :: ET+
Graph:: simple bipartite
	v = 90 e = 120 f = 20
	degree seq :: [ 2^60, 4^30 ]

E6.398 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1 * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1)^3, T2^6 ]
Map:: polyhedral non-degenerate
	R = (1, 3, 10, 24, 14, 5)(2, 7, 17, 35, 20, 8)(4, 12, 26, 41, 22, 9)(6, 15, 30, 51, 33, 16)(11, 19, 37, 59, 43, 23)(13, 28, 48, 70, 46, 27)(18, 32, 53, 76, 56, 34)(21, 39, 61, 73, 50, 31)(25, 40, 63, 85, 68, 44)(29, 45, 66, 81, 57, 36)(38, 58, 79, 95, 74, 52)(42, 65, 87, 102, 83, 62)(47, 54, 75, 93, 84, 64)(49, 55, 78, 97, 91, 71)(60, 72, 92, 107, 100, 82)(67, 89, 105, 115, 104, 88)(69, 90, 106, 110, 96, 77)(80, 99, 112, 118, 111, 98)(86, 101, 113, 119, 114, 103)(94, 109, 117, 120, 116, 108)(121, 122, 126, 124)(123, 129, 141, 131)(125, 133, 138, 127)(128, 139, 151, 135)(130, 143, 162, 145)(132, 136, 152, 147)(134, 149, 169, 148)(137, 154, 175, 156)(140, 158, 180, 157)(142, 160, 182, 159)(144, 164, 187, 165)(146, 166, 189, 167)(150, 170, 192, 172)(153, 174, 197, 173)(155, 177, 200, 178)(161, 184, 206, 183)(163, 186, 208, 185)(168, 191, 209, 188)(171, 194, 214, 195)(176, 199, 218, 198)(179, 202, 219, 201)(181, 203, 221, 204)(190, 205, 223, 210)(193, 213, 228, 212)(196, 216, 229, 215)(207, 224, 232, 220)(211, 226, 234, 225)(217, 231, 237, 230)(222, 227, 236, 233)(235, 239, 240, 238)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 4^4 ), ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E6.402
Transitivity :: ET+
Graph:: simple bipartite
	v = 50 e = 120 f = 60
	degree seq :: [ 4^30, 6^20 ]

E6.399 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T2 * T1^-2)^3 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 34)(19, 36)(20, 31)(23, 42)(24, 43)(25, 37)(28, 48)(29, 49)(32, 52)(33, 55)(35, 58)(38, 62)(39, 59)(40, 63)(41, 64)(44, 61)(45, 66)(46, 51)(47, 69)(50, 73)(53, 76)(54, 77)(56, 79)(57, 80)(60, 81)(65, 83)(67, 87)(68, 88)(70, 90)(71, 91)(72, 92)(74, 94)(75, 95)(78, 97)(82, 102)(84, 104)(85, 100)(86, 105)(89, 107)(93, 98)(96, 112)(99, 108)(101, 114)(103, 109)(106, 115)(110, 117)(111, 118)(113, 119)(116, 120)(121, 122, 125, 131, 130, 124)(123, 127, 135, 149, 138, 128)(126, 133, 145, 165, 148, 134)(129, 139, 155, 177, 157, 140)(132, 143, 154, 176, 164, 144)(136, 151, 171, 194, 173, 152)(137, 153, 174, 187, 166, 146)(141, 158, 181, 170, 150, 159)(142, 160, 168, 190, 178, 161)(147, 167, 188, 198, 175, 162)(156, 179, 172, 195, 202, 180)(163, 185, 204, 209, 189, 183)(169, 191, 196, 216, 197, 192)(182, 184, 201, 221, 223, 203)(186, 205, 207, 226, 208, 206)(193, 213, 229, 231, 215, 211)(199, 212, 217, 233, 224, 218)(200, 219, 222, 230, 214, 220)(210, 225, 227, 236, 234, 228)(232, 237, 238, 240, 239, 235)
	L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)
	local type(s) :: { ( 8, 8 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E6.400
Transitivity :: ET+
Graph:: simple bipartite
	v = 80 e = 120 f = 30
	degree seq :: [ 2^60, 6^20 ]

E6.400 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2, (T1 * T2)^6 ]
Map::
	R = (1, 121, 3, 123, 8, 128, 4, 124)(2, 122, 5, 125, 11, 131, 6, 126)(7, 127, 13, 133, 24, 144, 14, 134)(9, 129, 16, 136, 29, 149, 17, 137)(10, 130, 18, 138, 32, 152, 19, 139)(12, 132, 21, 141, 35, 155, 22, 142)(15, 135, 26, 146, 20, 140, 27, 147)(23, 143, 37, 157, 55, 175, 38, 158)(25, 145, 39, 159, 58, 178, 40, 160)(28, 148, 43, 163, 65, 185, 44, 164)(30, 150, 45, 165, 68, 188, 46, 166)(31, 151, 47, 167, 69, 189, 48, 168)(33, 153, 49, 169, 72, 192, 50, 170)(34, 154, 51, 171, 75, 195, 52, 172)(36, 156, 53, 173, 78, 198, 54, 174)(41, 161, 60, 180, 85, 205, 61, 181)(42, 162, 62, 182, 88, 208, 63, 183)(56, 176, 79, 199, 77, 197, 80, 200)(57, 177, 81, 201, 102, 222, 82, 202)(59, 179, 83, 203, 104, 224, 84, 204)(64, 184, 89, 209, 107, 227, 90, 210)(66, 186, 91, 211, 109, 229, 92, 212)(67, 187, 93, 213, 70, 190, 94, 214)(71, 191, 95, 215, 111, 231, 96, 216)(73, 193, 97, 217, 106, 226, 87, 207)(74, 194, 86, 206, 105, 225, 98, 218)(76, 196, 99, 219, 114, 234, 100, 220)(101, 221, 115, 235, 110, 230, 116, 236)(103, 223, 117, 237, 108, 228, 118, 238)(112, 232, 119, 239, 113, 233, 120, 240)
	L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 130)(6, 132)(7, 123)(8, 135)(9, 124)(10, 125)(11, 140)(12, 126)(13, 143)(14, 145)(15, 128)(16, 148)(17, 150)(18, 151)(19, 153)(20, 131)(21, 154)(22, 156)(23, 133)(24, 149)(25, 134)(26, 161)(27, 162)(28, 136)(29, 144)(30, 137)(31, 138)(32, 155)(33, 139)(34, 141)(35, 152)(36, 142)(37, 174)(38, 176)(39, 177)(40, 179)(41, 146)(42, 147)(43, 184)(44, 186)(45, 187)(46, 167)(47, 166)(48, 190)(49, 191)(50, 193)(51, 194)(52, 196)(53, 197)(54, 157)(55, 178)(56, 158)(57, 159)(58, 175)(59, 160)(60, 204)(61, 206)(62, 207)(63, 209)(64, 163)(65, 188)(66, 164)(67, 165)(68, 185)(69, 192)(70, 168)(71, 169)(72, 189)(73, 170)(74, 171)(75, 198)(76, 172)(77, 173)(78, 195)(79, 221)(80, 213)(81, 212)(82, 223)(83, 218)(84, 180)(85, 208)(86, 181)(87, 182)(88, 205)(89, 183)(90, 217)(91, 228)(92, 201)(93, 200)(94, 230)(95, 220)(96, 232)(97, 210)(98, 203)(99, 233)(100, 215)(101, 199)(102, 224)(103, 202)(104, 222)(105, 234)(106, 231)(107, 229)(108, 211)(109, 227)(110, 214)(111, 226)(112, 216)(113, 219)(114, 225)(115, 238)(116, 240)(117, 239)(118, 235)(119, 237)(120, 236)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.399
Transitivity :: ET+ VT+ AT
Graph::
	v = 30 e = 120 f = 80
	degree seq :: [ 8^30 ]

E6.401 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (T1 * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1)^3, T2^6 ]
Map::
	R = (1, 121, 3, 123, 10, 130, 24, 144, 14, 134, 5, 125)(2, 122, 7, 127, 17, 137, 35, 155, 20, 140, 8, 128)(4, 124, 12, 132, 26, 146, 41, 161, 22, 142, 9, 129)(6, 126, 15, 135, 30, 150, 51, 171, 33, 153, 16, 136)(11, 131, 19, 139, 37, 157, 59, 179, 43, 163, 23, 143)(13, 133, 28, 148, 48, 168, 70, 190, 46, 166, 27, 147)(18, 138, 32, 152, 53, 173, 76, 196, 56, 176, 34, 154)(21, 141, 39, 159, 61, 181, 73, 193, 50, 170, 31, 151)(25, 145, 40, 160, 63, 183, 85, 205, 68, 188, 44, 164)(29, 149, 45, 165, 66, 186, 81, 201, 57, 177, 36, 156)(38, 158, 58, 178, 79, 199, 95, 215, 74, 194, 52, 172)(42, 162, 65, 185, 87, 207, 102, 222, 83, 203, 62, 182)(47, 167, 54, 174, 75, 195, 93, 213, 84, 204, 64, 184)(49, 169, 55, 175, 78, 198, 97, 217, 91, 211, 71, 191)(60, 180, 72, 192, 92, 212, 107, 227, 100, 220, 82, 202)(67, 187, 89, 209, 105, 225, 115, 235, 104, 224, 88, 208)(69, 189, 90, 210, 106, 226, 110, 230, 96, 216, 77, 197)(80, 200, 99, 219, 112, 232, 118, 238, 111, 231, 98, 218)(86, 206, 101, 221, 113, 233, 119, 239, 114, 234, 103, 223)(94, 214, 109, 229, 117, 237, 120, 240, 116, 236, 108, 228)
	L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 133)(6, 124)(7, 125)(8, 139)(9, 141)(10, 143)(11, 123)(12, 136)(13, 138)(14, 149)(15, 128)(16, 152)(17, 154)(18, 127)(19, 151)(20, 158)(21, 131)(22, 160)(23, 162)(24, 164)(25, 130)(26, 166)(27, 132)(28, 134)(29, 169)(30, 170)(31, 135)(32, 147)(33, 174)(34, 175)(35, 177)(36, 137)(37, 140)(38, 180)(39, 142)(40, 182)(41, 184)(42, 145)(43, 186)(44, 187)(45, 144)(46, 189)(47, 146)(48, 191)(49, 148)(50, 192)(51, 194)(52, 150)(53, 153)(54, 197)(55, 156)(56, 199)(57, 200)(58, 155)(59, 202)(60, 157)(61, 203)(62, 159)(63, 161)(64, 206)(65, 163)(66, 208)(67, 165)(68, 168)(69, 167)(70, 205)(71, 209)(72, 172)(73, 213)(74, 214)(75, 171)(76, 216)(77, 173)(78, 176)(79, 218)(80, 178)(81, 179)(82, 219)(83, 221)(84, 181)(85, 223)(86, 183)(87, 224)(88, 185)(89, 188)(90, 190)(91, 226)(92, 193)(93, 228)(94, 195)(95, 196)(96, 229)(97, 231)(98, 198)(99, 201)(100, 207)(101, 204)(102, 227)(103, 210)(104, 232)(105, 211)(106, 234)(107, 236)(108, 212)(109, 215)(110, 217)(111, 237)(112, 220)(113, 222)(114, 225)(115, 239)(116, 233)(117, 230)(118, 235)(119, 240)(120, 238)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.397
Transitivity :: ET+ VT+ AT
Graph::
	v = 20 e = 120 f = 90
	degree seq :: [ 12^20 ]

E6.402 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T2 * T1^-2)^3 ]
Map:: polyhedral non-degenerate
	R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 12, 132)(7, 127, 16, 136)(8, 128, 17, 137)(10, 130, 21, 141)(11, 131, 22, 142)(13, 133, 26, 146)(14, 134, 27, 147)(15, 135, 30, 150)(18, 138, 34, 154)(19, 139, 36, 156)(20, 140, 31, 151)(23, 143, 42, 162)(24, 144, 43, 163)(25, 145, 37, 157)(28, 148, 48, 168)(29, 149, 49, 169)(32, 152, 52, 172)(33, 153, 55, 175)(35, 155, 58, 178)(38, 158, 62, 182)(39, 159, 59, 179)(40, 160, 63, 183)(41, 161, 64, 184)(44, 164, 61, 181)(45, 165, 66, 186)(46, 166, 51, 171)(47, 167, 69, 189)(50, 170, 73, 193)(53, 173, 76, 196)(54, 174, 77, 197)(56, 176, 79, 199)(57, 177, 80, 200)(60, 180, 81, 201)(65, 185, 83, 203)(67, 187, 87, 207)(68, 188, 88, 208)(70, 190, 90, 210)(71, 191, 91, 211)(72, 192, 92, 212)(74, 194, 94, 214)(75, 195, 95, 215)(78, 198, 97, 217)(82, 202, 102, 222)(84, 204, 104, 224)(85, 205, 100, 220)(86, 206, 105, 225)(89, 209, 107, 227)(93, 213, 98, 218)(96, 216, 112, 232)(99, 219, 108, 228)(101, 221, 114, 234)(103, 223, 109, 229)(106, 226, 115, 235)(110, 230, 117, 237)(111, 231, 118, 238)(113, 233, 119, 239)(116, 236, 120, 240)
	L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 139)(10, 124)(11, 130)(12, 143)(13, 145)(14, 126)(15, 149)(16, 151)(17, 153)(18, 128)(19, 155)(20, 129)(21, 158)(22, 160)(23, 154)(24, 132)(25, 165)(26, 137)(27, 167)(28, 134)(29, 138)(30, 159)(31, 171)(32, 136)(33, 174)(34, 176)(35, 177)(36, 179)(37, 140)(38, 181)(39, 141)(40, 168)(41, 142)(42, 147)(43, 185)(44, 144)(45, 148)(46, 146)(47, 188)(48, 190)(49, 191)(50, 150)(51, 194)(52, 195)(53, 152)(54, 187)(55, 162)(56, 164)(57, 157)(58, 161)(59, 172)(60, 156)(61, 170)(62, 184)(63, 163)(64, 201)(65, 204)(66, 205)(67, 166)(68, 198)(69, 183)(70, 178)(71, 196)(72, 169)(73, 213)(74, 173)(75, 202)(76, 216)(77, 192)(78, 175)(79, 212)(80, 219)(81, 221)(82, 180)(83, 182)(84, 209)(85, 207)(86, 186)(87, 226)(88, 206)(89, 189)(90, 225)(91, 193)(92, 217)(93, 229)(94, 220)(95, 211)(96, 197)(97, 233)(98, 199)(99, 222)(100, 200)(101, 223)(102, 230)(103, 203)(104, 218)(105, 227)(106, 208)(107, 236)(108, 210)(109, 231)(110, 214)(111, 215)(112, 237)(113, 224)(114, 228)(115, 232)(116, 234)(117, 238)(118, 240)(119, 235)(120, 239)
	local type(s) :: { ( 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.398
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 60 e = 120 f = 50
	degree seq :: [ 4^60 ]

E6.403 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2, (Y1 * Y2)^6, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 10, 130)(6, 126, 12, 132)(8, 128, 15, 135)(11, 131, 20, 140)(13, 133, 23, 143)(14, 134, 25, 145)(16, 136, 28, 148)(17, 137, 30, 150)(18, 138, 31, 151)(19, 139, 33, 153)(21, 141, 34, 154)(22, 142, 36, 156)(24, 144, 29, 149)(26, 146, 41, 161)(27, 147, 42, 162)(32, 152, 35, 155)(37, 157, 54, 174)(38, 158, 56, 176)(39, 159, 57, 177)(40, 160, 59, 179)(43, 163, 64, 184)(44, 164, 66, 186)(45, 165, 67, 187)(46, 166, 47, 167)(48, 168, 70, 190)(49, 169, 71, 191)(50, 170, 73, 193)(51, 171, 74, 194)(52, 172, 76, 196)(53, 173, 77, 197)(55, 175, 58, 178)(60, 180, 84, 204)(61, 181, 86, 206)(62, 182, 87, 207)(63, 183, 89, 209)(65, 185, 68, 188)(69, 189, 72, 192)(75, 195, 78, 198)(79, 199, 101, 221)(80, 200, 93, 213)(81, 201, 92, 212)(82, 202, 103, 223)(83, 203, 98, 218)(85, 205, 88, 208)(90, 210, 97, 217)(91, 211, 108, 228)(94, 214, 110, 230)(95, 215, 100, 220)(96, 216, 112, 232)(99, 219, 113, 233)(102, 222, 104, 224)(105, 225, 114, 234)(106, 226, 111, 231)(107, 227, 109, 229)(115, 235, 118, 238)(116, 236, 120, 240)(117, 237, 119, 239)(241, 361, 243, 363, 248, 368, 244, 364)(242, 362, 245, 365, 251, 371, 246, 366)(247, 367, 253, 373, 264, 384, 254, 374)(249, 369, 256, 376, 269, 389, 257, 377)(250, 370, 258, 378, 272, 392, 259, 379)(252, 372, 261, 381, 275, 395, 262, 382)(255, 375, 266, 386, 260, 380, 267, 387)(263, 383, 277, 397, 295, 415, 278, 398)(265, 385, 279, 399, 298, 418, 280, 400)(268, 388, 283, 403, 305, 425, 284, 404)(270, 390, 285, 405, 308, 428, 286, 406)(271, 391, 287, 407, 309, 429, 288, 408)(273, 393, 289, 409, 312, 432, 290, 410)(274, 394, 291, 411, 315, 435, 292, 412)(276, 396, 293, 413, 318, 438, 294, 414)(281, 401, 300, 420, 325, 445, 301, 421)(282, 402, 302, 422, 328, 448, 303, 423)(296, 416, 319, 439, 317, 437, 320, 440)(297, 417, 321, 441, 342, 462, 322, 442)(299, 419, 323, 443, 344, 464, 324, 444)(304, 424, 329, 449, 347, 467, 330, 450)(306, 426, 331, 451, 349, 469, 332, 452)(307, 427, 333, 453, 310, 430, 334, 454)(311, 431, 335, 455, 351, 471, 336, 456)(313, 433, 337, 457, 346, 466, 327, 447)(314, 434, 326, 446, 345, 465, 338, 458)(316, 436, 339, 459, 354, 474, 340, 460)(341, 461, 355, 475, 350, 470, 356, 476)(343, 463, 357, 477, 348, 468, 358, 478)(352, 472, 359, 479, 353, 473, 360, 480)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 250)(6, 252)(7, 243)(8, 255)(9, 244)(10, 245)(11, 260)(12, 246)(13, 263)(14, 265)(15, 248)(16, 268)(17, 270)(18, 271)(19, 273)(20, 251)(21, 274)(22, 276)(23, 253)(24, 269)(25, 254)(26, 281)(27, 282)(28, 256)(29, 264)(30, 257)(31, 258)(32, 275)(33, 259)(34, 261)(35, 272)(36, 262)(37, 294)(38, 296)(39, 297)(40, 299)(41, 266)(42, 267)(43, 304)(44, 306)(45, 307)(46, 287)(47, 286)(48, 310)(49, 311)(50, 313)(51, 314)(52, 316)(53, 317)(54, 277)(55, 298)(56, 278)(57, 279)(58, 295)(59, 280)(60, 324)(61, 326)(62, 327)(63, 329)(64, 283)(65, 308)(66, 284)(67, 285)(68, 305)(69, 312)(70, 288)(71, 289)(72, 309)(73, 290)(74, 291)(75, 318)(76, 292)(77, 293)(78, 315)(79, 341)(80, 333)(81, 332)(82, 343)(83, 338)(84, 300)(85, 328)(86, 301)(87, 302)(88, 325)(89, 303)(90, 337)(91, 348)(92, 321)(93, 320)(94, 350)(95, 340)(96, 352)(97, 330)(98, 323)(99, 353)(100, 335)(101, 319)(102, 344)(103, 322)(104, 342)(105, 354)(106, 351)(107, 349)(108, 331)(109, 347)(110, 334)(111, 346)(112, 336)(113, 339)(114, 345)(115, 358)(116, 360)(117, 359)(118, 355)(119, 357)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.406
Graph:: bipartite
	v = 90 e = 240 f = 140
	degree seq :: [ 4^60, 8^30 ]

E6.404 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1^-1)^3, Y2^6 ]
Map::
	R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 21, 141, 11, 131)(5, 125, 13, 133, 18, 138, 7, 127)(8, 128, 19, 139, 31, 151, 15, 135)(10, 130, 23, 143, 42, 162, 25, 145)(12, 132, 16, 136, 32, 152, 27, 147)(14, 134, 29, 149, 49, 169, 28, 148)(17, 137, 34, 154, 55, 175, 36, 156)(20, 140, 38, 158, 60, 180, 37, 157)(22, 142, 40, 160, 62, 182, 39, 159)(24, 144, 44, 164, 67, 187, 45, 165)(26, 146, 46, 166, 69, 189, 47, 167)(30, 150, 50, 170, 72, 192, 52, 172)(33, 153, 54, 174, 77, 197, 53, 173)(35, 155, 57, 177, 80, 200, 58, 178)(41, 161, 64, 184, 86, 206, 63, 183)(43, 163, 66, 186, 88, 208, 65, 185)(48, 168, 71, 191, 89, 209, 68, 188)(51, 171, 74, 194, 94, 214, 75, 195)(56, 176, 79, 199, 98, 218, 78, 198)(59, 179, 82, 202, 99, 219, 81, 201)(61, 181, 83, 203, 101, 221, 84, 204)(70, 190, 85, 205, 103, 223, 90, 210)(73, 193, 93, 213, 108, 228, 92, 212)(76, 196, 96, 216, 109, 229, 95, 215)(87, 207, 104, 224, 112, 232, 100, 220)(91, 211, 106, 226, 114, 234, 105, 225)(97, 217, 111, 231, 117, 237, 110, 230)(102, 222, 107, 227, 116, 236, 113, 233)(115, 235, 119, 239, 120, 240, 118, 238)(241, 361, 243, 363, 250, 370, 264, 384, 254, 374, 245, 365)(242, 362, 247, 367, 257, 377, 275, 395, 260, 380, 248, 368)(244, 364, 252, 372, 266, 386, 281, 401, 262, 382, 249, 369)(246, 366, 255, 375, 270, 390, 291, 411, 273, 393, 256, 376)(251, 371, 259, 379, 277, 397, 299, 419, 283, 403, 263, 383)(253, 373, 268, 388, 288, 408, 310, 430, 286, 406, 267, 387)(258, 378, 272, 392, 293, 413, 316, 436, 296, 416, 274, 394)(261, 381, 279, 399, 301, 421, 313, 433, 290, 410, 271, 391)(265, 385, 280, 400, 303, 423, 325, 445, 308, 428, 284, 404)(269, 389, 285, 405, 306, 426, 321, 441, 297, 417, 276, 396)(278, 398, 298, 418, 319, 439, 335, 455, 314, 434, 292, 412)(282, 402, 305, 425, 327, 447, 342, 462, 323, 443, 302, 422)(287, 407, 294, 414, 315, 435, 333, 453, 324, 444, 304, 424)(289, 409, 295, 415, 318, 438, 337, 457, 331, 451, 311, 431)(300, 420, 312, 432, 332, 452, 347, 467, 340, 460, 322, 442)(307, 427, 329, 449, 345, 465, 355, 475, 344, 464, 328, 448)(309, 429, 330, 450, 346, 466, 350, 470, 336, 456, 317, 437)(320, 440, 339, 459, 352, 472, 358, 478, 351, 471, 338, 458)(326, 446, 341, 461, 353, 473, 359, 479, 354, 474, 343, 463)(334, 454, 349, 469, 357, 477, 360, 480, 356, 476, 348, 468)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 264)(11, 259)(12, 266)(13, 268)(14, 245)(15, 270)(16, 246)(17, 275)(18, 272)(19, 277)(20, 248)(21, 279)(22, 249)(23, 251)(24, 254)(25, 280)(26, 281)(27, 253)(28, 288)(29, 285)(30, 291)(31, 261)(32, 293)(33, 256)(34, 258)(35, 260)(36, 269)(37, 299)(38, 298)(39, 301)(40, 303)(41, 262)(42, 305)(43, 263)(44, 265)(45, 306)(46, 267)(47, 294)(48, 310)(49, 295)(50, 271)(51, 273)(52, 278)(53, 316)(54, 315)(55, 318)(56, 274)(57, 276)(58, 319)(59, 283)(60, 312)(61, 313)(62, 282)(63, 325)(64, 287)(65, 327)(66, 321)(67, 329)(68, 284)(69, 330)(70, 286)(71, 289)(72, 332)(73, 290)(74, 292)(75, 333)(76, 296)(77, 309)(78, 337)(79, 335)(80, 339)(81, 297)(82, 300)(83, 302)(84, 304)(85, 308)(86, 341)(87, 342)(88, 307)(89, 345)(90, 346)(91, 311)(92, 347)(93, 324)(94, 349)(95, 314)(96, 317)(97, 331)(98, 320)(99, 352)(100, 322)(101, 353)(102, 323)(103, 326)(104, 328)(105, 355)(106, 350)(107, 340)(108, 334)(109, 357)(110, 336)(111, 338)(112, 358)(113, 359)(114, 343)(115, 344)(116, 348)(117, 360)(118, 351)(119, 354)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.405
Graph:: bipartite
	v = 50 e = 240 f = 180
	degree seq :: [ 8^30, 12^20 ]

E6.405 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, (Y2 * Y3)^4, (Y2 * Y3^-2)^3, (Y3 * Y2 * Y3^-2 * Y2 * Y3)^2, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	R = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(241, 361, 242, 362)(243, 363, 247, 367)(244, 364, 249, 369)(245, 365, 251, 371)(246, 366, 253, 373)(248, 368, 257, 377)(250, 370, 261, 381)(252, 372, 264, 384)(254, 374, 268, 388)(255, 375, 267, 387)(256, 376, 270, 390)(258, 378, 274, 394)(259, 379, 275, 395)(260, 380, 262, 382)(263, 383, 281, 401)(265, 385, 284, 404)(266, 386, 285, 405)(269, 389, 277, 397)(271, 391, 292, 412)(272, 392, 291, 411)(273, 393, 293, 413)(276, 396, 299, 419)(278, 398, 301, 421)(279, 399, 297, 417)(280, 400, 287, 407)(282, 402, 305, 425)(283, 403, 306, 426)(286, 406, 310, 430)(288, 408, 312, 432)(289, 409, 313, 433)(290, 410, 314, 434)(294, 414, 302, 422)(295, 415, 318, 438)(296, 416, 319, 439)(298, 418, 320, 440)(300, 420, 322, 442)(303, 423, 324, 444)(304, 424, 325, 445)(307, 427, 328, 448)(308, 428, 329, 449)(309, 429, 330, 450)(311, 431, 331, 451)(315, 435, 336, 456)(316, 436, 337, 457)(317, 437, 323, 443)(321, 441, 340, 460)(326, 446, 346, 466)(327, 447, 332, 452)(333, 453, 342, 462)(334, 454, 351, 471)(335, 455, 352, 472)(338, 458, 350, 470)(339, 459, 354, 474)(341, 461, 353, 473)(343, 463, 347, 467)(344, 464, 355, 475)(345, 465, 356, 476)(348, 468, 358, 478)(349, 469, 357, 477)(359, 479, 360, 480)
	L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 258)(9, 259)(10, 244)(11, 262)(12, 265)(13, 266)(14, 246)(15, 269)(16, 247)(17, 272)(18, 250)(19, 276)(20, 249)(21, 278)(22, 280)(23, 251)(24, 279)(25, 254)(26, 286)(27, 253)(28, 288)(29, 289)(30, 290)(31, 256)(32, 268)(33, 257)(34, 295)(35, 297)(36, 300)(37, 260)(38, 302)(39, 261)(40, 303)(41, 304)(42, 263)(43, 264)(44, 307)(45, 291)(46, 311)(47, 267)(48, 294)(49, 271)(50, 315)(51, 270)(52, 316)(53, 317)(54, 273)(55, 292)(56, 274)(57, 281)(58, 275)(59, 296)(60, 277)(61, 319)(62, 283)(63, 282)(64, 321)(65, 326)(66, 327)(67, 305)(68, 284)(69, 285)(70, 308)(71, 287)(72, 329)(73, 333)(74, 318)(75, 309)(76, 299)(77, 338)(78, 293)(79, 320)(80, 339)(81, 298)(82, 341)(83, 301)(84, 342)(85, 328)(86, 310)(87, 347)(88, 306)(89, 330)(90, 348)(91, 349)(92, 312)(93, 331)(94, 313)(95, 314)(96, 334)(97, 351)(98, 335)(99, 343)(100, 344)(101, 340)(102, 322)(103, 323)(104, 324)(105, 325)(106, 355)(107, 345)(108, 350)(109, 336)(110, 332)(111, 352)(112, 359)(113, 337)(114, 353)(115, 356)(116, 360)(117, 346)(118, 357)(119, 354)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.404
Graph:: simple bipartite
	v = 180 e = 240 f = 50
	degree seq :: [ 2^120, 4^60 ]

E6.406 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^6, (Y3 * Y1^-1)^4, (Y1^2 * Y3)^3 ]
Map:: polytopal
	R = (1, 121, 2, 122, 5, 125, 11, 131, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 29, 149, 18, 138, 8, 128)(6, 126, 13, 133, 25, 145, 45, 165, 28, 148, 14, 134)(9, 129, 19, 139, 35, 155, 57, 177, 37, 157, 20, 140)(12, 132, 23, 143, 34, 154, 56, 176, 44, 164, 24, 144)(16, 136, 31, 151, 51, 171, 74, 194, 53, 173, 32, 152)(17, 137, 33, 153, 54, 174, 67, 187, 46, 166, 26, 146)(21, 141, 38, 158, 61, 181, 50, 170, 30, 150, 39, 159)(22, 142, 40, 160, 48, 168, 70, 190, 58, 178, 41, 161)(27, 147, 47, 167, 68, 188, 78, 198, 55, 175, 42, 162)(36, 156, 59, 179, 52, 172, 75, 195, 82, 202, 60, 180)(43, 163, 65, 185, 84, 204, 89, 209, 69, 189, 63, 183)(49, 169, 71, 191, 76, 196, 96, 216, 77, 197, 72, 192)(62, 182, 64, 184, 81, 201, 101, 221, 103, 223, 83, 203)(66, 186, 85, 205, 87, 207, 106, 226, 88, 208, 86, 206)(73, 193, 93, 213, 109, 229, 111, 231, 95, 215, 91, 211)(79, 199, 92, 212, 97, 217, 113, 233, 104, 224, 98, 218)(80, 200, 99, 219, 102, 222, 110, 230, 94, 214, 100, 220)(90, 210, 105, 225, 107, 227, 116, 236, 114, 234, 108, 228)(112, 232, 117, 237, 118, 238, 120, 240, 119, 239, 115, 235)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480)
	L = (1, 243)(2, 246)(3, 241)(4, 249)(5, 252)(6, 242)(7, 256)(8, 257)(9, 244)(10, 261)(11, 262)(12, 245)(13, 266)(14, 267)(15, 270)(16, 247)(17, 248)(18, 274)(19, 276)(20, 271)(21, 250)(22, 251)(23, 282)(24, 283)(25, 277)(26, 253)(27, 254)(28, 288)(29, 289)(30, 255)(31, 260)(32, 292)(33, 295)(34, 258)(35, 298)(36, 259)(37, 265)(38, 302)(39, 299)(40, 303)(41, 304)(42, 263)(43, 264)(44, 301)(45, 306)(46, 291)(47, 309)(48, 268)(49, 269)(50, 313)(51, 286)(52, 272)(53, 316)(54, 317)(55, 273)(56, 319)(57, 320)(58, 275)(59, 279)(60, 321)(61, 284)(62, 278)(63, 280)(64, 281)(65, 323)(66, 285)(67, 327)(68, 328)(69, 287)(70, 330)(71, 331)(72, 332)(73, 290)(74, 334)(75, 335)(76, 293)(77, 294)(78, 337)(79, 296)(80, 297)(81, 300)(82, 342)(83, 305)(84, 344)(85, 340)(86, 345)(87, 307)(88, 308)(89, 347)(90, 310)(91, 311)(92, 312)(93, 338)(94, 314)(95, 315)(96, 352)(97, 318)(98, 333)(99, 348)(100, 325)(101, 354)(102, 322)(103, 349)(104, 324)(105, 326)(106, 355)(107, 329)(108, 339)(109, 343)(110, 357)(111, 358)(112, 336)(113, 359)(114, 341)(115, 346)(116, 360)(117, 350)(118, 351)(119, 353)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.403
Graph:: simple bipartite
	v = 140 e = 240 f = 90
	degree seq :: [ 2^120, 12^20 ]

E6.407 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y1 * Y2)^4, (Y3 * Y2^-1)^4, (Y1 * Y2^-2)^3, (Y2 * Y1 * Y2^-2 * Y1 * Y2)^2 ]
Map::
	R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 17, 137)(10, 130, 21, 141)(12, 132, 24, 144)(14, 134, 28, 148)(15, 135, 27, 147)(16, 136, 30, 150)(18, 138, 34, 154)(19, 139, 35, 155)(20, 140, 22, 142)(23, 143, 41, 161)(25, 145, 44, 164)(26, 146, 45, 165)(29, 149, 37, 157)(31, 151, 52, 172)(32, 152, 51, 171)(33, 153, 53, 173)(36, 156, 59, 179)(38, 158, 61, 181)(39, 159, 57, 177)(40, 160, 47, 167)(42, 162, 65, 185)(43, 163, 66, 186)(46, 166, 70, 190)(48, 168, 72, 192)(49, 169, 73, 193)(50, 170, 74, 194)(54, 174, 62, 182)(55, 175, 78, 198)(56, 176, 79, 199)(58, 178, 80, 200)(60, 180, 82, 202)(63, 183, 84, 204)(64, 184, 85, 205)(67, 187, 88, 208)(68, 188, 89, 209)(69, 189, 90, 210)(71, 191, 91, 211)(75, 195, 96, 216)(76, 196, 97, 217)(77, 197, 83, 203)(81, 201, 100, 220)(86, 206, 106, 226)(87, 207, 92, 212)(93, 213, 102, 222)(94, 214, 111, 231)(95, 215, 112, 232)(98, 218, 110, 230)(99, 219, 114, 234)(101, 221, 113, 233)(103, 223, 107, 227)(104, 224, 115, 235)(105, 225, 116, 236)(108, 228, 118, 238)(109, 229, 117, 237)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 265, 385, 254, 374, 246, 366)(247, 367, 255, 375, 269, 389, 289, 409, 271, 391, 256, 376)(249, 369, 259, 379, 276, 396, 300, 420, 277, 397, 260, 380)(251, 371, 262, 382, 280, 400, 303, 423, 282, 402, 263, 383)(253, 373, 266, 386, 286, 406, 311, 431, 287, 407, 267, 387)(257, 377, 272, 392, 268, 388, 288, 408, 294, 414, 273, 393)(261, 381, 278, 398, 302, 422, 283, 403, 264, 384, 279, 399)(270, 390, 290, 410, 315, 435, 309, 429, 285, 405, 291, 411)(274, 394, 295, 415, 292, 412, 316, 436, 299, 419, 296, 416)(275, 395, 297, 417, 281, 401, 304, 424, 321, 441, 298, 418)(284, 404, 307, 427, 305, 425, 326, 446, 310, 430, 308, 428)(293, 413, 317, 437, 338, 458, 335, 455, 314, 434, 318, 438)(301, 421, 319, 439, 320, 440, 339, 459, 343, 463, 323, 443)(306, 426, 327, 447, 347, 467, 345, 465, 325, 445, 328, 448)(312, 432, 329, 449, 330, 450, 348, 468, 350, 470, 332, 452)(313, 433, 333, 453, 331, 451, 349, 469, 336, 456, 334, 454)(322, 442, 341, 461, 340, 460, 344, 464, 324, 444, 342, 462)(337, 457, 351, 471, 352, 472, 359, 479, 354, 474, 353, 473)(346, 466, 355, 475, 356, 476, 360, 480, 358, 478, 357, 477)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 261)(11, 245)(12, 264)(13, 246)(14, 268)(15, 267)(16, 270)(17, 248)(18, 274)(19, 275)(20, 262)(21, 250)(22, 260)(23, 281)(24, 252)(25, 284)(26, 285)(27, 255)(28, 254)(29, 277)(30, 256)(31, 292)(32, 291)(33, 293)(34, 258)(35, 259)(36, 299)(37, 269)(38, 301)(39, 297)(40, 287)(41, 263)(42, 305)(43, 306)(44, 265)(45, 266)(46, 310)(47, 280)(48, 312)(49, 313)(50, 314)(51, 272)(52, 271)(53, 273)(54, 302)(55, 318)(56, 319)(57, 279)(58, 320)(59, 276)(60, 322)(61, 278)(62, 294)(63, 324)(64, 325)(65, 282)(66, 283)(67, 328)(68, 329)(69, 330)(70, 286)(71, 331)(72, 288)(73, 289)(74, 290)(75, 336)(76, 337)(77, 323)(78, 295)(79, 296)(80, 298)(81, 340)(82, 300)(83, 317)(84, 303)(85, 304)(86, 346)(87, 332)(88, 307)(89, 308)(90, 309)(91, 311)(92, 327)(93, 342)(94, 351)(95, 352)(96, 315)(97, 316)(98, 350)(99, 354)(100, 321)(101, 353)(102, 333)(103, 347)(104, 355)(105, 356)(106, 326)(107, 343)(108, 358)(109, 357)(110, 338)(111, 334)(112, 335)(113, 341)(114, 339)(115, 344)(116, 345)(117, 349)(118, 348)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E6.408
Graph:: bipartite
	v = 80 e = 240 f = 150
	degree seq :: [ 4^60, 12^20 ]

E6.408 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = S5 (small group id <120, 34>)
Aut   = C2 x S5 (small group id <240, 189>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y1^-1)^3, (Y3 * Y2^-1)^6 ]
Map:: polytopal
	R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 21, 141, 11, 131)(5, 125, 13, 133, 18, 138, 7, 127)(8, 128, 19, 139, 31, 151, 15, 135)(10, 130, 23, 143, 42, 162, 25, 145)(12, 132, 16, 136, 32, 152, 27, 147)(14, 134, 29, 149, 49, 169, 28, 148)(17, 137, 34, 154, 55, 175, 36, 156)(20, 140, 38, 158, 60, 180, 37, 157)(22, 142, 40, 160, 62, 182, 39, 159)(24, 144, 44, 164, 67, 187, 45, 165)(26, 146, 46, 166, 69, 189, 47, 167)(30, 150, 50, 170, 72, 192, 52, 172)(33, 153, 54, 174, 77, 197, 53, 173)(35, 155, 57, 177, 80, 200, 58, 178)(41, 161, 64, 184, 86, 206, 63, 183)(43, 163, 66, 186, 88, 208, 65, 185)(48, 168, 71, 191, 89, 209, 68, 188)(51, 171, 74, 194, 94, 214, 75, 195)(56, 176, 79, 199, 98, 218, 78, 198)(59, 179, 82, 202, 99, 219, 81, 201)(61, 181, 83, 203, 101, 221, 84, 204)(70, 190, 85, 205, 103, 223, 90, 210)(73, 193, 93, 213, 108, 228, 92, 212)(76, 196, 96, 216, 109, 229, 95, 215)(87, 207, 104, 224, 112, 232, 100, 220)(91, 211, 106, 226, 114, 234, 105, 225)(97, 217, 111, 231, 117, 237, 110, 230)(102, 222, 107, 227, 116, 236, 113, 233)(115, 235, 119, 239, 120, 240, 118, 238)(241, 361)(242, 362)(243, 363)(244, 364)(245, 365)(246, 366)(247, 367)(248, 368)(249, 369)(250, 370)(251, 371)(252, 372)(253, 373)(254, 374)(255, 375)(256, 376)(257, 377)(258, 378)(259, 379)(260, 380)(261, 381)(262, 382)(263, 383)(264, 384)(265, 385)(266, 386)(267, 387)(268, 388)(269, 389)(270, 390)(271, 391)(272, 392)(273, 393)(274, 394)(275, 395)(276, 396)(277, 397)(278, 398)(279, 399)(280, 400)(281, 401)(282, 402)(283, 403)(284, 404)(285, 405)(286, 406)(287, 407)(288, 408)(289, 409)(290, 410)(291, 411)(292, 412)(293, 413)(294, 414)(295, 415)(296, 416)(297, 417)(298, 418)(299, 419)(300, 420)(301, 421)(302, 422)(303, 423)(304, 424)(305, 425)(306, 426)(307, 427)(308, 428)(309, 429)(310, 430)(311, 431)(312, 432)(313, 433)(314, 434)(315, 435)(316, 436)(317, 437)(318, 438)(319, 439)(320, 440)(321, 441)(322, 442)(323, 443)(324, 444)(325, 445)(326, 446)(327, 447)(328, 448)(329, 449)(330, 450)(331, 451)(332, 452)(333, 453)(334, 454)(335, 455)(336, 456)(337, 457)(338, 458)(339, 459)(340, 460)(341, 461)(342, 462)(343, 463)(344, 464)(345, 465)(346, 466)(347, 467)(348, 468)(349, 469)(350, 470)(351, 471)(352, 472)(353, 473)(354, 474)(355, 475)(356, 476)(357, 477)(358, 478)(359, 479)(360, 480)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 264)(11, 259)(12, 266)(13, 268)(14, 245)(15, 270)(16, 246)(17, 275)(18, 272)(19, 277)(20, 248)(21, 279)(22, 249)(23, 251)(24, 254)(25, 280)(26, 281)(27, 253)(28, 288)(29, 285)(30, 291)(31, 261)(32, 293)(33, 256)(34, 258)(35, 260)(36, 269)(37, 299)(38, 298)(39, 301)(40, 303)(41, 262)(42, 305)(43, 263)(44, 265)(45, 306)(46, 267)(47, 294)(48, 310)(49, 295)(50, 271)(51, 273)(52, 278)(53, 316)(54, 315)(55, 318)(56, 274)(57, 276)(58, 319)(59, 283)(60, 312)(61, 313)(62, 282)(63, 325)(64, 287)(65, 327)(66, 321)(67, 329)(68, 284)(69, 330)(70, 286)(71, 289)(72, 332)(73, 290)(74, 292)(75, 333)(76, 296)(77, 309)(78, 337)(79, 335)(80, 339)(81, 297)(82, 300)(83, 302)(84, 304)(85, 308)(86, 341)(87, 342)(88, 307)(89, 345)(90, 346)(91, 311)(92, 347)(93, 324)(94, 349)(95, 314)(96, 317)(97, 331)(98, 320)(99, 352)(100, 322)(101, 353)(102, 323)(103, 326)(104, 328)(105, 355)(106, 350)(107, 340)(108, 334)(109, 357)(110, 336)(111, 338)(112, 358)(113, 359)(114, 343)(115, 344)(116, 348)(117, 360)(118, 351)(119, 354)(120, 356)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480)
	local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E6.407
Graph:: simple bipartite
	v = 150 e = 240 f = 80
	degree seq :: [ 2^120, 8^30 ]

E6.409 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 3, 10})
Quotient :: regular
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2)^3, T1^10, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 5, 11, 21, 37, 36, 20, 10, 4)(3, 7, 15, 27, 47, 77, 54, 31, 17, 8)(6, 13, 25, 43, 71, 102, 76, 46, 26, 14)(9, 18, 32, 55, 85, 113, 82, 51, 29, 16)(12, 23, 41, 67, 98, 132, 101, 70, 42, 24)(19, 34, 58, 88, 121, 139, 104, 72, 57, 33)(22, 39, 65, 53, 83, 114, 131, 97, 66, 40)(28, 49, 68, 45, 74, 96, 129, 111, 81, 50)(30, 52, 69, 99, 127, 120, 87, 56, 73, 44)(35, 60, 89, 123, 145, 110, 80, 48, 79, 59)(38, 63, 94, 75, 105, 140, 147, 128, 95, 64)(61, 91, 124, 130, 148, 136, 119, 86, 118, 90)(62, 92, 125, 100, 134, 107, 143, 122, 126, 93)(78, 108, 133, 112, 141, 106, 142, 149, 144, 109)(84, 116, 135, 150, 146, 117, 138, 103, 137, 115)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 62)(40, 63)(41, 68)(42, 69)(43, 72)(46, 75)(47, 78)(50, 79)(51, 67)(52, 65)(54, 84)(55, 86)(57, 73)(58, 81)(60, 90)(64, 92)(66, 96)(70, 100)(71, 103)(74, 94)(76, 106)(77, 107)(80, 108)(82, 112)(83, 115)(85, 117)(87, 118)(88, 122)(89, 120)(91, 93)(95, 127)(97, 130)(98, 133)(99, 125)(101, 135)(102, 136)(104, 137)(105, 141)(109, 143)(110, 132)(111, 126)(113, 140)(114, 139)(116, 134)(119, 138)(121, 144)(123, 128)(124, 129)(131, 149)(142, 148)(145, 150)(146, 147)
	local type(s) :: { ( 3^10 ) }
Outer automorphisms :: reflexible
Dual of E6.410
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 15 e = 75 f = 50
	degree seq :: [ 10^15 ]

E6.410 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 3, 10})
Quotient :: regular
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1 * T2 * T1^-1)^3, (T1^-1 * T2)^10 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 37, 41)(29, 42, 43)(30, 44, 45)(35, 49, 50)(36, 47, 51)(38, 52, 53)(46, 60, 61)(48, 62, 63)(54, 69, 70)(55, 58, 71)(56, 72, 73)(57, 74, 75)(59, 76, 77)(64, 82, 83)(65, 67, 84)(66, 85, 86)(68, 87, 88)(78, 98, 99)(79, 80, 100)(81, 101, 102)(89, 110, 111)(90, 92, 112)(91, 113, 114)(93, 108, 115)(94, 116, 117)(95, 96, 118)(97, 119, 103)(104, 106, 123)(105, 124, 125)(107, 122, 126)(109, 127, 120)(121, 136, 137)(128, 130, 143)(129, 141, 144)(131, 135, 139)(132, 145, 133)(134, 146, 138)(140, 142, 147)(148, 149, 150)
	L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 21)(14, 22)(17, 27)(18, 28)(19, 29)(20, 30)(23, 35)(24, 36)(25, 37)(26, 38)(31, 46)(32, 43)(33, 47)(34, 48)(39, 54)(40, 55)(41, 56)(42, 57)(44, 58)(45, 59)(49, 64)(50, 65)(51, 66)(52, 67)(53, 68)(60, 78)(61, 79)(62, 80)(63, 81)(69, 89)(70, 90)(71, 91)(72, 92)(73, 93)(74, 94)(75, 95)(76, 96)(77, 97)(82, 103)(83, 104)(84, 105)(85, 106)(86, 107)(87, 108)(88, 109)(98, 120)(99, 117)(100, 121)(101, 122)(102, 110)(111, 128)(112, 129)(113, 130)(114, 131)(115, 132)(116, 133)(118, 134)(119, 135)(123, 138)(124, 139)(125, 140)(126, 141)(127, 142)(136, 147)(137, 143)(144, 148)(145, 149)(146, 150)
	local type(s) :: { ( 10^3 ) }
Outer automorphisms :: reflexible
Dual of E6.409
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 50 e = 75 f = 15
	degree seq :: [ 3^50 ]

E6.411 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 10})
Quotient :: edge
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1 * T2^-1)^3, (T2^-1 * T1)^10 ]
Map:: polytopal
	R = (1, 3, 4)(2, 5, 6)(7, 11, 12)(8, 13, 14)(9, 15, 16)(10, 17, 18)(19, 27, 28)(20, 29, 30)(21, 31, 32)(22, 33, 34)(23, 35, 36)(24, 37, 38)(25, 39, 40)(26, 41, 42)(43, 55, 56)(44, 47, 57)(45, 58, 59)(46, 60, 61)(48, 62, 63)(49, 64, 65)(50, 53, 66)(51, 67, 68)(52, 69, 70)(54, 71, 72)(73, 91, 92)(74, 76, 93)(75, 94, 95)(77, 96, 97)(78, 98, 99)(79, 80, 100)(81, 101, 102)(82, 103, 104)(83, 85, 105)(84, 106, 107)(86, 108, 109)(87, 110, 111)(88, 89, 112)(90, 113, 114)(115, 117, 131)(116, 132, 133)(118, 122, 134)(119, 135, 120)(121, 136, 137)(123, 125, 138)(124, 139, 140)(126, 130, 141)(127, 142, 128)(129, 143, 144)(145, 146, 147)(148, 149, 150)(151, 152)(153, 157)(154, 158)(155, 159)(156, 160)(161, 169)(162, 170)(163, 171)(164, 172)(165, 173)(166, 174)(167, 175)(168, 176)(177, 193)(178, 194)(179, 187)(180, 195)(181, 196)(182, 190)(183, 197)(184, 198)(185, 199)(186, 200)(188, 201)(189, 202)(191, 203)(192, 204)(205, 223)(206, 224)(207, 225)(208, 226)(209, 227)(210, 228)(211, 229)(212, 230)(213, 231)(214, 232)(215, 233)(216, 234)(217, 235)(218, 236)(219, 237)(220, 238)(221, 239)(222, 240)(241, 264)(242, 265)(243, 266)(244, 267)(245, 268)(246, 258)(247, 269)(248, 270)(249, 261)(250, 271)(251, 272)(252, 253)(254, 273)(255, 274)(256, 275)(257, 276)(259, 277)(260, 278)(262, 279)(263, 280)(281, 294)(282, 291)(283, 295)(284, 289)(285, 296)(286, 297)(287, 288)(290, 298)(292, 299)(293, 300)
	L = (1, 151)(2, 152)(3, 153)(4, 154)(5, 155)(6, 156)(7, 157)(8, 158)(9, 159)(10, 160)(11, 161)(12, 162)(13, 163)(14, 164)(15, 165)(16, 166)(17, 167)(18, 168)(19, 169)(20, 170)(21, 171)(22, 172)(23, 173)(24, 174)(25, 175)(26, 176)(27, 177)(28, 178)(29, 179)(30, 180)(31, 181)(32, 182)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 188)(39, 189)(40, 190)(41, 191)(42, 192)(43, 193)(44, 194)(45, 195)(46, 196)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 207)(58, 208)(59, 209)(60, 210)(61, 211)(62, 212)(63, 213)(64, 214)(65, 215)(66, 216)(67, 217)(68, 218)(69, 219)(70, 220)(71, 221)(72, 222)(73, 223)(74, 224)(75, 225)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)
	local type(s) :: { ( 20, 20 ), ( 20^3 ) }
Outer automorphisms :: reflexible
Dual of E6.415
Transitivity :: ET+
Graph:: simple bipartite
	v = 125 e = 150 f = 15
	degree seq :: [ 2^75, 3^50 ]

E6.412 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 10})
Quotient :: edge
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1^-1)^3, T2^10, T2 * T1^-1 * T2^3 * T1^-2 * T2^2 * T1^-1 * T2^-2 * T1^-1 ]
Map:: polyhedral non-degenerate
	R = (1, 3, 9, 19, 37, 64, 48, 26, 13, 5)(2, 6, 14, 27, 50, 79, 57, 32, 16, 7)(4, 11, 22, 41, 69, 90, 60, 34, 17, 8)(10, 21, 40, 67, 98, 124, 92, 61, 35, 18)(12, 23, 43, 71, 103, 133, 105, 72, 44, 24)(15, 29, 53, 81, 114, 141, 115, 82, 54, 30)(20, 39, 31, 55, 83, 116, 126, 93, 62, 36)(25, 45, 73, 106, 134, 130, 100, 68, 42, 46)(28, 52, 33, 58, 87, 119, 137, 109, 77, 49)(38, 66, 59, 88, 120, 144, 147, 127, 94, 63)(47, 74, 107, 136, 149, 138, 110, 78, 51, 75)(56, 84, 117, 143, 150, 148, 131, 101, 70, 85)(65, 97, 91, 118, 86, 112, 140, 135, 128, 95)(76, 96, 129, 125, 146, 123, 102, 132, 104, 108)(80, 113, 99, 122, 89, 121, 145, 142, 139, 111)(151, 152, 154)(153, 158, 160)(155, 162, 156)(157, 165, 161)(159, 168, 170)(163, 175, 173)(164, 174, 178)(166, 181, 179)(167, 183, 171)(169, 186, 188)(172, 180, 192)(176, 197, 195)(177, 199, 201)(182, 206, 205)(184, 209, 208)(185, 203, 189)(187, 213, 215)(190, 202, 194)(191, 218, 220)(193, 196, 204)(198, 226, 224)(200, 228, 230)(207, 236, 234)(210, 239, 238)(211, 241, 231)(212, 237, 216)(214, 245, 246)(217, 222, 249)(219, 251, 252)(221, 232, 254)(223, 225, 227)(229, 261, 262)(233, 235, 250)(240, 273, 271)(242, 267, 268)(243, 275, 269)(244, 264, 247)(248, 263, 260)(253, 282, 281)(255, 270, 272)(256, 259, 285)(257, 258, 265)(266, 280, 292)(274, 288, 293)(276, 295, 296)(277, 286, 291)(278, 287, 279)(283, 298, 294)(284, 290, 289)(297, 300, 299)
	L = (1, 151)(2, 152)(3, 153)(4, 154)(5, 155)(6, 156)(7, 157)(8, 158)(9, 159)(10, 160)(11, 161)(12, 162)(13, 163)(14, 164)(15, 165)(16, 166)(17, 167)(18, 168)(19, 169)(20, 170)(21, 171)(22, 172)(23, 173)(24, 174)(25, 175)(26, 176)(27, 177)(28, 178)(29, 179)(30, 180)(31, 181)(32, 182)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 188)(39, 189)(40, 190)(41, 191)(42, 192)(43, 193)(44, 194)(45, 195)(46, 196)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 207)(58, 208)(59, 209)(60, 210)(61, 211)(62, 212)(63, 213)(64, 214)(65, 215)(66, 216)(67, 217)(68, 218)(69, 219)(70, 220)(71, 221)(72, 222)(73, 223)(74, 224)(75, 225)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)
	local type(s) :: { ( 4^3 ), ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E6.416
Transitivity :: ET+
Graph:: simple bipartite
	v = 65 e = 150 f = 75
	degree seq :: [ 3^50, 10^15 ]

E6.413 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 10})
Quotient :: edge
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2)^3, T1^10, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 38)(24, 39)(25, 44)(26, 45)(27, 48)(29, 49)(31, 53)(32, 56)(34, 59)(36, 61)(37, 62)(40, 63)(41, 68)(42, 69)(43, 72)(46, 75)(47, 78)(50, 79)(51, 67)(52, 65)(54, 84)(55, 86)(57, 73)(58, 81)(60, 90)(64, 92)(66, 96)(70, 100)(71, 103)(74, 94)(76, 106)(77, 107)(80, 108)(82, 112)(83, 115)(85, 117)(87, 118)(88, 122)(89, 120)(91, 93)(95, 127)(97, 130)(98, 133)(99, 125)(101, 135)(102, 136)(104, 137)(105, 141)(109, 143)(110, 132)(111, 126)(113, 140)(114, 139)(116, 134)(119, 138)(121, 144)(123, 128)(124, 129)(131, 149)(142, 148)(145, 150)(146, 147)(151, 152, 155, 161, 171, 187, 186, 170, 160, 154)(153, 157, 165, 177, 197, 227, 204, 181, 167, 158)(156, 163, 175, 193, 221, 252, 226, 196, 176, 164)(159, 168, 182, 205, 235, 263, 232, 201, 179, 166)(162, 173, 191, 217, 248, 282, 251, 220, 192, 174)(169, 184, 208, 238, 271, 289, 254, 222, 207, 183)(172, 189, 215, 203, 233, 264, 281, 247, 216, 190)(178, 199, 218, 195, 224, 246, 279, 261, 231, 200)(180, 202, 219, 249, 277, 270, 237, 206, 223, 194)(185, 210, 239, 273, 295, 260, 230, 198, 229, 209)(188, 213, 244, 225, 255, 290, 297, 278, 245, 214)(211, 241, 274, 280, 298, 286, 269, 236, 268, 240)(212, 242, 275, 250, 284, 257, 293, 272, 276, 243)(228, 258, 283, 262, 291, 256, 292, 299, 294, 259)(234, 266, 285, 300, 296, 267, 288, 253, 287, 265)
	L = (1, 151)(2, 152)(3, 153)(4, 154)(5, 155)(6, 156)(7, 157)(8, 158)(9, 159)(10, 160)(11, 161)(12, 162)(13, 163)(14, 164)(15, 165)(16, 166)(17, 167)(18, 168)(19, 169)(20, 170)(21, 171)(22, 172)(23, 173)(24, 174)(25, 175)(26, 176)(27, 177)(28, 178)(29, 179)(30, 180)(31, 181)(32, 182)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 188)(39, 189)(40, 190)(41, 191)(42, 192)(43, 193)(44, 194)(45, 195)(46, 196)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 207)(58, 208)(59, 209)(60, 210)(61, 211)(62, 212)(63, 213)(64, 214)(65, 215)(66, 216)(67, 217)(68, 218)(69, 219)(70, 220)(71, 221)(72, 222)(73, 223)(74, 224)(75, 225)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)
	local type(s) :: { ( 6, 6 ), ( 6^10 ) }
Outer automorphisms :: reflexible
Dual of E6.414
Transitivity :: ET+
Graph:: simple bipartite
	v = 90 e = 150 f = 50
	degree seq :: [ 2^75, 10^15 ]

E6.414 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 10})
Quotient :: loop
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1 * T2^-1)^3, (T2^-1 * T1)^10 ]
Map::
	R = (1, 151, 3, 153, 4, 154)(2, 152, 5, 155, 6, 156)(7, 157, 11, 161, 12, 162)(8, 158, 13, 163, 14, 164)(9, 159, 15, 165, 16, 166)(10, 160, 17, 167, 18, 168)(19, 169, 27, 177, 28, 178)(20, 170, 29, 179, 30, 180)(21, 171, 31, 181, 32, 182)(22, 172, 33, 183, 34, 184)(23, 173, 35, 185, 36, 186)(24, 174, 37, 187, 38, 188)(25, 175, 39, 189, 40, 190)(26, 176, 41, 191, 42, 192)(43, 193, 55, 205, 56, 206)(44, 194, 47, 197, 57, 207)(45, 195, 58, 208, 59, 209)(46, 196, 60, 210, 61, 211)(48, 198, 62, 212, 63, 213)(49, 199, 64, 214, 65, 215)(50, 200, 53, 203, 66, 216)(51, 201, 67, 217, 68, 218)(52, 202, 69, 219, 70, 220)(54, 204, 71, 221, 72, 222)(73, 223, 91, 241, 92, 242)(74, 224, 76, 226, 93, 243)(75, 225, 94, 244, 95, 245)(77, 227, 96, 246, 97, 247)(78, 228, 98, 248, 99, 249)(79, 229, 80, 230, 100, 250)(81, 231, 101, 251, 102, 252)(82, 232, 103, 253, 104, 254)(83, 233, 85, 235, 105, 255)(84, 234, 106, 256, 107, 257)(86, 236, 108, 258, 109, 259)(87, 237, 110, 260, 111, 261)(88, 238, 89, 239, 112, 262)(90, 240, 113, 263, 114, 264)(115, 265, 117, 267, 131, 281)(116, 266, 132, 282, 133, 283)(118, 268, 122, 272, 134, 284)(119, 269, 135, 285, 120, 270)(121, 271, 136, 286, 137, 287)(123, 273, 125, 275, 138, 288)(124, 274, 139, 289, 140, 290)(126, 276, 130, 280, 141, 291)(127, 277, 142, 292, 128, 278)(129, 279, 143, 293, 144, 294)(145, 295, 146, 296, 147, 297)(148, 298, 149, 299, 150, 300)
	L = (1, 152)(2, 151)(3, 157)(4, 158)(5, 159)(6, 160)(7, 153)(8, 154)(9, 155)(10, 156)(11, 169)(12, 170)(13, 171)(14, 172)(15, 173)(16, 174)(17, 175)(18, 176)(19, 161)(20, 162)(21, 163)(22, 164)(23, 165)(24, 166)(25, 167)(26, 168)(27, 193)(28, 194)(29, 187)(30, 195)(31, 196)(32, 190)(33, 197)(34, 198)(35, 199)(36, 200)(37, 179)(38, 201)(39, 202)(40, 182)(41, 203)(42, 204)(43, 177)(44, 178)(45, 180)(46, 181)(47, 183)(48, 184)(49, 185)(50, 186)(51, 188)(52, 189)(53, 191)(54, 192)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 264)(92, 265)(93, 266)(94, 267)(95, 268)(96, 258)(97, 269)(98, 270)(99, 261)(100, 271)(101, 272)(102, 253)(103, 252)(104, 273)(105, 274)(106, 275)(107, 276)(108, 246)(109, 277)(110, 278)(111, 249)(112, 279)(113, 280)(114, 241)(115, 242)(116, 243)(117, 244)(118, 245)(119, 247)(120, 248)(121, 250)(122, 251)(123, 254)(124, 255)(125, 256)(126, 257)(127, 259)(128, 260)(129, 262)(130, 263)(131, 294)(132, 291)(133, 295)(134, 289)(135, 296)(136, 297)(137, 288)(138, 287)(139, 284)(140, 298)(141, 282)(142, 299)(143, 300)(144, 281)(145, 283)(146, 285)(147, 286)(148, 290)(149, 292)(150, 293)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.413
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 50 e = 150 f = 90
	degree seq :: [ 6^50 ]

E6.415 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 10})
Quotient :: loop
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ F^2, T1^3, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, (T2^2 * T1^-1)^3, T2^10, T2 * T1^-1 * T2^3 * T1^-2 * T2^2 * T1^-1 * T2^-2 * T1^-1 ]
Map::
	R = (1, 151, 3, 153, 9, 159, 19, 169, 37, 187, 64, 214, 48, 198, 26, 176, 13, 163, 5, 155)(2, 152, 6, 156, 14, 164, 27, 177, 50, 200, 79, 229, 57, 207, 32, 182, 16, 166, 7, 157)(4, 154, 11, 161, 22, 172, 41, 191, 69, 219, 90, 240, 60, 210, 34, 184, 17, 167, 8, 158)(10, 160, 21, 171, 40, 190, 67, 217, 98, 248, 124, 274, 92, 242, 61, 211, 35, 185, 18, 168)(12, 162, 23, 173, 43, 193, 71, 221, 103, 253, 133, 283, 105, 255, 72, 222, 44, 194, 24, 174)(15, 165, 29, 179, 53, 203, 81, 231, 114, 264, 141, 291, 115, 265, 82, 232, 54, 204, 30, 180)(20, 170, 39, 189, 31, 181, 55, 205, 83, 233, 116, 266, 126, 276, 93, 243, 62, 212, 36, 186)(25, 175, 45, 195, 73, 223, 106, 256, 134, 284, 130, 280, 100, 250, 68, 218, 42, 192, 46, 196)(28, 178, 52, 202, 33, 183, 58, 208, 87, 237, 119, 269, 137, 287, 109, 259, 77, 227, 49, 199)(38, 188, 66, 216, 59, 209, 88, 238, 120, 270, 144, 294, 147, 297, 127, 277, 94, 244, 63, 213)(47, 197, 74, 224, 107, 257, 136, 286, 149, 299, 138, 288, 110, 260, 78, 228, 51, 201, 75, 225)(56, 206, 84, 234, 117, 267, 143, 293, 150, 300, 148, 298, 131, 281, 101, 251, 70, 220, 85, 235)(65, 215, 97, 247, 91, 241, 118, 268, 86, 236, 112, 262, 140, 290, 135, 285, 128, 278, 95, 245)(76, 226, 96, 246, 129, 279, 125, 275, 146, 296, 123, 273, 102, 252, 132, 282, 104, 254, 108, 258)(80, 230, 113, 263, 99, 249, 122, 272, 89, 239, 121, 271, 145, 295, 142, 292, 139, 289, 111, 261)
	L = (1, 152)(2, 154)(3, 158)(4, 151)(5, 162)(6, 155)(7, 165)(8, 160)(9, 168)(10, 153)(11, 157)(12, 156)(13, 175)(14, 174)(15, 161)(16, 181)(17, 183)(18, 170)(19, 186)(20, 159)(21, 167)(22, 180)(23, 163)(24, 178)(25, 173)(26, 197)(27, 199)(28, 164)(29, 166)(30, 192)(31, 179)(32, 206)(33, 171)(34, 209)(35, 203)(36, 188)(37, 213)(38, 169)(39, 185)(40, 202)(41, 218)(42, 172)(43, 196)(44, 190)(45, 176)(46, 204)(47, 195)(48, 226)(49, 201)(50, 228)(51, 177)(52, 194)(53, 189)(54, 193)(55, 182)(56, 205)(57, 236)(58, 184)(59, 208)(60, 239)(61, 241)(62, 237)(63, 215)(64, 245)(65, 187)(66, 212)(67, 222)(68, 220)(69, 251)(70, 191)(71, 232)(72, 249)(73, 225)(74, 198)(75, 227)(76, 224)(77, 223)(78, 230)(79, 261)(80, 200)(81, 211)(82, 254)(83, 235)(84, 207)(85, 250)(86, 234)(87, 216)(88, 210)(89, 238)(90, 273)(91, 231)(92, 267)(93, 275)(94, 264)(95, 246)(96, 214)(97, 244)(98, 263)(99, 217)(100, 233)(101, 252)(102, 219)(103, 282)(104, 221)(105, 270)(106, 259)(107, 258)(108, 265)(109, 285)(110, 248)(111, 262)(112, 229)(113, 260)(114, 247)(115, 257)(116, 280)(117, 268)(118, 242)(119, 243)(120, 272)(121, 240)(122, 255)(123, 271)(124, 288)(125, 269)(126, 295)(127, 286)(128, 287)(129, 278)(130, 292)(131, 253)(132, 281)(133, 298)(134, 290)(135, 256)(136, 291)(137, 279)(138, 293)(139, 284)(140, 289)(141, 277)(142, 266)(143, 274)(144, 283)(145, 296)(146, 276)(147, 300)(148, 294)(149, 297)(150, 299)
	local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) }
Outer automorphisms :: reflexible
Dual of E6.411
Transitivity :: ET+ VT+ AT
Graph::
	v = 15 e = 150 f = 125
	degree seq :: [ 20^15 ]

E6.416 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 10})
Quotient :: loop
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2)^3, T1^10, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2 ]
Map:: polyhedral non-degenerate
	R = (1, 151, 3, 153)(2, 152, 6, 156)(4, 154, 9, 159)(5, 155, 12, 162)(7, 157, 16, 166)(8, 158, 13, 163)(10, 160, 19, 169)(11, 161, 22, 172)(14, 164, 23, 173)(15, 165, 28, 178)(17, 167, 30, 180)(18, 168, 33, 183)(20, 170, 35, 185)(21, 171, 38, 188)(24, 174, 39, 189)(25, 175, 44, 194)(26, 176, 45, 195)(27, 177, 48, 198)(29, 179, 49, 199)(31, 181, 53, 203)(32, 182, 56, 206)(34, 184, 59, 209)(36, 186, 61, 211)(37, 187, 62, 212)(40, 190, 63, 213)(41, 191, 68, 218)(42, 192, 69, 219)(43, 193, 72, 222)(46, 196, 75, 225)(47, 197, 78, 228)(50, 200, 79, 229)(51, 201, 67, 217)(52, 202, 65, 215)(54, 204, 84, 234)(55, 205, 86, 236)(57, 207, 73, 223)(58, 208, 81, 231)(60, 210, 90, 240)(64, 214, 92, 242)(66, 216, 96, 246)(70, 220, 100, 250)(71, 221, 103, 253)(74, 224, 94, 244)(76, 226, 106, 256)(77, 227, 107, 257)(80, 230, 108, 258)(82, 232, 112, 262)(83, 233, 115, 265)(85, 235, 117, 267)(87, 237, 118, 268)(88, 238, 122, 272)(89, 239, 120, 270)(91, 241, 93, 243)(95, 245, 127, 277)(97, 247, 130, 280)(98, 248, 133, 283)(99, 249, 125, 275)(101, 251, 135, 285)(102, 252, 136, 286)(104, 254, 137, 287)(105, 255, 141, 291)(109, 259, 143, 293)(110, 260, 132, 282)(111, 261, 126, 276)(113, 263, 140, 290)(114, 264, 139, 289)(116, 266, 134, 284)(119, 269, 138, 288)(121, 271, 144, 294)(123, 273, 128, 278)(124, 274, 129, 279)(131, 281, 149, 299)(142, 292, 148, 298)(145, 295, 150, 300)(146, 296, 147, 297)
	L = (1, 152)(2, 155)(3, 157)(4, 151)(5, 161)(6, 163)(7, 165)(8, 153)(9, 168)(10, 154)(11, 171)(12, 173)(13, 175)(14, 156)(15, 177)(16, 159)(17, 158)(18, 182)(19, 184)(20, 160)(21, 187)(22, 189)(23, 191)(24, 162)(25, 193)(26, 164)(27, 197)(28, 199)(29, 166)(30, 202)(31, 167)(32, 205)(33, 169)(34, 208)(35, 210)(36, 170)(37, 186)(38, 213)(39, 215)(40, 172)(41, 217)(42, 174)(43, 221)(44, 180)(45, 224)(46, 176)(47, 227)(48, 229)(49, 218)(50, 178)(51, 179)(52, 219)(53, 233)(54, 181)(55, 235)(56, 223)(57, 183)(58, 238)(59, 185)(60, 239)(61, 241)(62, 242)(63, 244)(64, 188)(65, 203)(66, 190)(67, 248)(68, 195)(69, 249)(70, 192)(71, 252)(72, 207)(73, 194)(74, 246)(75, 255)(76, 196)(77, 204)(78, 258)(79, 209)(80, 198)(81, 200)(82, 201)(83, 264)(84, 266)(85, 263)(86, 268)(87, 206)(88, 271)(89, 273)(90, 211)(91, 274)(92, 275)(93, 212)(94, 225)(95, 214)(96, 279)(97, 216)(98, 282)(99, 277)(100, 284)(101, 220)(102, 226)(103, 287)(104, 222)(105, 290)(106, 292)(107, 293)(108, 283)(109, 228)(110, 230)(111, 231)(112, 291)(113, 232)(114, 281)(115, 234)(116, 285)(117, 288)(118, 240)(119, 236)(120, 237)(121, 289)(122, 276)(123, 295)(124, 280)(125, 250)(126, 243)(127, 270)(128, 245)(129, 261)(130, 298)(131, 247)(132, 251)(133, 262)(134, 257)(135, 300)(136, 269)(137, 265)(138, 253)(139, 254)(140, 297)(141, 256)(142, 299)(143, 272)(144, 259)(145, 260)(146, 267)(147, 278)(148, 286)(149, 294)(150, 296)
	local type(s) :: { ( 3, 10, 3, 10 ) }
Outer automorphisms :: reflexible
Dual of E6.412
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 75 e = 150 f = 65
	degree seq :: [ 4^75 ]

E6.417 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2 * Y1 * Y2^-1)^3, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 151, 2, 152)(3, 153, 7, 157)(4, 154, 8, 158)(5, 155, 9, 159)(6, 156, 10, 160)(11, 161, 19, 169)(12, 162, 20, 170)(13, 163, 21, 171)(14, 164, 22, 172)(15, 165, 23, 173)(16, 166, 24, 174)(17, 167, 25, 175)(18, 168, 26, 176)(27, 177, 43, 193)(28, 178, 44, 194)(29, 179, 37, 187)(30, 180, 45, 195)(31, 181, 46, 196)(32, 182, 40, 190)(33, 183, 47, 197)(34, 184, 48, 198)(35, 185, 49, 199)(36, 186, 50, 200)(38, 188, 51, 201)(39, 189, 52, 202)(41, 191, 53, 203)(42, 192, 54, 204)(55, 205, 73, 223)(56, 206, 74, 224)(57, 207, 75, 225)(58, 208, 76, 226)(59, 209, 77, 227)(60, 210, 78, 228)(61, 211, 79, 229)(62, 212, 80, 230)(63, 213, 81, 231)(64, 214, 82, 232)(65, 215, 83, 233)(66, 216, 84, 234)(67, 217, 85, 235)(68, 218, 86, 236)(69, 219, 87, 237)(70, 220, 88, 238)(71, 221, 89, 239)(72, 222, 90, 240)(91, 241, 114, 264)(92, 242, 115, 265)(93, 243, 116, 266)(94, 244, 117, 267)(95, 245, 118, 268)(96, 246, 108, 258)(97, 247, 119, 269)(98, 248, 120, 270)(99, 249, 111, 261)(100, 250, 121, 271)(101, 251, 122, 272)(102, 252, 103, 253)(104, 254, 123, 273)(105, 255, 124, 274)(106, 256, 125, 275)(107, 257, 126, 276)(109, 259, 127, 277)(110, 260, 128, 278)(112, 262, 129, 279)(113, 263, 130, 280)(131, 281, 144, 294)(132, 282, 141, 291)(133, 283, 145, 295)(134, 284, 139, 289)(135, 285, 146, 296)(136, 286, 147, 297)(137, 287, 138, 288)(140, 290, 148, 298)(142, 292, 149, 299)(143, 293, 150, 300)(301, 451, 303, 453, 304, 454)(302, 452, 305, 455, 306, 456)(307, 457, 311, 461, 312, 462)(308, 458, 313, 463, 314, 464)(309, 459, 315, 465, 316, 466)(310, 460, 317, 467, 318, 468)(319, 469, 327, 477, 328, 478)(320, 470, 329, 479, 330, 480)(321, 471, 331, 481, 332, 482)(322, 472, 333, 483, 334, 484)(323, 473, 335, 485, 336, 486)(324, 474, 337, 487, 338, 488)(325, 475, 339, 489, 340, 490)(326, 476, 341, 491, 342, 492)(343, 493, 355, 505, 356, 506)(344, 494, 347, 497, 357, 507)(345, 495, 358, 508, 359, 509)(346, 496, 360, 510, 361, 511)(348, 498, 362, 512, 363, 513)(349, 499, 364, 514, 365, 515)(350, 500, 353, 503, 366, 516)(351, 501, 367, 517, 368, 518)(352, 502, 369, 519, 370, 520)(354, 504, 371, 521, 372, 522)(373, 523, 391, 541, 392, 542)(374, 524, 376, 526, 393, 543)(375, 525, 394, 544, 395, 545)(377, 527, 396, 546, 397, 547)(378, 528, 398, 548, 399, 549)(379, 529, 380, 530, 400, 550)(381, 531, 401, 551, 402, 552)(382, 532, 403, 553, 404, 554)(383, 533, 385, 535, 405, 555)(384, 534, 406, 556, 407, 557)(386, 536, 408, 558, 409, 559)(387, 537, 410, 560, 411, 561)(388, 538, 389, 539, 412, 562)(390, 540, 413, 563, 414, 564)(415, 565, 417, 567, 431, 581)(416, 566, 432, 582, 433, 583)(418, 568, 422, 572, 434, 584)(419, 569, 435, 585, 420, 570)(421, 571, 436, 586, 437, 587)(423, 573, 425, 575, 438, 588)(424, 574, 439, 589, 440, 590)(426, 576, 430, 580, 441, 591)(427, 577, 442, 592, 428, 578)(429, 579, 443, 593, 444, 594)(445, 595, 446, 596, 447, 597)(448, 598, 449, 599, 450, 600)
	L = (1, 302)(2, 301)(3, 307)(4, 308)(5, 309)(6, 310)(7, 303)(8, 304)(9, 305)(10, 306)(11, 319)(12, 320)(13, 321)(14, 322)(15, 323)(16, 324)(17, 325)(18, 326)(19, 311)(20, 312)(21, 313)(22, 314)(23, 315)(24, 316)(25, 317)(26, 318)(27, 343)(28, 344)(29, 337)(30, 345)(31, 346)(32, 340)(33, 347)(34, 348)(35, 349)(36, 350)(37, 329)(38, 351)(39, 352)(40, 332)(41, 353)(42, 354)(43, 327)(44, 328)(45, 330)(46, 331)(47, 333)(48, 334)(49, 335)(50, 336)(51, 338)(52, 339)(53, 341)(54, 342)(55, 373)(56, 374)(57, 375)(58, 376)(59, 377)(60, 378)(61, 379)(62, 380)(63, 381)(64, 382)(65, 383)(66, 384)(67, 385)(68, 386)(69, 387)(70, 388)(71, 389)(72, 390)(73, 355)(74, 356)(75, 357)(76, 358)(77, 359)(78, 360)(79, 361)(80, 362)(81, 363)(82, 364)(83, 365)(84, 366)(85, 367)(86, 368)(87, 369)(88, 370)(89, 371)(90, 372)(91, 414)(92, 415)(93, 416)(94, 417)(95, 418)(96, 408)(97, 419)(98, 420)(99, 411)(100, 421)(101, 422)(102, 403)(103, 402)(104, 423)(105, 424)(106, 425)(107, 426)(108, 396)(109, 427)(110, 428)(111, 399)(112, 429)(113, 430)(114, 391)(115, 392)(116, 393)(117, 394)(118, 395)(119, 397)(120, 398)(121, 400)(122, 401)(123, 404)(124, 405)(125, 406)(126, 407)(127, 409)(128, 410)(129, 412)(130, 413)(131, 444)(132, 441)(133, 445)(134, 439)(135, 446)(136, 447)(137, 438)(138, 437)(139, 434)(140, 448)(141, 432)(142, 449)(143, 450)(144, 431)(145, 433)(146, 435)(147, 436)(148, 440)(149, 442)(150, 443)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.420
Graph:: bipartite
	v = 125 e = 300 f = 165
	degree seq :: [ 4^75, 6^50 ]

E6.418 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^2 * Y1^-1)^3, Y2^10, Y2 * Y1^-1 * Y2^3 * Y1^-2 * Y2^2 * Y1^-1 * Y2^-2 * Y1^-1 ]
Map::
	R = (1, 151, 2, 152, 4, 154)(3, 153, 8, 158, 10, 160)(5, 155, 12, 162, 6, 156)(7, 157, 15, 165, 11, 161)(9, 159, 18, 168, 20, 170)(13, 163, 25, 175, 23, 173)(14, 164, 24, 174, 28, 178)(16, 166, 31, 181, 29, 179)(17, 167, 33, 183, 21, 171)(19, 169, 36, 186, 38, 188)(22, 172, 30, 180, 42, 192)(26, 176, 47, 197, 45, 195)(27, 177, 49, 199, 51, 201)(32, 182, 56, 206, 55, 205)(34, 184, 59, 209, 58, 208)(35, 185, 53, 203, 39, 189)(37, 187, 63, 213, 65, 215)(40, 190, 52, 202, 44, 194)(41, 191, 68, 218, 70, 220)(43, 193, 46, 196, 54, 204)(48, 198, 76, 226, 74, 224)(50, 200, 78, 228, 80, 230)(57, 207, 86, 236, 84, 234)(60, 210, 89, 239, 88, 238)(61, 211, 91, 241, 81, 231)(62, 212, 87, 237, 66, 216)(64, 214, 95, 245, 96, 246)(67, 217, 72, 222, 99, 249)(69, 219, 101, 251, 102, 252)(71, 221, 82, 232, 104, 254)(73, 223, 75, 225, 77, 227)(79, 229, 111, 261, 112, 262)(83, 233, 85, 235, 100, 250)(90, 240, 123, 273, 121, 271)(92, 242, 117, 267, 118, 268)(93, 243, 125, 275, 119, 269)(94, 244, 114, 264, 97, 247)(98, 248, 113, 263, 110, 260)(103, 253, 132, 282, 131, 281)(105, 255, 120, 270, 122, 272)(106, 256, 109, 259, 135, 285)(107, 257, 108, 258, 115, 265)(116, 266, 130, 280, 142, 292)(124, 274, 138, 288, 143, 293)(126, 276, 145, 295, 146, 296)(127, 277, 136, 286, 141, 291)(128, 278, 137, 287, 129, 279)(133, 283, 148, 298, 144, 294)(134, 284, 140, 290, 139, 289)(147, 297, 150, 300, 149, 299)(301, 451, 303, 453, 309, 459, 319, 469, 337, 487, 364, 514, 348, 498, 326, 476, 313, 463, 305, 455)(302, 452, 306, 456, 314, 464, 327, 477, 350, 500, 379, 529, 357, 507, 332, 482, 316, 466, 307, 457)(304, 454, 311, 461, 322, 472, 341, 491, 369, 519, 390, 540, 360, 510, 334, 484, 317, 467, 308, 458)(310, 460, 321, 471, 340, 490, 367, 517, 398, 548, 424, 574, 392, 542, 361, 511, 335, 485, 318, 468)(312, 462, 323, 473, 343, 493, 371, 521, 403, 553, 433, 583, 405, 555, 372, 522, 344, 494, 324, 474)(315, 465, 329, 479, 353, 503, 381, 531, 414, 564, 441, 591, 415, 565, 382, 532, 354, 504, 330, 480)(320, 470, 339, 489, 331, 481, 355, 505, 383, 533, 416, 566, 426, 576, 393, 543, 362, 512, 336, 486)(325, 475, 345, 495, 373, 523, 406, 556, 434, 584, 430, 580, 400, 550, 368, 518, 342, 492, 346, 496)(328, 478, 352, 502, 333, 483, 358, 508, 387, 537, 419, 569, 437, 587, 409, 559, 377, 527, 349, 499)(338, 488, 366, 516, 359, 509, 388, 538, 420, 570, 444, 594, 447, 597, 427, 577, 394, 544, 363, 513)(347, 497, 374, 524, 407, 557, 436, 586, 449, 599, 438, 588, 410, 560, 378, 528, 351, 501, 375, 525)(356, 506, 384, 534, 417, 567, 443, 593, 450, 600, 448, 598, 431, 581, 401, 551, 370, 520, 385, 535)(365, 515, 397, 547, 391, 541, 418, 568, 386, 536, 412, 562, 440, 590, 435, 585, 428, 578, 395, 545)(376, 526, 396, 546, 429, 579, 425, 575, 446, 596, 423, 573, 402, 552, 432, 582, 404, 554, 408, 558)(380, 530, 413, 563, 399, 549, 422, 572, 389, 539, 421, 571, 445, 595, 442, 592, 439, 589, 411, 561)
	L = (1, 303)(2, 306)(3, 309)(4, 311)(5, 301)(6, 314)(7, 302)(8, 304)(9, 319)(10, 321)(11, 322)(12, 323)(13, 305)(14, 327)(15, 329)(16, 307)(17, 308)(18, 310)(19, 337)(20, 339)(21, 340)(22, 341)(23, 343)(24, 312)(25, 345)(26, 313)(27, 350)(28, 352)(29, 353)(30, 315)(31, 355)(32, 316)(33, 358)(34, 317)(35, 318)(36, 320)(37, 364)(38, 366)(39, 331)(40, 367)(41, 369)(42, 346)(43, 371)(44, 324)(45, 373)(46, 325)(47, 374)(48, 326)(49, 328)(50, 379)(51, 375)(52, 333)(53, 381)(54, 330)(55, 383)(56, 384)(57, 332)(58, 387)(59, 388)(60, 334)(61, 335)(62, 336)(63, 338)(64, 348)(65, 397)(66, 359)(67, 398)(68, 342)(69, 390)(70, 385)(71, 403)(72, 344)(73, 406)(74, 407)(75, 347)(76, 396)(77, 349)(78, 351)(79, 357)(80, 413)(81, 414)(82, 354)(83, 416)(84, 417)(85, 356)(86, 412)(87, 419)(88, 420)(89, 421)(90, 360)(91, 418)(92, 361)(93, 362)(94, 363)(95, 365)(96, 429)(97, 391)(98, 424)(99, 422)(100, 368)(101, 370)(102, 432)(103, 433)(104, 408)(105, 372)(106, 434)(107, 436)(108, 376)(109, 377)(110, 378)(111, 380)(112, 440)(113, 399)(114, 441)(115, 382)(116, 426)(117, 443)(118, 386)(119, 437)(120, 444)(121, 445)(122, 389)(123, 402)(124, 392)(125, 446)(126, 393)(127, 394)(128, 395)(129, 425)(130, 400)(131, 401)(132, 404)(133, 405)(134, 430)(135, 428)(136, 449)(137, 409)(138, 410)(139, 411)(140, 435)(141, 415)(142, 439)(143, 450)(144, 447)(145, 442)(146, 423)(147, 427)(148, 431)(149, 438)(150, 448)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E6.419
Graph:: bipartite
	v = 65 e = 300 f = 225
	degree seq :: [ 6^50, 20^15 ]

E6.419 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y3^-3 * Y2)^3, Y3^5 * Y2 * Y3^-2 * Y2 * Y3^3 * Y2 * Y3^-2 * Y2, (Y3^-1 * Y1^-1)^10 ]
Map:: polytopal
	R = (1, 151)(2, 152)(3, 153)(4, 154)(5, 155)(6, 156)(7, 157)(8, 158)(9, 159)(10, 160)(11, 161)(12, 162)(13, 163)(14, 164)(15, 165)(16, 166)(17, 167)(18, 168)(19, 169)(20, 170)(21, 171)(22, 172)(23, 173)(24, 174)(25, 175)(26, 176)(27, 177)(28, 178)(29, 179)(30, 180)(31, 181)(32, 182)(33, 183)(34, 184)(35, 185)(36, 186)(37, 187)(38, 188)(39, 189)(40, 190)(41, 191)(42, 192)(43, 193)(44, 194)(45, 195)(46, 196)(47, 197)(48, 198)(49, 199)(50, 200)(51, 201)(52, 202)(53, 203)(54, 204)(55, 205)(56, 206)(57, 207)(58, 208)(59, 209)(60, 210)(61, 211)(62, 212)(63, 213)(64, 214)(65, 215)(66, 216)(67, 217)(68, 218)(69, 219)(70, 220)(71, 221)(72, 222)(73, 223)(74, 224)(75, 225)(76, 226)(77, 227)(78, 228)(79, 229)(80, 230)(81, 231)(82, 232)(83, 233)(84, 234)(85, 235)(86, 236)(87, 237)(88, 238)(89, 239)(90, 240)(91, 241)(92, 242)(93, 243)(94, 244)(95, 245)(96, 246)(97, 247)(98, 248)(99, 249)(100, 250)(101, 251)(102, 252)(103, 253)(104, 254)(105, 255)(106, 256)(107, 257)(108, 258)(109, 259)(110, 260)(111, 261)(112, 262)(113, 263)(114, 264)(115, 265)(116, 266)(117, 267)(118, 268)(119, 269)(120, 270)(121, 271)(122, 272)(123, 273)(124, 274)(125, 275)(126, 276)(127, 277)(128, 278)(129, 279)(130, 280)(131, 281)(132, 282)(133, 283)(134, 284)(135, 285)(136, 286)(137, 287)(138, 288)(139, 289)(140, 290)(141, 291)(142, 292)(143, 293)(144, 294)(145, 295)(146, 296)(147, 297)(148, 298)(149, 299)(150, 300)(301, 451, 302, 452)(303, 453, 307, 457)(304, 454, 309, 459)(305, 455, 311, 461)(306, 456, 313, 463)(308, 458, 316, 466)(310, 460, 319, 469)(312, 462, 322, 472)(314, 464, 325, 475)(315, 465, 327, 477)(317, 467, 330, 480)(318, 468, 332, 482)(320, 470, 335, 485)(321, 471, 337, 487)(323, 473, 340, 490)(324, 474, 342, 492)(326, 476, 345, 495)(328, 478, 348, 498)(329, 479, 350, 500)(331, 481, 353, 503)(333, 483, 356, 506)(334, 484, 358, 508)(336, 486, 361, 511)(338, 488, 363, 513)(339, 489, 365, 515)(341, 491, 368, 518)(343, 493, 371, 521)(344, 494, 373, 523)(346, 496, 376, 526)(347, 497, 362, 512)(349, 499, 378, 528)(351, 501, 374, 524)(352, 502, 381, 531)(354, 504, 384, 534)(355, 505, 370, 520)(357, 507, 386, 536)(359, 509, 366, 516)(360, 510, 389, 539)(364, 514, 393, 543)(367, 517, 396, 546)(369, 519, 399, 549)(372, 522, 401, 551)(375, 525, 404, 554)(377, 527, 407, 557)(379, 529, 410, 560)(380, 530, 411, 561)(382, 532, 408, 558)(383, 533, 414, 564)(385, 535, 417, 567)(387, 537, 420, 570)(388, 538, 421, 571)(390, 540, 418, 568)(391, 541, 416, 566)(392, 542, 425, 575)(394, 544, 428, 578)(395, 545, 429, 579)(397, 547, 426, 576)(398, 548, 432, 582)(400, 550, 435, 585)(402, 552, 438, 588)(403, 553, 439, 589)(405, 555, 436, 586)(406, 556, 434, 584)(409, 559, 427, 577)(412, 562, 442, 592)(413, 563, 444, 594)(415, 565, 440, 590)(419, 569, 437, 587)(422, 572, 433, 583)(423, 573, 445, 595)(424, 574, 430, 580)(431, 581, 448, 598)(441, 591, 449, 599)(443, 593, 450, 600)(446, 596, 447, 597)
	L = (1, 303)(2, 305)(3, 308)(4, 301)(5, 312)(6, 302)(7, 313)(8, 317)(9, 318)(10, 304)(11, 309)(12, 323)(13, 324)(14, 306)(15, 307)(16, 327)(17, 331)(18, 333)(19, 334)(20, 310)(21, 311)(22, 337)(23, 341)(24, 343)(25, 344)(26, 314)(27, 347)(28, 315)(29, 316)(30, 350)(31, 354)(32, 319)(33, 357)(34, 359)(35, 360)(36, 320)(37, 362)(38, 321)(39, 322)(40, 365)(41, 369)(42, 325)(43, 372)(44, 374)(45, 375)(46, 326)(47, 363)(48, 377)(49, 328)(50, 373)(51, 329)(52, 330)(53, 381)(54, 336)(55, 332)(56, 370)(57, 387)(58, 335)(59, 388)(60, 390)(61, 391)(62, 348)(63, 392)(64, 338)(65, 358)(66, 339)(67, 340)(68, 396)(69, 346)(70, 342)(71, 355)(72, 402)(73, 345)(74, 403)(75, 405)(76, 406)(77, 408)(78, 409)(79, 349)(80, 351)(81, 407)(82, 352)(83, 353)(84, 414)(85, 356)(86, 417)(87, 394)(88, 422)(89, 361)(90, 423)(91, 424)(92, 426)(93, 427)(94, 364)(95, 366)(96, 425)(97, 367)(98, 368)(99, 432)(100, 371)(101, 435)(102, 379)(103, 440)(104, 376)(105, 441)(106, 442)(107, 378)(108, 430)(109, 428)(110, 443)(111, 434)(112, 380)(113, 382)(114, 439)(115, 383)(116, 384)(117, 389)(118, 385)(119, 386)(120, 437)(121, 429)(122, 436)(123, 431)(124, 444)(125, 393)(126, 412)(127, 410)(128, 447)(129, 416)(130, 395)(131, 397)(132, 421)(133, 398)(134, 399)(135, 404)(136, 400)(137, 401)(138, 419)(139, 411)(140, 418)(141, 413)(142, 448)(143, 449)(144, 450)(145, 415)(146, 420)(147, 445)(148, 446)(149, 433)(150, 438)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 6, 20 ), ( 6, 20, 6, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.418
Graph:: simple bipartite
	v = 225 e = 300 f = 65
	degree seq :: [ 2^150, 4^75 ]

E6.420 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (Y1 * Y3)^3, Y1^10, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-2 ]
Map:: polytopal
	R = (1, 151, 2, 152, 5, 155, 11, 161, 21, 171, 37, 187, 36, 186, 20, 170, 10, 160, 4, 154)(3, 153, 7, 157, 15, 165, 27, 177, 47, 197, 77, 227, 54, 204, 31, 181, 17, 167, 8, 158)(6, 156, 13, 163, 25, 175, 43, 193, 71, 221, 102, 252, 76, 226, 46, 196, 26, 176, 14, 164)(9, 159, 18, 168, 32, 182, 55, 205, 85, 235, 113, 263, 82, 232, 51, 201, 29, 179, 16, 166)(12, 162, 23, 173, 41, 191, 67, 217, 98, 248, 132, 282, 101, 251, 70, 220, 42, 192, 24, 174)(19, 169, 34, 184, 58, 208, 88, 238, 121, 271, 139, 289, 104, 254, 72, 222, 57, 207, 33, 183)(22, 172, 39, 189, 65, 215, 53, 203, 83, 233, 114, 264, 131, 281, 97, 247, 66, 216, 40, 190)(28, 178, 49, 199, 68, 218, 45, 195, 74, 224, 96, 246, 129, 279, 111, 261, 81, 231, 50, 200)(30, 180, 52, 202, 69, 219, 99, 249, 127, 277, 120, 270, 87, 237, 56, 206, 73, 223, 44, 194)(35, 185, 60, 210, 89, 239, 123, 273, 145, 295, 110, 260, 80, 230, 48, 198, 79, 229, 59, 209)(38, 188, 63, 213, 94, 244, 75, 225, 105, 255, 140, 290, 147, 297, 128, 278, 95, 245, 64, 214)(61, 211, 91, 241, 124, 274, 130, 280, 148, 298, 136, 286, 119, 269, 86, 236, 118, 268, 90, 240)(62, 212, 92, 242, 125, 275, 100, 250, 134, 284, 107, 257, 143, 293, 122, 272, 126, 276, 93, 243)(78, 228, 108, 258, 133, 283, 112, 262, 141, 291, 106, 256, 142, 292, 149, 299, 144, 294, 109, 259)(84, 234, 116, 266, 135, 285, 150, 300, 146, 296, 117, 267, 138, 288, 103, 253, 137, 287, 115, 265)(301, 451)(302, 452)(303, 453)(304, 454)(305, 455)(306, 456)(307, 457)(308, 458)(309, 459)(310, 460)(311, 461)(312, 462)(313, 463)(314, 464)(315, 465)(316, 466)(317, 467)(318, 468)(319, 469)(320, 470)(321, 471)(322, 472)(323, 473)(324, 474)(325, 475)(326, 476)(327, 477)(328, 478)(329, 479)(330, 480)(331, 481)(332, 482)(333, 483)(334, 484)(335, 485)(336, 486)(337, 487)(338, 488)(339, 489)(340, 490)(341, 491)(342, 492)(343, 493)(344, 494)(345, 495)(346, 496)(347, 497)(348, 498)(349, 499)(350, 500)(351, 501)(352, 502)(353, 503)(354, 504)(355, 505)(356, 506)(357, 507)(358, 508)(359, 509)(360, 510)(361, 511)(362, 512)(363, 513)(364, 514)(365, 515)(366, 516)(367, 517)(368, 518)(369, 519)(370, 520)(371, 521)(372, 522)(373, 523)(374, 524)(375, 525)(376, 526)(377, 527)(378, 528)(379, 529)(380, 530)(381, 531)(382, 532)(383, 533)(384, 534)(385, 535)(386, 536)(387, 537)(388, 538)(389, 539)(390, 540)(391, 541)(392, 542)(393, 543)(394, 544)(395, 545)(396, 546)(397, 547)(398, 548)(399, 549)(400, 550)(401, 551)(402, 552)(403, 553)(404, 554)(405, 555)(406, 556)(407, 557)(408, 558)(409, 559)(410, 560)(411, 561)(412, 562)(413, 563)(414, 564)(415, 565)(416, 566)(417, 567)(418, 568)(419, 569)(420, 570)(421, 571)(422, 572)(423, 573)(424, 574)(425, 575)(426, 576)(427, 577)(428, 578)(429, 579)(430, 580)(431, 581)(432, 582)(433, 583)(434, 584)(435, 585)(436, 586)(437, 587)(438, 588)(439, 589)(440, 590)(441, 591)(442, 592)(443, 593)(444, 594)(445, 595)(446, 596)(447, 597)(448, 598)(449, 599)(450, 600)
	L = (1, 303)(2, 306)(3, 301)(4, 309)(5, 312)(6, 302)(7, 316)(8, 313)(9, 304)(10, 319)(11, 322)(12, 305)(13, 308)(14, 323)(15, 328)(16, 307)(17, 330)(18, 333)(19, 310)(20, 335)(21, 338)(22, 311)(23, 314)(24, 339)(25, 344)(26, 345)(27, 348)(28, 315)(29, 349)(30, 317)(31, 353)(32, 356)(33, 318)(34, 359)(35, 320)(36, 361)(37, 362)(38, 321)(39, 324)(40, 363)(41, 368)(42, 369)(43, 372)(44, 325)(45, 326)(46, 375)(47, 378)(48, 327)(49, 329)(50, 379)(51, 367)(52, 365)(53, 331)(54, 384)(55, 386)(56, 332)(57, 373)(58, 381)(59, 334)(60, 390)(61, 336)(62, 337)(63, 340)(64, 392)(65, 352)(66, 396)(67, 351)(68, 341)(69, 342)(70, 400)(71, 403)(72, 343)(73, 357)(74, 394)(75, 346)(76, 406)(77, 407)(78, 347)(79, 350)(80, 408)(81, 358)(82, 412)(83, 415)(84, 354)(85, 417)(86, 355)(87, 418)(88, 422)(89, 420)(90, 360)(91, 393)(92, 364)(93, 391)(94, 374)(95, 427)(96, 366)(97, 430)(98, 433)(99, 425)(100, 370)(101, 435)(102, 436)(103, 371)(104, 437)(105, 441)(106, 376)(107, 377)(108, 380)(109, 443)(110, 432)(111, 426)(112, 382)(113, 440)(114, 439)(115, 383)(116, 434)(117, 385)(118, 387)(119, 438)(120, 389)(121, 444)(122, 388)(123, 428)(124, 429)(125, 399)(126, 411)(127, 395)(128, 423)(129, 424)(130, 397)(131, 449)(132, 410)(133, 398)(134, 416)(135, 401)(136, 402)(137, 404)(138, 419)(139, 414)(140, 413)(141, 405)(142, 448)(143, 409)(144, 421)(145, 450)(146, 447)(147, 446)(148, 442)(149, 431)(150, 445)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.417
Graph:: simple bipartite
	v = 165 e = 300 f = 125
	degree seq :: [ 2^150, 20^15 ]

E6.421 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, (Y3 * Y2^-1)^3, Y2^10, Y2^2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1 ]
Map::
	R = (1, 151, 2, 152)(3, 153, 7, 157)(4, 154, 9, 159)(5, 155, 11, 161)(6, 156, 13, 163)(8, 158, 16, 166)(10, 160, 19, 169)(12, 162, 22, 172)(14, 164, 25, 175)(15, 165, 27, 177)(17, 167, 30, 180)(18, 168, 32, 182)(20, 170, 35, 185)(21, 171, 37, 187)(23, 173, 40, 190)(24, 174, 42, 192)(26, 176, 45, 195)(28, 178, 48, 198)(29, 179, 50, 200)(31, 181, 53, 203)(33, 183, 56, 206)(34, 184, 58, 208)(36, 186, 61, 211)(38, 188, 63, 213)(39, 189, 65, 215)(41, 191, 68, 218)(43, 193, 71, 221)(44, 194, 73, 223)(46, 196, 76, 226)(47, 197, 62, 212)(49, 199, 78, 228)(51, 201, 74, 224)(52, 202, 81, 231)(54, 204, 84, 234)(55, 205, 70, 220)(57, 207, 86, 236)(59, 209, 66, 216)(60, 210, 89, 239)(64, 214, 93, 243)(67, 217, 96, 246)(69, 219, 99, 249)(72, 222, 101, 251)(75, 225, 104, 254)(77, 227, 107, 257)(79, 229, 110, 260)(80, 230, 111, 261)(82, 232, 108, 258)(83, 233, 114, 264)(85, 235, 117, 267)(87, 237, 120, 270)(88, 238, 121, 271)(90, 240, 118, 268)(91, 241, 116, 266)(92, 242, 125, 275)(94, 244, 128, 278)(95, 245, 129, 279)(97, 247, 126, 276)(98, 248, 132, 282)(100, 250, 135, 285)(102, 252, 138, 288)(103, 253, 139, 289)(105, 255, 136, 286)(106, 256, 134, 284)(109, 259, 127, 277)(112, 262, 142, 292)(113, 263, 144, 294)(115, 265, 140, 290)(119, 269, 137, 287)(122, 272, 133, 283)(123, 273, 145, 295)(124, 274, 130, 280)(131, 281, 148, 298)(141, 291, 149, 299)(143, 293, 150, 300)(146, 296, 147, 297)(301, 451, 303, 453, 308, 458, 317, 467, 331, 481, 354, 504, 336, 486, 320, 470, 310, 460, 304, 454)(302, 452, 305, 455, 312, 462, 323, 473, 341, 491, 369, 519, 346, 496, 326, 476, 314, 464, 306, 456)(307, 457, 313, 463, 324, 474, 343, 493, 372, 522, 402, 552, 379, 529, 349, 499, 328, 478, 315, 465)(309, 459, 318, 468, 333, 483, 357, 507, 387, 537, 394, 544, 364, 514, 338, 488, 321, 471, 311, 461)(316, 466, 327, 477, 347, 497, 363, 513, 392, 542, 426, 576, 412, 562, 380, 530, 351, 501, 329, 479)(319, 469, 334, 484, 359, 509, 388, 538, 422, 572, 436, 586, 400, 550, 371, 521, 355, 505, 332, 482)(322, 472, 337, 487, 362, 512, 348, 498, 377, 527, 408, 558, 430, 580, 395, 545, 366, 516, 339, 489)(325, 475, 344, 494, 374, 524, 403, 553, 440, 590, 418, 568, 385, 535, 356, 506, 370, 520, 342, 492)(330, 480, 350, 500, 373, 523, 345, 495, 375, 525, 405, 555, 441, 591, 413, 563, 382, 532, 352, 502)(335, 485, 360, 510, 390, 540, 423, 573, 431, 581, 397, 547, 367, 517, 340, 490, 365, 515, 358, 508)(353, 503, 381, 531, 407, 557, 378, 528, 409, 559, 428, 578, 447, 597, 445, 595, 415, 565, 383, 533)(361, 511, 391, 541, 424, 574, 444, 594, 450, 600, 438, 588, 419, 569, 386, 536, 417, 567, 389, 539)(368, 518, 396, 546, 425, 575, 393, 543, 427, 577, 410, 560, 443, 593, 449, 599, 433, 583, 398, 548)(376, 526, 406, 556, 442, 592, 448, 598, 446, 596, 420, 570, 437, 587, 401, 551, 435, 585, 404, 554)(384, 534, 414, 564, 439, 589, 411, 561, 434, 584, 399, 549, 432, 582, 421, 571, 429, 579, 416, 566)
	L = (1, 302)(2, 301)(3, 307)(4, 309)(5, 311)(6, 313)(7, 303)(8, 316)(9, 304)(10, 319)(11, 305)(12, 322)(13, 306)(14, 325)(15, 327)(16, 308)(17, 330)(18, 332)(19, 310)(20, 335)(21, 337)(22, 312)(23, 340)(24, 342)(25, 314)(26, 345)(27, 315)(28, 348)(29, 350)(30, 317)(31, 353)(32, 318)(33, 356)(34, 358)(35, 320)(36, 361)(37, 321)(38, 363)(39, 365)(40, 323)(41, 368)(42, 324)(43, 371)(44, 373)(45, 326)(46, 376)(47, 362)(48, 328)(49, 378)(50, 329)(51, 374)(52, 381)(53, 331)(54, 384)(55, 370)(56, 333)(57, 386)(58, 334)(59, 366)(60, 389)(61, 336)(62, 347)(63, 338)(64, 393)(65, 339)(66, 359)(67, 396)(68, 341)(69, 399)(70, 355)(71, 343)(72, 401)(73, 344)(74, 351)(75, 404)(76, 346)(77, 407)(78, 349)(79, 410)(80, 411)(81, 352)(82, 408)(83, 414)(84, 354)(85, 417)(86, 357)(87, 420)(88, 421)(89, 360)(90, 418)(91, 416)(92, 425)(93, 364)(94, 428)(95, 429)(96, 367)(97, 426)(98, 432)(99, 369)(100, 435)(101, 372)(102, 438)(103, 439)(104, 375)(105, 436)(106, 434)(107, 377)(108, 382)(109, 427)(110, 379)(111, 380)(112, 442)(113, 444)(114, 383)(115, 440)(116, 391)(117, 385)(118, 390)(119, 437)(120, 387)(121, 388)(122, 433)(123, 445)(124, 430)(125, 392)(126, 397)(127, 409)(128, 394)(129, 395)(130, 424)(131, 448)(132, 398)(133, 422)(134, 406)(135, 400)(136, 405)(137, 419)(138, 402)(139, 403)(140, 415)(141, 449)(142, 412)(143, 450)(144, 413)(145, 423)(146, 447)(147, 446)(148, 431)(149, 441)(150, 443)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E6.422
Graph:: bipartite
	v = 90 e = 300 f = 200
	degree seq :: [ 4^75, 20^15 ]

E6.422 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 10})
Quotient :: dipole
Aut^+ = ((C5 x C5) : C3) : C2 (small group id <150, 5>)
Aut   = (((C5 x C5) : C3) : C2) : C2 (small group id <300, 25>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y1^-1)^3, Y1^-1 * Y3^3 * Y1 * Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^2 * Y1^-1, (Y3 * Y2^-1)^10 ]
Map:: polytopal
	R = (1, 151, 2, 152, 4, 154)(3, 153, 8, 158, 10, 160)(5, 155, 12, 162, 6, 156)(7, 157, 15, 165, 11, 161)(9, 159, 18, 168, 20, 170)(13, 163, 25, 175, 23, 173)(14, 164, 24, 174, 28, 178)(16, 166, 31, 181, 29, 179)(17, 167, 33, 183, 21, 171)(19, 169, 36, 186, 38, 188)(22, 172, 30, 180, 42, 192)(26, 176, 47, 197, 45, 195)(27, 177, 49, 199, 51, 201)(32, 182, 56, 206, 55, 205)(34, 184, 59, 209, 58, 208)(35, 185, 53, 203, 39, 189)(37, 187, 63, 213, 65, 215)(40, 190, 52, 202, 44, 194)(41, 191, 68, 218, 70, 220)(43, 193, 46, 196, 54, 204)(48, 198, 76, 226, 74, 224)(50, 200, 78, 228, 80, 230)(57, 207, 86, 236, 84, 234)(60, 210, 89, 239, 88, 238)(61, 211, 91, 241, 81, 231)(62, 212, 87, 237, 66, 216)(64, 214, 95, 245, 96, 246)(67, 217, 72, 222, 99, 249)(69, 219, 101, 251, 102, 252)(71, 221, 82, 232, 104, 254)(73, 223, 75, 225, 77, 227)(79, 229, 111, 261, 112, 262)(83, 233, 85, 235, 100, 250)(90, 240, 123, 273, 121, 271)(92, 242, 117, 267, 118, 268)(93, 243, 125, 275, 119, 269)(94, 244, 114, 264, 97, 247)(98, 248, 113, 263, 110, 260)(103, 253, 132, 282, 131, 281)(105, 255, 120, 270, 122, 272)(106, 256, 109, 259, 135, 285)(107, 257, 108, 258, 115, 265)(116, 266, 130, 280, 142, 292)(124, 274, 138, 288, 143, 293)(126, 276, 145, 295, 146, 296)(127, 277, 136, 286, 141, 291)(128, 278, 137, 287, 129, 279)(133, 283, 148, 298, 144, 294)(134, 284, 140, 290, 139, 289)(147, 297, 150, 300, 149, 299)(301, 451)(302, 452)(303, 453)(304, 454)(305, 455)(306, 456)(307, 457)(308, 458)(309, 459)(310, 460)(311, 461)(312, 462)(313, 463)(314, 464)(315, 465)(316, 466)(317, 467)(318, 468)(319, 469)(320, 470)(321, 471)(322, 472)(323, 473)(324, 474)(325, 475)(326, 476)(327, 477)(328, 478)(329, 479)(330, 480)(331, 481)(332, 482)(333, 483)(334, 484)(335, 485)(336, 486)(337, 487)(338, 488)(339, 489)(340, 490)(341, 491)(342, 492)(343, 493)(344, 494)(345, 495)(346, 496)(347, 497)(348, 498)(349, 499)(350, 500)(351, 501)(352, 502)(353, 503)(354, 504)(355, 505)(356, 506)(357, 507)(358, 508)(359, 509)(360, 510)(361, 511)(362, 512)(363, 513)(364, 514)(365, 515)(366, 516)(367, 517)(368, 518)(369, 519)(370, 520)(371, 521)(372, 522)(373, 523)(374, 524)(375, 525)(376, 526)(377, 527)(378, 528)(379, 529)(380, 530)(381, 531)(382, 532)(383, 533)(384, 534)(385, 535)(386, 536)(387, 537)(388, 538)(389, 539)(390, 540)(391, 541)(392, 542)(393, 543)(394, 544)(395, 545)(396, 546)(397, 547)(398, 548)(399, 549)(400, 550)(401, 551)(402, 552)(403, 553)(404, 554)(405, 555)(406, 556)(407, 557)(408, 558)(409, 559)(410, 560)(411, 561)(412, 562)(413, 563)(414, 564)(415, 565)(416, 566)(417, 567)(418, 568)(419, 569)(420, 570)(421, 571)(422, 572)(423, 573)(424, 574)(425, 575)(426, 576)(427, 577)(428, 578)(429, 579)(430, 580)(431, 581)(432, 582)(433, 583)(434, 584)(435, 585)(436, 586)(437, 587)(438, 588)(439, 589)(440, 590)(441, 591)(442, 592)(443, 593)(444, 594)(445, 595)(446, 596)(447, 597)(448, 598)(449, 599)(450, 600)
	L = (1, 303)(2, 306)(3, 309)(4, 311)(5, 301)(6, 314)(7, 302)(8, 304)(9, 319)(10, 321)(11, 322)(12, 323)(13, 305)(14, 327)(15, 329)(16, 307)(17, 308)(18, 310)(19, 337)(20, 339)(21, 340)(22, 341)(23, 343)(24, 312)(25, 345)(26, 313)(27, 350)(28, 352)(29, 353)(30, 315)(31, 355)(32, 316)(33, 358)(34, 317)(35, 318)(36, 320)(37, 364)(38, 366)(39, 331)(40, 367)(41, 369)(42, 346)(43, 371)(44, 324)(45, 373)(46, 325)(47, 374)(48, 326)(49, 328)(50, 379)(51, 375)(52, 333)(53, 381)(54, 330)(55, 383)(56, 384)(57, 332)(58, 387)(59, 388)(60, 334)(61, 335)(62, 336)(63, 338)(64, 348)(65, 397)(66, 359)(67, 398)(68, 342)(69, 390)(70, 385)(71, 403)(72, 344)(73, 406)(74, 407)(75, 347)(76, 396)(77, 349)(78, 351)(79, 357)(80, 413)(81, 414)(82, 354)(83, 416)(84, 417)(85, 356)(86, 412)(87, 419)(88, 420)(89, 421)(90, 360)(91, 418)(92, 361)(93, 362)(94, 363)(95, 365)(96, 429)(97, 391)(98, 424)(99, 422)(100, 368)(101, 370)(102, 432)(103, 433)(104, 408)(105, 372)(106, 434)(107, 436)(108, 376)(109, 377)(110, 378)(111, 380)(112, 440)(113, 399)(114, 441)(115, 382)(116, 426)(117, 443)(118, 386)(119, 437)(120, 444)(121, 445)(122, 389)(123, 402)(124, 392)(125, 446)(126, 393)(127, 394)(128, 395)(129, 425)(130, 400)(131, 401)(132, 404)(133, 405)(134, 430)(135, 428)(136, 449)(137, 409)(138, 410)(139, 411)(140, 435)(141, 415)(142, 439)(143, 450)(144, 447)(145, 442)(146, 423)(147, 427)(148, 431)(149, 438)(150, 448)(151, 451)(152, 452)(153, 453)(154, 454)(155, 455)(156, 456)(157, 457)(158, 458)(159, 459)(160, 460)(161, 461)(162, 462)(163, 463)(164, 464)(165, 465)(166, 466)(167, 467)(168, 468)(169, 469)(170, 470)(171, 471)(172, 472)(173, 473)(174, 474)(175, 475)(176, 476)(177, 477)(178, 478)(179, 479)(180, 480)(181, 481)(182, 482)(183, 483)(184, 484)(185, 485)(186, 486)(187, 487)(188, 488)(189, 489)(190, 490)(191, 491)(192, 492)(193, 493)(194, 494)(195, 495)(196, 496)(197, 497)(198, 498)(199, 499)(200, 500)(201, 501)(202, 502)(203, 503)(204, 504)(205, 505)(206, 506)(207, 507)(208, 508)(209, 509)(210, 510)(211, 511)(212, 512)(213, 513)(214, 514)(215, 515)(216, 516)(217, 517)(218, 518)(219, 519)(220, 520)(221, 521)(222, 522)(223, 523)(224, 524)(225, 525)(226, 526)(227, 527)(228, 528)(229, 529)(230, 530)(231, 531)(232, 532)(233, 533)(234, 534)(235, 535)(236, 536)(237, 537)(238, 538)(239, 539)(240, 540)(241, 541)(242, 542)(243, 543)(244, 544)(245, 545)(246, 546)(247, 547)(248, 548)(249, 549)(250, 550)(251, 551)(252, 552)(253, 553)(254, 554)(255, 555)(256, 556)(257, 557)(258, 558)(259, 559)(260, 560)(261, 561)(262, 562)(263, 563)(264, 564)(265, 565)(266, 566)(267, 567)(268, 568)(269, 569)(270, 570)(271, 571)(272, 572)(273, 573)(274, 574)(275, 575)(276, 576)(277, 577)(278, 578)(279, 579)(280, 580)(281, 581)(282, 582)(283, 583)(284, 584)(285, 585)(286, 586)(287, 587)(288, 588)(289, 589)(290, 590)(291, 591)(292, 592)(293, 593)(294, 594)(295, 595)(296, 596)(297, 597)(298, 598)(299, 599)(300, 600)
	local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E6.421
Graph:: simple bipartite
	v = 200 e = 300 f = 90
	degree seq :: [ 2^150, 6^50 ]

## Checksum: 422 records.
## Written on: Tue Oct 15 13:51:37 CEST 2019