## Begin on: Tue Oct 15 08:42:23 CEST 2019

ENUMERATION
No. of records: 295

FAMILY (oriented family) : isomorphism classes
1     [ E1b] : 20 (16 non-degenerate)
2     [ E3b] : 50 (30 non-degenerate)
2*    [E3*b] : 50 (30 non-degenerate)
2ex   [E3*c] : 1 (1 non-degenerate)
2*ex  [ E3c] : 1 (1 non-degenerate)
2P    [  E2] : 7 (5 non-degenerate)
2Pex  [ E1a] : 0
3     [ E5a] : 132 (25 non-degenerate)
4     [  E4] : 13 (5 non-degenerate)
4*    [ E4*] : 13 (5 non-degenerate)
4P    [  E6] : 6 (2 non-degenerate)
5     [ E3a] : 1 (1 non-degenerate)
5*    [E3*a] : 1 (1 non-degenerate)
5P    [ E5b] : 0

E4.1 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {4, 4})
Quotient :: toric
Aut^+ = C4 (small group id <4, 1>)
Aut   = D8 (small group id <8, 3>)
|r| :: 2
Presentation :: [ A, A, B, B, A, B, A, B, S^2, Z^4, S^-1 * Z * S * Z, S^-1 * A * S * B, S^-1 * B * S * A, (Z^-1 * A * B^-1 * A^-1 * B)^4 ]
Map::
	R = (1, 6, 10, 14, 2, 8, 12, 16, 4, 7, 11, 15, 3, 5, 9, 13)
	L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16)
	local type(s) :: { ( 16^16 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 8 f = 1
	degree seq :: [ 16 ]

E4.2 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {4, 4})
Quotient :: toric
Aut^+ = C4 (small group id <4, 1>)
Aut   = D8 (small group id <8, 3>)
|r| :: 2
Presentation :: [ S^2, A^2, B * A, Z * A * Z, (S * Z)^2, S * A * S * B, (B * Z)^4 ]
Map::
	R = (1, 6, 10, 14, 2, 7, 11, 15, 3, 8, 12, 16, 4, 5, 9, 13)
	L = (1, 11)(2, 12)(3, 9)(4, 10)(5, 15)(6, 16)(7, 13)(8, 14)
	local type(s) :: { ( 16^16 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 1 e = 8 f = 1
	degree seq :: [ 16 ]

E4.3 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ Z^2, S^2, B * A^-1, A^3, S * B * S * A, (S * Z)^2, A * Z * A^-1 * Z ]
Map::
	R = (1, 8, 14, 20, 2, 7, 13, 19)(3, 11, 17, 23, 5, 9, 15, 21)(4, 12, 18, 24, 6, 10, 16, 22)
	L = (1, 15)(2, 17)(3, 16)(4, 13)(5, 18)(6, 14)(7, 22)(8, 24)(9, 19)(10, 21)(11, 20)(12, 23)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 3 e = 12 f = 3
	degree seq :: [ 8^3 ]

E4.4 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = S3 (small group id <6, 1>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ Z^2, A^2, S^2, B * A, (S * Z)^2, S * A * S * B, (A * Z)^3 ]
Map::
	R = (1, 8, 14, 20, 2, 7, 13, 19)(3, 11, 17, 23, 5, 9, 15, 21)(4, 12, 18, 24, 6, 10, 16, 22)
	L = (1, 15)(2, 16)(3, 13)(4, 14)(5, 18)(6, 17)(7, 21)(8, 22)(9, 19)(10, 20)(11, 24)(12, 23)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 3 e = 12 f = 3
	degree seq :: [ 8^3 ]

E4.5 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = S3 (small group id <6, 1>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^-1 * B^-1, A^2 * B^-1, S * A * S * B, (S * Z)^2, A * Z * B^-1 * Z ]
Map:: non-degenerate
	R = (1, 8, 14, 20, 2, 7, 13, 19)(3, 12, 18, 24, 6, 9, 15, 21)(4, 11, 17, 23, 5, 10, 16, 22)
	L = (1, 15)(2, 17)(3, 16)(4, 13)(5, 18)(6, 14)(7, 21)(8, 23)(9, 22)(10, 19)(11, 24)(12, 20)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 3 e = 12 f = 3
	degree seq :: [ 8^3 ]

E4.6 :: Family: { 4P } :: Oriented family(ies): { E6 }
Signature :: (1; {2, 2})
Quotient :: toric
Aut^+ = C6 (small group id <6, 2>)
Aut   = C6 x C2 (small group id <12, 5>)
|r| :: 2
Presentation :: [ Z^2, S^2, A^-1 * B^-1, A * B^-2, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, B * Z * B^-1 * Z ]
Map:: non-degenerate
	R = (1, 8, 14, 20, 2, 7, 13, 19)(3, 11, 17, 23, 5, 9, 15, 21)(4, 12, 18, 24, 6, 10, 16, 22)
	L = (1, 15)(2, 17)(3, 16)(4, 13)(5, 18)(6, 14)(7, 21)(8, 23)(9, 22)(10, 19)(11, 24)(12, 20)
	local type(s) :: { ( 8^8 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+
Graph::
	v = 3 e = 12 f = 3
	degree seq :: [ 8^3 ]

E4.7 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 5, 5, 5})
Quotient :: dipole
Aut^+ = C5 (small group id <5, 1>)
Aut   = D10 (small group id <10, 1>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, R^2, Y1^2 * Y2, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 6, 2, 7, 5, 10, 3, 8, 4, 9)(11, 16, 13, 18, 12, 17, 14, 19, 15, 20)
	L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.8 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 6, 6})
Quotient :: dipole
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, R^2, Y1^3, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 7, 2, 8, 4, 10)(3, 9, 5, 11, 6, 12)(13, 19, 15, 21, 16, 22, 18, 24, 14, 20, 17, 23)
	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) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 3 e = 12 f = 3
	degree seq :: [ 6^2, 12 ]

E4.9 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 6, 6})
Quotient :: dipole
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 7, 2, 8, 4, 10)(3, 9, 6, 12, 5, 11)(13, 19, 15, 21, 14, 20, 18, 24, 16, 22, 17, 23)
	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) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 3 e = 12 f = 3
	degree seq :: [ 6^2, 12 ]

E4.10 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 6, 6})
Quotient :: dipole
Aut^+ = C6 (small group id <6, 2>)
Aut   = D12 (small group id <12, 4>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y2^-2, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^6 ]
Map:: non-degenerate
	R = (1, 7, 2, 8, 4, 10)(3, 9, 6, 12, 5, 11)(13, 19, 15, 21, 14, 20, 18, 24, 16, 22, 17, 23)
	L = (1, 14)(2, 16)(3, 18)(4, 13)(5, 15)(6, 17)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 3 e = 12 f = 3
	degree seq :: [ 6^2, 12 ]

E4.11 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 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, Y1^2, R^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^4 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^8 ]
Map::
	R = (1, 9, 2, 10)(3, 11, 5, 13)(4, 12, 6, 14)(7, 15, 8, 16)(17, 25, 19, 27, 23, 31, 22, 30, 18, 26, 21, 29, 24, 32, 20, 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) :: { ( 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 5 e = 16 f = 5
	degree seq :: [ 4^4, 16 ]

E4.12 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 3, 3})
Quotient :: dipole
Aut^+ = C3 x C3 (small group id <9, 2>)
Aut   = (C3 x C3) : C2 (small group id <18, 4>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3, Y3^-3, Y2^3, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), (Y3^-1, Y1^-1), (Y3 * Y2^-1)^3 ]
Map:: non-degenerate
	R = (1, 10, 2, 11, 5, 14)(3, 12, 6, 15, 8, 17)(4, 13, 7, 16, 9, 18)(19, 28, 21, 30, 22, 31)(20, 29, 24, 33, 25, 34)(23, 32, 26, 35, 27, 36)
	L = (1, 22)(2, 25)(3, 19)(4, 21)(5, 27)(6, 20)(7, 24)(8, 23)(9, 26)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 6^6 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 6 e = 18 f = 6
	degree seq :: [ 6^6 ]

E4.13 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {9, 9, 9})
Quotient :: edge
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^2, (F * T2)^2, (F * T1)^2, T1 * T2^-4 ]
Map:: non-degenerate
	R = (1, 3, 7, 6, 2, 4, 8, 9, 5)(10, 11, 14, 15, 18, 16, 17, 12, 13)
	L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)
	local type(s) :: { ( 18^9 ) }
Outer automorphisms :: reflexible
Dual of E4.14
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 9 f = 1
	degree seq :: [ 9^2 ]

E4.14 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {9, 9, 9})
Quotient :: loop
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T2^9, T1^9, (T2^-1 * T1^-1)^9 ]
Map:: non-degenerate
	R = (1, 10, 2, 11, 4, 13, 6, 15, 8, 17, 9, 18, 7, 16, 5, 14, 3, 12)
	L = (1, 11)(2, 13)(3, 10)(4, 15)(5, 12)(6, 17)(7, 14)(8, 18)(9, 16)
	local type(s) :: { ( 9^18 ) }
Outer automorphisms :: reflexible
Dual of E4.13
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 9 f = 2
	degree seq :: [ 18 ]

E4.15 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 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, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3 * Y1^-1 * Y3 * Y2 * Y3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 10, 2, 11, 6, 15, 8, 17, 3, 12, 5, 14, 7, 16, 9, 18, 4, 13)(19, 28, 21, 30, 22, 31, 26, 35, 27, 36, 24, 33, 25, 34, 20, 29, 23, 32)
	L = (1, 22)(2, 19)(3, 26)(4, 27)(5, 21)(6, 20)(7, 23)(8, 24)(9, 25)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E4.16
Graph:: bipartite
	v = 2 e = 18 f = 10
	degree seq :: [ 18^2 ]

E4.16 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {9, 9, 9})
Quotient :: dipole
Aut^+ = C9 (small group id <9, 1>)
Aut   = D18 (small group id <18, 1>)
|r| :: 2
Presentation :: [ Y1, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^9, (Y3^-1 * Y1^-1)^9, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18)(19, 28, 20, 29, 22, 31, 24, 33, 26, 35, 27, 36, 25, 34, 23, 32, 21, 30)
	L = (1, 21)(2, 19)(3, 23)(4, 20)(5, 25)(6, 22)(7, 27)(8, 24)(9, 26)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36)
	local type(s) :: { ( 18, 18 ), ( 18^18 ) }
Outer automorphisms :: reflexible
Dual of E4.15
Graph:: bipartite
	v = 10 e = 18 f = 2
	degree seq :: [ 2^9, 18 ]

E4.17 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 5, 5})
Quotient :: halfedge^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y3 * R * Y2, (Y1^-1 * Y2)^2, Y1^5 ]
Map::
	R = (1, 12, 2, 15, 5, 18, 8, 14, 4, 11)(3, 17, 7, 20, 10, 19, 9, 16, 6, 13)
	L = (1, 3)(2, 6)(4, 7)(5, 9)(8, 10)(11, 13)(12, 16)(14, 17)(15, 19)(18, 20)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.18 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 5, 5})
Quotient :: halfedge^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y2^2, Y3^2, R^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y3 * R * Y2, (R * Y1)^2, Y1^5 ]
Map:: non-degenerate
	R = (1, 12, 2, 16, 6, 19, 9, 15, 5, 11)(3, 18, 8, 20, 10, 17, 7, 14, 4, 13)
	L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 10)(11, 14)(12, 17)(13, 15)(16, 20)(18, 19)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.19 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 5, 5})
Quotient :: edge^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^5 ]
Map::
	R = (1, 11, 3, 13, 7, 17, 8, 18, 4, 14)(2, 12, 5, 15, 9, 19, 10, 20, 6, 16)(21, 22)(23, 26)(24, 25)(27, 30)(28, 29)(31, 32)(33, 36)(34, 35)(37, 40)(38, 39)
	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) :: { ( 20, 20 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.22
Graph:: simple bipartite
	v = 12 e = 20 f = 2
	degree seq :: [ 2^10, 10^2 ]

E4.20 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 5, 5})
Quotient :: edge^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^5 ]
Map::
	R = (1, 11, 4, 14, 8, 18, 9, 19, 5, 15)(2, 12, 3, 13, 7, 17, 10, 20, 6, 16)(21, 22)(23, 25)(24, 26)(27, 29)(28, 30)(31, 33)(32, 34)(35, 37)(36, 38)(39, 40)
	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) :: { ( 20, 20 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.23
Graph:: simple bipartite
	v = 12 e = 20 f = 2
	degree seq :: [ 2^10, 10^2 ]

E4.21 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 5, 5})
Quotient :: edge^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y1^5, Y2^5 ]
Map:: non-degenerate
	R = (1, 11, 4, 14)(2, 12, 6, 16)(3, 13, 8, 18)(5, 15, 9, 19)(7, 17, 10, 20)(21, 22, 25, 27, 23)(24, 28, 30, 29, 26)(31, 33, 37, 35, 32)(34, 36, 39, 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) :: { ( 8^4 ), ( 8^5 ) }
Outer automorphisms :: reflexible
Dual of E4.24
Graph:: simple bipartite
	v = 9 e = 20 f = 5
	degree seq :: [ 4^5, 5^4 ]

E4.22 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 5, 5})
Quotient :: loop^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^5 ]
Map::
	R = (1, 11, 21, 31, 3, 13, 23, 33, 7, 17, 27, 37, 8, 18, 28, 38, 4, 14, 24, 34)(2, 12, 22, 32, 5, 15, 25, 35, 9, 19, 29, 39, 10, 20, 30, 40, 6, 16, 26, 36)
	L = (1, 12)(2, 11)(3, 16)(4, 15)(5, 14)(6, 13)(7, 20)(8, 19)(9, 18)(10, 17)(21, 32)(22, 31)(23, 36)(24, 35)(25, 34)(26, 33)(27, 40)(28, 39)(29, 38)(30, 37)
	local type(s) :: { ( 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 E4.19
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 20 f = 12
	degree seq :: [ 20^2 ]

E4.23 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 5, 5})
Quotient :: loop^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^5 ]
Map::
	R = (1, 11, 21, 31, 4, 14, 24, 34, 8, 18, 28, 38, 9, 19, 29, 39, 5, 15, 25, 35)(2, 12, 22, 32, 3, 13, 23, 33, 7, 17, 27, 37, 10, 20, 30, 40, 6, 16, 26, 36)
	L = (1, 12)(2, 11)(3, 15)(4, 16)(5, 13)(6, 14)(7, 19)(8, 20)(9, 17)(10, 18)(21, 33)(22, 34)(23, 31)(24, 32)(25, 37)(26, 38)(27, 35)(28, 36)(29, 40)(30, 39)
	local type(s) :: { ( 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 E4.20
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 20 f = 12
	degree seq :: [ 20^2 ]

E4.24 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 5, 5})
Quotient :: loop^2
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y1^5, Y2^5 ]
Map:: non-degenerate
	R = (1, 11, 21, 31, 4, 14, 24, 34)(2, 12, 22, 32, 6, 16, 26, 36)(3, 13, 23, 33, 8, 18, 28, 38)(5, 15, 25, 35, 9, 19, 29, 39)(7, 17, 27, 37, 10, 20, 30, 40)
	L = (1, 12)(2, 15)(3, 11)(4, 18)(5, 17)(6, 14)(7, 13)(8, 20)(9, 16)(10, 19)(21, 33)(22, 31)(23, 37)(24, 36)(25, 32)(26, 39)(27, 35)(28, 34)(29, 40)(30, 38)
	local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.21
Transitivity :: VT+
Graph::
	v = 5 e = 20 f = 9
	degree seq :: [ 8^5 ]

E4.25 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 5, 5})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	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, 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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 20 f = 7
	degree seq :: [ 4^5, 10^2 ]

E4.26 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 5, 5})
Quotient :: dipole
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 11, 2, 12)(3, 13, 6, 16)(4, 14, 5, 15)(7, 17, 10, 20)(8, 18, 9, 19)(21, 31, 23, 33, 27, 37, 28, 38, 24, 34)(22, 32, 25, 35, 29, 39, 30, 40, 26, 36)
	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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 20 f = 7
	degree seq :: [ 4^5, 10^2 ]

E4.27 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 5, 5})
Quotient :: dipole
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3 * Y2, (Y3^-1 * Y1)^2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^5, (Y3 * Y2^-1)^5 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 6, 16)(4, 14, 5, 15)(7, 17, 10, 20)(8, 18, 9, 19)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.29
Graph:: bipartite
	v = 7 e = 20 f = 7
	degree seq :: [ 4^5, 10^2 ]

E4.28 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 5, 5})
Quotient :: dipole
Aut^+ = D10 (small group id <10, 1>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, Y2 * Y3^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 9, 19)(4, 14, 10, 20)(5, 15, 7, 17)(6, 16, 8, 18)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 7 e = 20 f = 7
	degree seq :: [ 4^5, 10^2 ]

E4.29 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 5, 5})
Quotient :: dipole
Aut^+ = D10 (small group id <10, 1>)
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, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 11, 2, 12)(3, 13, 9, 19)(4, 14, 10, 20)(5, 15, 7, 17)(6, 16, 8, 18)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.27
Graph:: bipartite
	v = 7 e = 20 f = 7
	degree seq :: [ 4^5, 10^2 ]

E4.30 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 10, 10})
Quotient :: edge
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^10 ]
Map:: non-degenerate
	R = (1, 3, 6, 10, 4, 8, 2, 7, 9, 5)(11, 12, 16, 19, 14)(13, 17, 20, 15, 18)
	L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)
	local type(s) :: { ( 20^5 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.35
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 10 f = 1
	degree seq :: [ 5^2, 10 ]

E4.31 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 10, 10})
Quotient :: edge
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^5, (T2^-1 * T1^-1)^10 ]
Map:: non-degenerate
	R = (1, 3, 2, 7, 6, 10, 8, 9, 4, 5)(11, 12, 16, 18, 14)(13, 17, 20, 19, 15)
	L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)
	local type(s) :: { ( 20^5 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.34
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 10 f = 1
	degree seq :: [ 5^2, 10 ]

E4.32 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 10, 10})
Quotient :: edge
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1, (F * T1)^2, (F * T2)^2, T1^5 ]
Map:: non-degenerate
	R = (1, 3, 4, 8, 9, 10, 6, 7, 2, 5)(11, 12, 16, 19, 14)(13, 15, 17, 20, 18)
	L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)
	local type(s) :: { ( 20^5 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.36
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 10 f = 1
	degree seq :: [ 5^2, 10 ]

E4.33 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {5, 10, 10})
Quotient :: edge
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-3, T2^-1 * T1^-1 * T2^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1) ]
Map:: non-degenerate
	R = (1, 3, 9, 4, 6, 10, 8, 2, 7, 5)(11, 12, 16, 13, 17, 20, 19, 15, 18, 14)
	L = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible
Dual of E4.37
Transitivity :: ET+
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.34 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 10, 10})
Quotient :: loop
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^10 ]
Map:: non-degenerate
	R = (1, 11, 3, 13, 6, 16, 10, 20, 4, 14, 8, 18, 2, 12, 7, 17, 9, 19, 5, 15)
	L = (1, 12)(2, 16)(3, 17)(4, 11)(5, 18)(6, 19)(7, 20)(8, 13)(9, 14)(10, 15)
	local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.31
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 10 f = 3
	degree seq :: [ 20 ]

E4.35 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 10, 10})
Quotient :: loop
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^5, (T2^-1 * T1^-1)^10 ]
Map:: non-degenerate
	R = (1, 11, 3, 13, 2, 12, 7, 17, 6, 16, 10, 20, 8, 18, 9, 19, 4, 14, 5, 15)
	L = (1, 12)(2, 16)(3, 17)(4, 11)(5, 13)(6, 18)(7, 20)(8, 14)(9, 15)(10, 19)
	local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.30
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 10 f = 3
	degree seq :: [ 20 ]

E4.36 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 10, 10})
Quotient :: loop
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T2^2 * T1, (F * T1)^2, (F * T2)^2, T1^5 ]
Map:: non-degenerate
	R = (1, 11, 3, 13, 4, 14, 8, 18, 9, 19, 10, 20, 6, 16, 7, 17, 2, 12, 5, 15)
	L = (1, 12)(2, 16)(3, 15)(4, 11)(5, 17)(6, 19)(7, 20)(8, 13)(9, 14)(10, 18)
	local type(s) :: { ( 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.32
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 10 f = 3
	degree seq :: [ 20 ]

E4.37 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {5, 10, 10})
Quotient :: loop
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ F^2, T1^-1 * T2^2 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2 ]
Map:: non-degenerate
	R = (1, 11, 3, 13, 6, 16, 9, 19, 5, 15)(2, 12, 7, 17, 10, 20, 4, 14, 8, 18)
	L = (1, 12)(2, 16)(3, 17)(4, 11)(5, 18)(6, 20)(7, 19)(8, 13)(9, 14)(10, 15)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible
Dual of E4.33
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.38 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2^2 * Y1^-2, Y2 * Y3 * Y2^-1 * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2)^2, (R * Y1)^2, Y2^4 * Y3^-1, Y2^2 * Y1^3, (Y2^-1 * Y1^-1)^10 ]
Map::
	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, 24)(2, 21)(3, 28)(4, 29)(5, 30)(6, 22)(7, 23)(8, 25)(9, 26)(10, 27)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.44
Graph:: bipartite
	v = 3 e = 20 f = 11
	degree seq :: [ 10^2, 20 ]

E4.39 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 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^-1, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^5, Y1^5 ]
Map::
	R = (1, 11, 2, 12, 6, 16, 9, 19, 4, 14)(3, 13, 5, 15, 7, 17, 10, 20, 8, 18)(21, 31, 23, 33, 24, 34, 28, 38, 29, 39, 30, 40, 26, 36, 27, 37, 22, 32, 25, 35)
	L = (1, 24)(2, 21)(3, 28)(4, 29)(5, 23)(6, 22)(7, 25)(8, 30)(9, 26)(10, 27)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.45
Graph:: bipartite
	v = 3 e = 20 f = 11
	degree seq :: [ 10^2, 20 ]

E4.40 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 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^-1, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y1^5, 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 * Y1^-1 ]
Map::
	R = (1, 11, 2, 12, 6, 16, 8, 18, 4, 14)(3, 13, 7, 17, 10, 20, 9, 19, 5, 15)(21, 31, 23, 33, 22, 32, 27, 37, 26, 36, 30, 40, 28, 38, 29, 39, 24, 34, 25, 35)
	L = (1, 24)(2, 21)(3, 25)(4, 28)(5, 29)(6, 22)(7, 23)(8, 26)(9, 30)(10, 27)(11, 31)(12, 32)(13, 33)(14, 34)(15, 35)(16, 36)(17, 37)(18, 38)(19, 39)(20, 40)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.43
Graph:: bipartite
	v = 3 e = 20 f = 11
	degree seq :: [ 10^2, 20 ]

E4.41 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y1^-2 * Y2^-1 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, Y2^3 * Y1^-1, (Y3^-1 * Y1^-1)^5 ]
Map::
	R = (1, 11, 2, 12, 6, 16, 5, 15, 8, 18, 10, 20, 9, 19, 3, 13, 7, 17, 4, 14)(21, 31, 23, 33, 28, 38, 22, 32, 27, 37, 30, 40, 26, 36, 24, 34, 29, 39, 25, 35)
	L = (1, 23)(2, 27)(3, 28)(4, 29)(5, 21)(6, 24)(7, 30)(8, 22)(9, 25)(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) :: { ( 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 E4.42
Graph:: bipartite
	v = 2 e = 20 f = 12
	degree seq :: [ 20^2 ]

E4.42 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^-2 * Y3^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, Y3^-2 * Y2^3, (Y3^-1 * Y1^-1)^10 ]
Map::
	R = (1, 11)(2, 12)(3, 13)(4, 14)(5, 15)(6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21, 31, 22, 32, 26, 36, 29, 39, 24, 34)(23, 33, 27, 37, 25, 35, 28, 38, 30, 40)
	L = (1, 23)(2, 27)(3, 29)(4, 30)(5, 21)(6, 25)(7, 24)(8, 22)(9, 28)(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) :: { ( 20, 20 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.41
Graph:: simple bipartite
	v = 12 e = 20 f = 2
	degree seq :: [ 2^10, 10^2 ]

E4.43 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^2 * Y1 * Y3 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 11, 2, 12, 6, 16, 10, 20, 5, 15, 8, 18, 3, 13, 7, 17, 9, 19, 4, 14)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)
	L = (1, 23)(2, 27)(3, 26)(4, 28)(5, 21)(6, 29)(7, 30)(8, 22)(9, 25)(10, 24)(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, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.40
Graph:: bipartite
	v = 11 e = 20 f = 3
	degree seq :: [ 2^10, 20 ]

E4.44 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^5, (Y3^-1 * Y1^-1)^10 ]
Map::
	R = (1, 11, 2, 12, 3, 13, 6, 16, 7, 17, 10, 20, 9, 19, 8, 18, 5, 15, 4, 14)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)
	L = (1, 23)(2, 26)(3, 27)(4, 22)(5, 21)(6, 30)(7, 29)(8, 24)(9, 25)(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, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.38
Graph:: bipartite
	v = 11 e = 20 f = 3
	degree seq :: [ 2^10, 20 ]

E4.45 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {5, 10, 10})
Quotient :: dipole
Aut^+ = C10 (small group id <10, 2>)
Aut   = D20 (small group id <20, 4>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^2 * Y3, (R * Y3)^2, (R * Y1)^2, Y3^5, (R * Y2 * Y3^-1)^2, (Y3^2 * Y1^-1)^2, (Y3 * Y2^-1)^5 ]
Map::
	R = (1, 11, 2, 12, 5, 15, 6, 16, 9, 19, 10, 20, 7, 17, 8, 18, 3, 13, 4, 14)(21, 31)(22, 32)(23, 33)(24, 34)(25, 35)(26, 36)(27, 37)(28, 38)(29, 39)(30, 40)
	L = (1, 23)(2, 24)(3, 27)(4, 28)(5, 21)(6, 22)(7, 29)(8, 30)(9, 25)(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) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.39
Graph:: bipartite
	v = 11 e = 20 f = 3
	degree seq :: [ 2^10, 20 ]

E4.46 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 3, 3, 3})
Quotient :: edge^2
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^3, Y3^3, Y1 * Y3 * Y2, Y2 * Y1^-1 * Y3^-1 * Y1, Y2 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 13, 4, 16, 7, 19)(2, 14, 6, 18, 10, 22)(3, 15, 8, 20, 11, 23)(5, 17, 9, 21, 12, 24)(25, 26, 29)(27, 31, 33)(28, 32, 34)(30, 35, 36)(37, 39, 42)(38, 44, 45)(40, 41, 47)(43, 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) :: { ( 8^3 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E4.49
Graph:: simple bipartite
	v = 12 e = 24 f = 6
	degree seq :: [ 3^8, 6^4 ]

E4.47 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 3, 3, 3})
Quotient :: edge^2
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1, Y1^3, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1 * Y3)^3, (Y1^-1 * Y3 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 13, 3, 15)(2, 14, 5, 17)(4, 16, 8, 20)(6, 18, 11, 23)(7, 19, 9, 21)(10, 22, 12, 24)(25, 26, 28)(27, 30, 31)(29, 33, 34)(32, 36, 35)(37, 38, 40)(39, 42, 43)(41, 45, 46)(44, 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) :: { ( 12^3 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E4.48
Graph:: simple bipartite
	v = 14 e = 24 f = 4
	degree seq :: [ 3^8, 4^6 ]

E4.48 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 3, 3, 3})
Quotient :: loop^2
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ R^2, Y1^3, Y2^3, Y3^3, Y1 * Y3 * Y2, Y2 * Y1^-1 * Y3^-1 * Y1, Y2 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y3^-1 * Y2^-1, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 13, 25, 37, 4, 16, 28, 40, 7, 19, 31, 43)(2, 14, 26, 38, 6, 18, 30, 42, 10, 22, 34, 46)(3, 15, 27, 39, 8, 20, 32, 44, 11, 23, 35, 47)(5, 17, 29, 41, 9, 21, 33, 45, 12, 24, 36, 48)
	L = (1, 14)(2, 17)(3, 19)(4, 20)(5, 13)(6, 23)(7, 21)(8, 22)(9, 15)(10, 16)(11, 24)(12, 18)(25, 39)(26, 44)(27, 42)(28, 41)(29, 47)(30, 37)(31, 46)(32, 45)(33, 38)(34, 48)(35, 40)(36, 43)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.47
Transitivity :: VT+
Graph::
	v = 4 e = 24 f = 14
	degree seq :: [ 12^4 ]

E4.49 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 3, 3, 3})
Quotient :: loop^2
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1, Y1^3, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1 * Y3)^3, (Y1^-1 * Y3 * Y2^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 13, 25, 37, 3, 15, 27, 39)(2, 14, 26, 38, 5, 17, 29, 41)(4, 16, 28, 40, 8, 20, 32, 44)(6, 18, 30, 42, 11, 23, 35, 47)(7, 19, 31, 43, 9, 21, 33, 45)(10, 22, 34, 46, 12, 24, 36, 48)
	L = (1, 14)(2, 16)(3, 18)(4, 13)(5, 21)(6, 19)(7, 15)(8, 24)(9, 22)(10, 17)(11, 20)(12, 23)(25, 38)(26, 40)(27, 42)(28, 37)(29, 45)(30, 43)(31, 39)(32, 48)(33, 46)(34, 41)(35, 44)(36, 47)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.46
Transitivity :: VT+
Graph::
	v = 6 e = 24 f = 12
	degree seq :: [ 8^6 ]

E4.50 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 3, 3})
Quotient :: dipole
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2 * Y3, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^3, (Y3 * Y2^-1)^3 ]
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, 28, 40)(26, 38, 29, 41, 30, 42)(31, 43, 34, 46, 35, 47)(32, 44, 36, 48, 33, 45)
	L = (1, 28)(2, 30)(3, 25)(4, 27)(5, 26)(6, 29)(7, 35)(8, 33)(9, 36)(10, 31)(11, 34)(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) :: { ( 6^4 ), ( 6^6 ) }
Outer automorphisms :: reflexible
Dual of E4.51
Graph:: bipartite
	v = 10 e = 24 f = 8
	degree seq :: [ 4^6, 6^4 ]

E4.51 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 3, 3})
Quotient :: dipole
Aut^+ = A4 (small group id <12, 3>)
Aut   = S4 (small group id <24, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y2^-1, Y2 * Y3^-2, Y1^3, Y2^3, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 5, 17)(3, 15, 8, 20, 7, 19)(4, 16, 9, 21, 10, 22)(6, 18, 12, 24, 11, 23)(25, 37, 27, 39, 28, 40)(26, 38, 30, 42, 31, 43)(29, 41, 33, 45, 35, 47)(32, 44, 36, 48, 34, 46)
	L = (1, 28)(2, 31)(3, 25)(4, 27)(5, 35)(6, 26)(7, 30)(8, 34)(9, 29)(10, 36)(11, 33)(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) :: { ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.50
Graph:: bipartite
	v = 8 e = 24 f = 10
	degree seq :: [ 6^8 ]

E4.52 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 3, 6})
Quotient :: halfedge^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, (Y2 * Y3)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y3)^2, Y1 * Y3 * Y1^-2 * Y2, Y1 * Y2 * Y1^-2 * Y3, Y1^6 ]
Map:: non-degenerate
	R = (1, 14, 2, 18, 6, 22, 10, 24, 12, 17, 5, 13)(3, 21, 9, 20, 8, 16, 4, 23, 11, 19, 7, 15)
	L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 11)(8, 12)(13, 16)(14, 20)(15, 22)(17, 23)(18, 21)(19, 24)
	local type(s) :: { ( 6^12 ) }
Outer automorphisms :: reflexible
Dual of E4.53
Transitivity :: VT+ AT
Graph:: bipartite
	v = 2 e = 12 f = 4
	degree seq :: [ 12^2 ]

E4.53 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 3, 6})
Quotient :: halfedge^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2^2, Y3^2, R^2, Y1^3, (R * Y1)^2, R * Y2 * R * Y3, (Y3 * Y1^-1)^2, (Y1^-1 * Y2)^2, (Y3 * Y2)^2, (Y2 * Y1 * Y3)^6 ]
Map:: non-degenerate
	R = (1, 14, 2, 17, 5, 13)(3, 20, 8, 18, 6, 15)(4, 22, 10, 19, 7, 16)(9, 23, 11, 24, 12, 21)
	L = (1, 3)(2, 6)(4, 9)(5, 8)(7, 11)(10, 12)(13, 16)(14, 19)(15, 21)(17, 22)(18, 23)(20, 24)
	local type(s) :: { ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.52
Transitivity :: VT+ AT
Graph:: bipartite
	v = 4 e = 12 f = 2
	degree seq :: [ 6^4 ]

E4.54 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 6})
Quotient :: edge^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1 * Y2)^6 ]
Map::
	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)(27, 30)(28, 32)(29, 31)(33, 36)(34, 35)(37, 39)(38, 42)(40, 46)(41, 45)(43, 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) :: { ( 24, 24 ), ( 24^6 ) }
Outer automorphisms :: reflexible
Dual of E4.57
Graph:: simple bipartite
	v = 16 e = 24 f = 2
	degree seq :: [ 2^12, 6^4 ]

E4.55 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 6})
Quotient :: edge^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, Y2 * Y1 * Y3^3 ]
Map::
	R = (1, 13, 4, 16, 11, 23, 6, 18, 12, 24, 5, 17)(2, 14, 7, 19, 10, 22, 3, 15, 9, 21, 8, 20)(25, 26)(27, 30)(28, 32)(29, 31)(33, 35)(34, 36)(37, 39)(38, 42)(40, 46)(41, 45)(43, 47)(44, 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, 12 ), ( 12^12 ) }
Outer automorphisms :: reflexible
Dual of E4.56
Graph:: simple bipartite
	v = 14 e = 24 f = 4
	degree seq :: [ 2^12, 12^2 ]

E4.56 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 6})
Quotient :: loop^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1 * Y2)^6 ]
Map::
	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, 13)(3, 18)(4, 20)(5, 19)(6, 15)(7, 17)(8, 16)(9, 24)(10, 23)(11, 22)(12, 21)(25, 39)(26, 42)(27, 37)(28, 46)(29, 45)(30, 38)(31, 48)(32, 47)(33, 41)(34, 40)(35, 44)(36, 43)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.55
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 24 f = 14
	degree seq :: [ 12^4 ]

E4.57 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 6})
Quotient :: loop^2
Aut^+ = D12 (small group id <12, 4>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, Y2 * Y1 * Y3^3 ]
Map::
	R = (1, 13, 25, 37, 4, 16, 28, 40, 11, 23, 35, 47, 6, 18, 30, 42, 12, 24, 36, 48, 5, 17, 29, 41)(2, 14, 26, 38, 7, 19, 31, 43, 10, 22, 34, 46, 3, 15, 27, 39, 9, 21, 33, 45, 8, 20, 32, 44)
	L = (1, 14)(2, 13)(3, 18)(4, 20)(5, 19)(6, 15)(7, 17)(8, 16)(9, 23)(10, 24)(11, 21)(12, 22)(25, 39)(26, 42)(27, 37)(28, 46)(29, 45)(30, 38)(31, 47)(32, 48)(33, 41)(34, 40)(35, 43)(36, 44)
	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 E4.54
Transitivity :: VT+
Graph:: bipartite
	v = 2 e = 24 f = 16
	degree seq :: [ 24^2 ]

E4.58 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 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 :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 6, 18)(4, 16, 7, 19)(5, 17, 8, 20)(9, 21, 11, 23)(10, 22, 12, 24)(25, 37, 27, 39, 29, 41)(26, 38, 30, 42, 32, 44)(28, 40, 33, 45, 34, 46)(31, 43, 35, 47, 36, 48)
	L = (1, 28)(2, 31)(3, 33)(4, 25)(5, 34)(6, 35)(7, 26)(8, 36)(9, 27)(10, 29)(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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.61
Graph:: simple bipartite
	v = 10 e = 24 f = 8
	degree seq :: [ 4^6, 6^4 ]

E4.59 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 6})
Quotient :: dipole
Aut^+ = D12 (small group id <12, 4>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ Y1^2, Y3^2, R^2, Y2^3, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 8, 20)(4, 16, 7, 19)(5, 17, 6, 18)(9, 21, 12, 24)(10, 22, 11, 23)(25, 37, 27, 39, 29, 41)(26, 38, 30, 42, 32, 44)(28, 40, 33, 45, 34, 46)(31, 43, 35, 47, 36, 48)
	L = (1, 28)(2, 31)(3, 33)(4, 25)(5, 34)(6, 35)(7, 26)(8, 36)(9, 27)(10, 29)(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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.62
Graph:: simple bipartite
	v = 10 e = 24 f = 8
	degree seq :: [ 4^6, 6^4 ]

E4.60 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 6})
Quotient :: dipole
Aut^+ = D12 (small group id <12, 4>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14)(3, 15, 9, 21)(4, 16, 10, 22)(5, 17, 7, 19)(6, 18, 8, 20)(11, 23, 12, 24)(25, 37, 27, 39, 29, 41)(26, 38, 31, 43, 33, 45)(28, 40, 35, 47, 30, 42)(32, 44, 36, 48, 34, 46)
	L = (1, 28)(2, 32)(3, 35)(4, 27)(5, 30)(6, 25)(7, 36)(8, 31)(9, 34)(10, 26)(11, 29)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.63
Graph:: simple bipartite
	v = 10 e = 24 f = 8
	degree seq :: [ 4^6, 6^4 ]

E4.61 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 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, Y2^2, Y3^2, Y1^-3 * Y3, (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 6, 18, 4, 16, 8, 20, 5, 17)(3, 15, 7, 19, 11, 23, 9, 21, 12, 24, 10, 22)(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, 25)(5, 30)(6, 29)(7, 36)(8, 26)(9, 27)(10, 35)(11, 34)(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) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.58
Graph:: bipartite
	v = 8 e = 24 f = 10
	degree seq :: [ 4^6, 12^2 ]

E4.62 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 6})
Quotient :: dipole
Aut^+ = D12 (small group id <12, 4>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^-3 * Y3, (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 6, 18, 4, 16, 8, 20, 5, 17)(3, 15, 9, 21, 12, 24, 10, 22, 11, 23, 7, 19)(25, 37, 27, 39)(26, 38, 31, 43)(28, 40, 34, 46)(29, 41, 33, 45)(30, 42, 35, 47)(32, 44, 36, 48)
	L = (1, 28)(2, 32)(3, 34)(4, 25)(5, 30)(6, 29)(7, 36)(8, 26)(9, 35)(10, 27)(11, 33)(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) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.59
Graph:: bipartite
	v = 8 e = 24 f = 10
	degree seq :: [ 4^6, 12^2 ]

E4.63 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 6})
Quotient :: dipole
Aut^+ = D12 (small group id <12, 4>)
Aut   = C2 x C2 x S3 (small group id <24, 14>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^-1 * Y1, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1^6 ]
Map:: non-degenerate
	R = (1, 13, 2, 14, 5, 17, 9, 21, 8, 20, 4, 16)(3, 15, 7, 19, 11, 23, 12, 24, 10, 22, 6, 18)(25, 37, 27, 39)(26, 38, 30, 42)(28, 40, 31, 43)(29, 41, 34, 46)(32, 44, 35, 47)(33, 45, 36, 48)
	L = (1, 26)(2, 29)(3, 31)(4, 25)(5, 33)(6, 27)(7, 35)(8, 28)(9, 32)(10, 30)(11, 36)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.60
Graph:: bipartite
	v = 8 e = 24 f = 10
	degree seq :: [ 4^6, 12^2 ]

E4.64 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 12})
Quotient :: edge
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^-3 * T1^2 ]
Map:: non-degenerate
	R = (1, 3, 9, 6, 12, 5)(2, 7, 11, 4, 10, 8)(13, 14, 18, 16)(15, 19, 24, 22)(17, 20, 21, 23)
	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) :: { ( 24^4 ), ( 24^6 ) }
Outer automorphisms :: reflexible
Dual of E4.68
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 12 f = 1
	degree seq :: [ 4^3, 6^2 ]

E4.65 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 12})
Quotient :: edge
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^6, (T2^-1 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 3, 2, 7, 6, 11, 10, 12, 8, 9, 4, 5)(13, 14, 18, 22, 20, 16)(15, 19, 23, 24, 21, 17)
	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) :: { ( 8^6 ), ( 8^12 ) }
Outer automorphisms :: reflexible
Dual of E4.69
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 12 f = 3
	degree seq :: [ 6^2, 12 ]

E4.66 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 6, 12})
Quotient :: edge
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1) ]
Map:: non-degenerate
	R = (1, 3, 9, 5)(2, 7, 12, 8)(4, 10, 11, 6)(13, 14, 18, 17, 20, 23, 21, 24, 22, 15, 19, 16)
	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) :: { ( 12^4 ), ( 12^12 ) }
Outer automorphisms :: reflexible
Dual of E4.67
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 12 f = 2
	degree seq :: [ 4^3, 12 ]

E4.67 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 12})
Quotient :: loop
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^-3 * T1^2 ]
Map:: non-degenerate
	R = (1, 13, 3, 15, 9, 21, 6, 18, 12, 24, 5, 17)(2, 14, 7, 19, 11, 23, 4, 16, 10, 22, 8, 20)
	L = (1, 14)(2, 18)(3, 19)(4, 13)(5, 20)(6, 16)(7, 24)(8, 21)(9, 23)(10, 15)(11, 17)(12, 22)
	local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.66
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 12 f = 4
	degree seq :: [ 12^2 ]

E4.68 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 12})
Quotient :: loop
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^6, (T2^-1 * T1^-1)^4 ]
Map:: non-degenerate
	R = (1, 13, 3, 15, 2, 14, 7, 19, 6, 18, 11, 23, 10, 22, 12, 24, 8, 20, 9, 21, 4, 16, 5, 17)
	L = (1, 14)(2, 18)(3, 19)(4, 13)(5, 15)(6, 22)(7, 23)(8, 16)(9, 17)(10, 20)(11, 24)(12, 21)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.64
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 12 f = 5
	degree seq :: [ 24 ]

E4.69 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 6, 12})
Quotient :: loop
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1) ]
Map:: non-degenerate
	R = (1, 13, 3, 15, 9, 21, 5, 17)(2, 14, 7, 19, 12, 24, 8, 20)(4, 16, 10, 22, 11, 23, 6, 18)
	L = (1, 14)(2, 18)(3, 19)(4, 13)(5, 20)(6, 17)(7, 16)(8, 23)(9, 24)(10, 15)(11, 21)(12, 22)
	local type(s) :: { ( 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.65
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 12 f = 3
	degree seq :: [ 8^3 ]

E4.70 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 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, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^4, (Y2, Y1^-1), Y2^-3 * Y1^2, 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 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 12, 24, 10, 22)(5, 17, 8, 20, 9, 21, 11, 23)(25, 37, 27, 39, 33, 45, 30, 42, 36, 48, 29, 41)(26, 38, 31, 43, 35, 47, 28, 40, 34, 46, 32, 44)
	L = (1, 28)(2, 25)(3, 34)(4, 30)(5, 35)(6, 26)(7, 27)(8, 29)(9, 32)(10, 36)(11, 33)(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) :: { ( 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 E4.73
Graph:: bipartite
	v = 5 e = 24 f = 13
	degree seq :: [ 8^3, 12^2 ]

E4.71 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, Y1 * Y2^-2, (R * Y1)^2, R * Y2 * R * Y3, Y1^6, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 10, 22, 8, 20, 4, 16)(3, 15, 7, 19, 11, 23, 12, 24, 9, 21, 5, 17)(25, 37, 27, 39, 26, 38, 31, 43, 30, 42, 35, 47, 34, 46, 36, 48, 32, 44, 33, 45, 28, 40, 29, 41)
	L = (1, 27)(2, 31)(3, 26)(4, 29)(5, 25)(6, 35)(7, 30)(8, 33)(9, 28)(10, 36)(11, 34)(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) :: { ( 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 E4.72
Graph:: bipartite
	v = 3 e = 24 f = 15
	degree seq :: [ 12^2, 24 ]

E4.72 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^-1 * Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2, Y3^-1), (Y3^-1 * Y1^-1)^12 ]
Map::
	R = (1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24)(25, 37, 26, 38, 30, 42, 28, 40)(27, 39, 31, 43, 35, 47, 33, 45)(29, 41, 32, 44, 36, 48, 34, 46)
	L = (1, 27)(2, 31)(3, 32)(4, 33)(5, 25)(6, 35)(7, 36)(8, 26)(9, 29)(10, 28)(11, 34)(12, 30)(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, 24 ), ( 12, 24, 12, 24, 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.71
Graph:: simple bipartite
	v = 15 e = 24 f = 3
	degree seq :: [ 2^12, 8^3 ]

E4.73 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^-1 * Y1^-3, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 5, 17, 8, 20, 11, 23, 9, 21, 12, 24, 10, 22, 3, 15, 7, 19, 4, 16)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)
	L = (1, 27)(2, 31)(3, 33)(4, 34)(5, 25)(6, 28)(7, 36)(8, 26)(9, 29)(10, 35)(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) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.70
Graph:: bipartite
	v = 13 e = 24 f = 5
	degree seq :: [ 2^12, 24 ]

E4.74 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y1, Y2^-3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y2^-1), Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 11, 23, 10, 22)(5, 17, 8, 20, 12, 24, 9, 21)(25, 37, 27, 39, 33, 45, 28, 40, 34, 46, 36, 48, 30, 42, 35, 47, 32, 44, 26, 38, 31, 43, 29, 41)
	L = (1, 28)(2, 25)(3, 34)(4, 30)(5, 33)(6, 26)(7, 27)(8, 29)(9, 36)(10, 35)(11, 31)(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) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 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 E4.75
Graph:: bipartite
	v = 4 e = 24 f = 14
	degree seq :: [ 8^3, 24 ]

E4.75 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 6, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 10, 22, 8, 20, 4, 16)(3, 15, 7, 19, 11, 23, 12, 24, 9, 21, 5, 17)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)
	L = (1, 27)(2, 31)(3, 26)(4, 29)(5, 25)(6, 35)(7, 30)(8, 33)(9, 28)(10, 36)(11, 34)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24, 8, 24, 8, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.74
Graph:: simple bipartite
	v = 14 e = 24 f = 4
	degree seq :: [ 2^12, 12^2 ]

E4.76 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 12, 12})
Quotient :: edge
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-4 * T1, (T1^-1 * T2^-1)^12 ]
Map:: non-degenerate
	R = (1, 3, 8, 7, 2, 6, 12, 10, 4, 9, 11, 5)(13, 14, 16)(15, 18, 21)(17, 19, 22)(20, 24, 23)
	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) :: { ( 24^3 ), ( 24^12 ) }
Outer automorphisms :: reflexible
Dual of E4.77
Transitivity :: ET+
Graph:: bipartite
	v = 5 e = 12 f = 1
	degree seq :: [ 3^4, 12 ]

E4.77 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 12, 12})
Quotient :: loop
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-4 * T1, (T1^-1 * T2^-1)^12 ]
Map:: non-degenerate
	R = (1, 13, 3, 15, 8, 20, 7, 19, 2, 14, 6, 18, 12, 24, 10, 22, 4, 16, 9, 21, 11, 23, 5, 17)
	L = (1, 14)(2, 16)(3, 18)(4, 13)(5, 19)(6, 21)(7, 22)(8, 24)(9, 15)(10, 17)(11, 20)(12, 23)
	local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.76
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 12 f = 5
	degree seq :: [ 24 ]

E4.78 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 12, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|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 * Y2^4, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 ]
Map::
	R = (1, 13, 2, 14, 4, 16)(3, 15, 6, 18, 9, 21)(5, 17, 7, 19, 10, 22)(8, 20, 12, 24, 11, 23)(25, 37, 27, 39, 32, 44, 31, 43, 26, 38, 30, 42, 36, 48, 34, 46, 28, 40, 33, 45, 35, 47, 29, 41)
	L = (1, 28)(2, 25)(3, 33)(4, 26)(5, 34)(6, 27)(7, 29)(8, 35)(9, 30)(10, 31)(11, 36)(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) :: { ( 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 E4.79
Graph:: bipartite
	v = 5 e = 24 f = 13
	degree seq :: [ 6^4, 24 ]

E4.79 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 12, 12})
Quotient :: dipole
Aut^+ = C12 (small group id <12, 2>)
Aut   = D24 (small group id <24, 6>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, (Y1^-1 * Y3^-1)^12 ]
Map::
	R = (1, 13, 2, 14, 6, 18, 9, 21, 3, 15, 7, 19, 12, 24, 11, 23, 5, 17, 8, 20, 10, 22, 4, 16)(25, 37)(26, 38)(27, 39)(28, 40)(29, 41)(30, 42)(31, 43)(32, 44)(33, 45)(34, 46)(35, 47)(36, 48)
	L = (1, 27)(2, 31)(3, 29)(4, 33)(5, 25)(6, 36)(7, 32)(8, 26)(9, 35)(10, 30)(11, 28)(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) :: { ( 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.78
Graph:: bipartite
	v = 13 e = 24 f = 5
	degree seq :: [ 2^12, 24 ]

E4.80 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 5, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^5 ]
Map:: non-degenerate
	R = (1, 3, 8, 11, 5)(2, 6, 12, 13, 7)(4, 9, 14, 15, 10)(16, 17, 19)(18, 21, 24)(20, 22, 25)(23, 27, 29)(26, 28, 30)
	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) :: { ( 30^3 ), ( 30^5 ) }
Outer automorphisms :: reflexible
Dual of E4.84
Transitivity :: ET+
Graph:: simple bipartite
	v = 8 e = 15 f = 1
	degree seq :: [ 3^5, 5^3 ]

E4.81 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 5, 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^-1)^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 6, 14, 12, 4, 10, 8, 2, 7, 15, 11, 13, 5)(16, 17, 21, 26, 19)(18, 22, 29, 28, 25)(20, 23, 24, 30, 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) :: { ( 6^5 ), ( 6^15 ) }
Outer automorphisms :: reflexible
Dual of E4.85
Transitivity :: ET+
Graph:: bipartite
	v = 4 e = 15 f = 5
	degree seq :: [ 5^3, 15 ]

E4.82 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 5, 15})
Quotient :: edge
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-5, (T1^-1 * T2^-1)^5 ]
Map:: non-degenerate
	R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 13, 14)(10, 12, 15)(16, 17, 21, 27, 24, 18, 22, 28, 30, 26, 20, 23, 29, 25, 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) :: { ( 10^3 ), ( 10^15 ) }
Outer automorphisms :: reflexible
Dual of E4.83
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 15 f = 3
	degree seq :: [ 3^5, 15 ]

E4.83 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 5, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^5 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 8, 23, 11, 26, 5, 20)(2, 17, 6, 21, 12, 27, 13, 28, 7, 22)(4, 19, 9, 24, 14, 29, 15, 30, 10, 25)
	L = (1, 17)(2, 19)(3, 21)(4, 16)(5, 22)(6, 24)(7, 25)(8, 27)(9, 18)(10, 20)(11, 28)(12, 29)(13, 30)(14, 23)(15, 26)
	local type(s) :: { ( 3, 15, 3, 15, 3, 15, 3, 15, 3, 15 ) }
Outer automorphisms :: reflexible
Dual of E4.82
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 15 f = 6
	degree seq :: [ 10^3 ]

E4.84 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 5, 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^-1)^3 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 9, 24, 6, 21, 14, 29, 12, 27, 4, 19, 10, 25, 8, 23, 2, 17, 7, 22, 15, 30, 11, 26, 13, 28, 5, 20)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 26)(7, 29)(8, 24)(9, 30)(10, 18)(11, 19)(12, 20)(13, 25)(14, 28)(15, 27)
	local type(s) :: { ( 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.80
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 15 f = 8
	degree seq :: [ 30 ]

E4.85 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 5, 15})
Quotient :: loop
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-5, (T1^-1 * T2^-1)^5 ]
Map:: non-degenerate
	R = (1, 16, 3, 18, 5, 20)(2, 17, 7, 22, 8, 23)(4, 19, 9, 24, 11, 26)(6, 21, 13, 28, 14, 29)(10, 25, 12, 27, 15, 30)
	L = (1, 17)(2, 21)(3, 22)(4, 16)(5, 23)(6, 27)(7, 28)(8, 29)(9, 18)(10, 19)(11, 20)(12, 24)(13, 30)(14, 25)(15, 26)
	local type(s) :: { ( 5, 15, 5, 15, 5, 15 ) }
Outer automorphisms :: reflexible
Dual of E4.81
Transitivity :: ET+ VT+ AT
Graph::
	v = 5 e = 15 f = 4
	degree seq :: [ 6^5 ]

E4.86 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 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, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^5, Y3^15 ]
Map::
	R = (1, 16, 2, 17, 4, 19)(3, 18, 6, 21, 9, 24)(5, 20, 7, 22, 10, 25)(8, 23, 12, 27, 14, 29)(11, 26, 13, 28, 15, 30)(31, 46, 33, 48, 38, 53, 41, 56, 35, 50)(32, 47, 36, 51, 42, 57, 43, 58, 37, 52)(34, 49, 39, 54, 44, 59, 45, 60, 40, 55)
	L = (1, 34)(2, 31)(3, 39)(4, 32)(5, 40)(6, 33)(7, 35)(8, 44)(9, 36)(10, 37)(11, 45)(12, 38)(13, 41)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.89
Graph:: bipartite
	v = 8 e = 30 f = 16
	degree seq :: [ 6^5, 10^3 ]

E4.87 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^2 * Y2^-3, Y1^5, (Y3^-1 * Y1^-1)^3 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 14, 29, 13, 28, 10, 25)(5, 20, 8, 23, 9, 24, 15, 30, 12, 27)(31, 46, 33, 48, 39, 54, 36, 51, 44, 59, 42, 57, 34, 49, 40, 55, 38, 53, 32, 47, 37, 52, 45, 60, 41, 56, 43, 58, 35, 50)
	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) :: { ( 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 E4.88
Graph:: bipartite
	v = 4 e = 30 f = 20
	degree seq :: [ 10^3, 30 ]

E4.88 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^-5, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3^2, (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, 34, 49)(33, 48, 36, 51, 39, 54)(35, 50, 37, 52, 40, 55)(38, 53, 42, 57, 45, 60)(41, 56, 43, 58, 44, 59)
	L = (1, 33)(2, 36)(3, 38)(4, 39)(5, 31)(6, 42)(7, 32)(8, 44)(9, 45)(10, 34)(11, 35)(12, 41)(13, 37)(14, 40)(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) :: { ( 10, 30 ), ( 10, 30, 10, 30, 10, 30 ) }
Outer automorphisms :: reflexible
Dual of E4.87
Graph:: simple bipartite
	v = 20 e = 30 f = 4
	degree seq :: [ 2^15, 6^5 ]

E4.89 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 15})
Quotient :: dipole
Aut^+ = C15 (small group id <15, 1>)
Aut   = D30 (small group id <30, 3>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3 * Y1^-5, (Y3 * Y2^-1)^3, (Y1^-1 * Y3^-1)^5 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 12, 27, 9, 24, 3, 18, 7, 22, 13, 28, 15, 30, 11, 26, 5, 20, 8, 23, 14, 29, 10, 25, 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, 35)(4, 39)(5, 31)(6, 43)(7, 38)(8, 32)(9, 41)(10, 42)(11, 34)(12, 45)(13, 44)(14, 36)(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) :: { ( 6, 10 ), ( 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.86
Graph:: bipartite
	v = 16 e = 30 f = 8
	degree seq :: [ 2^15, 30 ]

E4.90 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 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, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^5 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ]
Map::
	R = (1, 16, 2, 17, 4, 19)(3, 18, 6, 21, 9, 24)(5, 20, 7, 22, 10, 25)(8, 23, 12, 27, 14, 29)(11, 26, 13, 28, 15, 30)(31, 46, 33, 48, 38, 53, 43, 58, 37, 52, 32, 47, 36, 51, 42, 57, 45, 60, 40, 55, 34, 49, 39, 54, 44, 59, 41, 56, 35, 50)
	L = (1, 34)(2, 31)(3, 39)(4, 32)(5, 40)(6, 33)(7, 35)(8, 44)(9, 36)(10, 37)(11, 45)(12, 38)(13, 41)(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, 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 E4.91
Graph:: bipartite
	v = 6 e = 30 f = 18
	degree seq :: [ 6^5, 30 ]

E4.91 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 5, 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^-3 * Y1^2, Y1^5, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, (Y3 * Y2^-1)^15 ]
Map::
	R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 14, 29, 13, 28, 10, 25)(5, 20, 8, 23, 9, 24, 15, 30, 12, 27)(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, 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) :: { ( 6, 30 ), ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) }
Outer automorphisms :: reflexible
Dual of E4.90
Graph:: simple bipartite
	v = 18 e = 30 f = 6
	degree seq :: [ 2^15, 10^3 ]

E4.92 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 8})
Quotient :: dipole
Aut^+ = D16 (small group id <16, 7>)
Aut   = C2 x D16 (small group id <32, 39>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ]
Map:: non-degenerate
	R = (1, 17, 2, 18)(3, 19, 5, 21)(4, 20, 8, 24)(6, 22, 10, 26)(7, 23, 11, 27)(9, 25, 13, 29)(12, 28, 16, 32)(14, 30, 15, 31)(33, 49, 35, 51)(34, 50, 37, 53)(36, 52, 39, 55)(38, 54, 41, 57)(40, 56, 43, 59)(42, 58, 45, 61)(44, 60, 47, 63)(46, 62, 48, 64)
	L = (1, 36)(2, 38)(3, 39)(4, 33)(5, 41)(6, 34)(7, 35)(8, 44)(9, 37)(10, 46)(11, 47)(12, 40)(13, 48)(14, 42)(15, 43)(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) :: { ( 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E4.93
Graph:: simple bipartite
	v = 16 e = 32 f = 10
	degree seq :: [ 4^16 ]

E4.93 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 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, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y3 * Y1^4, Y1^-1 * Y2 * Y1 * Y3 * Y1^-2 ]
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, 8, 24, 4, 20, 11, 27, 14, 30, 7, 23)(33, 49, 35, 51)(34, 50, 39, 55)(36, 52, 42, 58)(37, 53, 41, 57)(38, 54, 46, 62)(40, 56, 48, 64)(43, 59, 45, 61)(44, 60, 47, 63)
	L = (1, 36)(2, 40)(3, 42)(4, 33)(5, 43)(6, 47)(7, 48)(8, 34)(9, 45)(10, 35)(11, 37)(12, 46)(13, 41)(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) :: { ( 4^4 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E4.92
Graph:: bipartite
	v = 10 e = 32 f = 16
	degree seq :: [ 4^8, 16^2 ]

E4.94 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 8})
Quotient :: edge
Aut^+ = Q16 (small group id <16, 9>)
Aut   = (C8 x C2) : C2 (small group id <32, 42>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, T2 * T1 * T2 * T1^-1, (F * T1)^2, T2^2 * T1^-1 * T2^-2 * T1^-1 ]
Map:: non-degenerate
	R = (1, 3, 9, 14, 6, 13, 12, 5)(2, 7, 15, 10, 4, 11, 16, 8)(17, 18, 22, 20)(19, 24, 29, 26)(21, 23, 30, 27)(25, 32, 28, 31)
	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) :: { ( 8^4 ), ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E4.95
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 16 f = 4
	degree seq :: [ 4^4, 8^2 ]

E4.95 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 8})
Quotient :: loop
Aut^+ = Q16 (small group id <16, 9>)
Aut   = (C8 x C2) : C2 (small group id <32, 42>)
|r| :: 2
Presentation :: [ F^2, T1^-2 * T2^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-2 * T2^-1, T2^-1 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 ]
Map:: non-degenerate
	R = (1, 17, 3, 19, 6, 22, 5, 21)(2, 18, 7, 23, 4, 20, 8, 24)(9, 25, 13, 29, 10, 26, 14, 30)(11, 27, 15, 31, 12, 28, 16, 32)
	L = (1, 18)(2, 22)(3, 25)(4, 17)(5, 26)(6, 20)(7, 27)(8, 28)(9, 21)(10, 19)(11, 24)(12, 23)(13, 32)(14, 31)(15, 29)(16, 30)
	local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.94
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 16 f = 6
	degree seq :: [ 8^4 ]

E4.96 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8})
Quotient :: dipole
Aut^+ = Q16 (small group id <16, 9>)
Aut   = (C8 x C2) : C2 (small group id <32, 42>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2^-4 * Y1^-1, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 8, 24, 13, 29, 10, 26)(5, 21, 7, 23, 14, 30, 11, 27)(9, 25, 16, 32, 12, 28, 15, 31)(33, 49, 35, 51, 41, 57, 46, 62, 38, 54, 45, 61, 44, 60, 37, 53)(34, 50, 39, 55, 47, 63, 42, 58, 36, 52, 43, 59, 48, 64, 40, 56)
	L = (1, 35)(2, 39)(3, 41)(4, 43)(5, 33)(6, 45)(7, 47)(8, 34)(9, 46)(10, 36)(11, 48)(12, 37)(13, 44)(14, 38)(15, 42)(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) :: { ( 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 E4.97
Graph:: bipartite
	v = 6 e = 32 f = 20
	degree seq :: [ 8^4, 16^2 ]

E4.97 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 8})
Quotient :: dipole
Aut^+ = Q16 (small group id <16, 9>)
Aut   = (C8 x C2) : C2 (small group id <32, 42>)
|r| :: 2
Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^8 ]
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, 40, 56, 45, 61, 42, 58)(37, 53, 39, 55, 46, 62, 43, 59)(41, 57, 48, 64, 44, 60, 47, 63)
	L = (1, 35)(2, 39)(3, 41)(4, 43)(5, 33)(6, 45)(7, 47)(8, 34)(9, 46)(10, 36)(11, 48)(12, 37)(13, 44)(14, 38)(15, 42)(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) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16 ) }
Outer automorphisms :: reflexible
Dual of E4.96
Graph:: simple bipartite
	v = 20 e = 32 f = 6
	degree seq :: [ 2^16, 8^4 ]

E4.98 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 16, 16})
Quotient :: regular
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2 * T1^8 ]
Map::
	R = (1, 2, 5, 9, 13, 15, 11, 7, 3, 6, 10, 14, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 16)
	local type(s) :: { ( 16^16 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 8 f = 1
	degree seq :: [ 16 ]

E4.99 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 16, 16})
Quotient :: edge
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^8 * T1 ]
Map::
	R = (1, 3, 7, 11, 15, 14, 10, 6, 2, 5, 9, 13, 16, 12, 8, 4)(17, 18)(19, 21)(20, 22)(23, 25)(24, 26)(27, 29)(28, 30)(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, 32 ), ( 32^16 ) }
Outer automorphisms :: reflexible
Dual of E4.100
Transitivity :: ET+
Graph:: bipartite
	v = 9 e = 16 f = 1
	degree seq :: [ 2^8, 16 ]

E4.100 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 16, 16})
Quotient :: loop
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^8 * T1 ]
Map::
	R = (1, 17, 3, 19, 7, 23, 11, 27, 15, 31, 14, 30, 10, 26, 6, 22, 2, 18, 5, 21, 9, 25, 13, 29, 16, 32, 12, 28, 8, 24, 4, 20)
	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)
	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, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E4.99
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 16 f = 9
	degree seq :: [ 32 ]

E4.101 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|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, Y2^8 * Y1, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 17, 2, 18)(3, 19, 5, 21)(4, 20, 6, 22)(7, 23, 9, 25)(8, 24, 10, 26)(11, 27, 13, 29)(12, 28, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 39, 55, 43, 59, 47, 63, 46, 62, 42, 58, 38, 54, 34, 50, 37, 53, 41, 57, 45, 61, 48, 64, 44, 60, 40, 56, 36, 52)
	L = (1, 34)(2, 33)(3, 37)(4, 38)(5, 35)(6, 36)(7, 41)(8, 42)(9, 39)(10, 40)(11, 45)(12, 46)(13, 43)(14, 44)(15, 48)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.102
Graph:: bipartite
	v = 9 e = 32 f = 17
	degree seq :: [ 4^8, 32 ]

E4.102 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 16, 16})
Quotient :: dipole
Aut^+ = C16 (small group id <16, 1>)
Aut   = D32 (small group id <32, 18>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^8 ]
Map::
	R = (1, 17, 2, 18, 5, 21, 9, 25, 13, 29, 15, 31, 11, 27, 7, 23, 3, 19, 6, 22, 10, 26, 14, 30, 16, 32, 12, 28, 8, 24, 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, 38)(3, 33)(4, 39)(5, 42)(6, 34)(7, 36)(8, 43)(9, 46)(10, 37)(11, 40)(12, 47)(13, 48)(14, 41)(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) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E4.101
Graph:: bipartite
	v = 17 e = 32 f = 9
	degree seq :: [ 2^16, 32 ]

E4.103 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 3, 3})
Quotient :: halfedge^2
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, Y1^3, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 ]
Map::
	R = (1, 20, 2, 22, 4, 19)(3, 24, 6, 25, 7, 21)(5, 27, 9, 28, 10, 23)(8, 31, 13, 32, 14, 26)(11, 33, 15, 35, 17, 29)(12, 34, 16, 36, 18, 30)
	L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 12)(9, 15)(10, 16)(13, 17)(14, 18)(19, 21)(20, 23)(22, 26)(24, 29)(25, 30)(27, 33)(28, 34)(31, 35)(32, 36)
	local type(s) :: { ( 6^6 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: VT+ AT
Graph:: bipartite
	v = 6 e = 18 f = 6
	degree seq :: [ 6^6 ]

E4.104 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 3})
Quotient :: edge^2
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 19, 3, 21, 4, 22)(2, 20, 5, 23, 6, 24)(7, 25, 11, 29, 12, 30)(8, 26, 13, 31, 14, 32)(9, 27, 15, 33, 16, 34)(10, 28, 17, 35, 18, 36)(37, 38)(39, 43)(40, 44)(41, 45)(42, 46)(47, 51)(48, 53)(49, 52)(50, 54)(55, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(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) :: { ( 12, 12 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.106
Graph:: simple bipartite
	v = 24 e = 36 f = 6
	degree seq :: [ 2^18, 6^6 ]

E4.105 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 3, 3})
Quotient :: edge^2
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = C6 x S3 (small group id <36, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^3, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 19, 4, 22)(2, 20, 5, 23)(3, 21, 6, 24)(7, 25, 13, 31)(8, 26, 14, 32)(9, 27, 15, 33)(10, 28, 16, 34)(11, 29, 17, 35)(12, 30, 18, 36)(37, 38, 39)(40, 43, 44)(41, 45, 46)(42, 47, 48)(49, 51, 53)(50, 52, 54)(55, 57, 56)(58, 62, 61)(59, 64, 63)(60, 66, 65)(67, 71, 69)(68, 72, 70)
	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) :: { ( 8^3 ), ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E4.107
Graph:: simple bipartite
	v = 21 e = 36 f = 9
	degree seq :: [ 3^12, 4^9 ]

E4.106 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 3})
Quotient :: loop^2
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ]
Map::
	R = (1, 19, 37, 55, 3, 21, 39, 57, 4, 22, 40, 58)(2, 20, 38, 56, 5, 23, 41, 59, 6, 24, 42, 60)(7, 25, 43, 61, 11, 29, 47, 65, 12, 30, 48, 66)(8, 26, 44, 62, 13, 31, 49, 67, 14, 32, 50, 68)(9, 27, 45, 63, 15, 33, 51, 69, 16, 34, 52, 70)(10, 28, 46, 64, 17, 35, 53, 71, 18, 36, 54, 72)
	L = (1, 20)(2, 19)(3, 25)(4, 26)(5, 27)(6, 28)(7, 21)(8, 22)(9, 23)(10, 24)(11, 33)(12, 35)(13, 34)(14, 36)(15, 29)(16, 31)(17, 30)(18, 32)(37, 56)(38, 55)(39, 61)(40, 62)(41, 63)(42, 64)(43, 57)(44, 58)(45, 59)(46, 60)(47, 69)(48, 71)(49, 70)(50, 72)(51, 65)(52, 67)(53, 66)(54, 68)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.104
Transitivity :: VT+
Graph:: bipartite
	v = 6 e = 36 f = 24
	degree seq :: [ 12^6 ]

E4.107 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 3, 3})
Quotient :: loop^2
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = C6 x S3 (small group id <36, 12>)
|r| :: 2
Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^3, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 ]
Map:: non-degenerate
	R = (1, 19, 37, 55, 4, 22, 40, 58)(2, 20, 38, 56, 5, 23, 41, 59)(3, 21, 39, 57, 6, 24, 42, 60)(7, 25, 43, 61, 13, 31, 49, 67)(8, 26, 44, 62, 14, 32, 50, 68)(9, 27, 45, 63, 15, 33, 51, 69)(10, 28, 46, 64, 16, 34, 52, 70)(11, 29, 47, 65, 17, 35, 53, 71)(12, 30, 48, 66, 18, 36, 54, 72)
	L = (1, 20)(2, 21)(3, 19)(4, 25)(5, 27)(6, 29)(7, 26)(8, 22)(9, 28)(10, 23)(11, 30)(12, 24)(13, 33)(14, 34)(15, 35)(16, 36)(17, 31)(18, 32)(37, 57)(38, 55)(39, 56)(40, 62)(41, 64)(42, 66)(43, 58)(44, 61)(45, 59)(46, 63)(47, 60)(48, 65)(49, 71)(50, 72)(51, 67)(52, 68)(53, 69)(54, 70)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.105
Transitivity :: VT+
Graph::
	v = 9 e = 36 f = 21
	degree seq :: [ 8^9 ]

E4.108 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 3})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 10, 28)(5, 23, 9, 27)(6, 24, 8, 26)(11, 29, 16, 34)(12, 30, 15, 33)(13, 31, 18, 36)(14, 32, 17, 35)(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, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.110
Graph:: simple bipartite
	v = 15 e = 36 f = 15
	degree seq :: [ 4^9, 6^6 ]

E4.109 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 3})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y3, Y3, Y3, Y3, Y1^2, R^2, Y2^3, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ]
Map::
	R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 15, 33)(12, 30, 17, 35)(13, 31, 16, 34)(14, 32, 18, 36)(37, 55, 39, 57, 40, 58)(38, 56, 41, 59, 42, 60)(43, 61, 47, 65, 48, 66)(44, 62, 49, 67, 50, 68)(45, 63, 51, 69, 52, 70)(46, 64, 53, 71, 54, 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) :: { ( 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible selfdual
Graph:: bipartite
	v = 15 e = 36 f = 15
	degree seq :: [ 4^9, 6^6 ]

E4.110 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 3})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y3 * Y1 * Y2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 19, 2, 20)(3, 21, 11, 29)(4, 22, 10, 28)(5, 23, 15, 33)(6, 24, 8, 26)(7, 25, 12, 30)(9, 27, 16, 34)(13, 31, 17, 35)(14, 32, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 48, 66, 50, 68)(42, 60, 49, 67, 52, 70)(44, 62, 47, 65, 54, 72)(46, 64, 53, 71, 51, 69)
	L = (1, 40)(2, 44)(3, 48)(4, 42)(5, 50)(6, 37)(7, 47)(8, 46)(9, 54)(10, 38)(11, 53)(12, 49)(13, 39)(14, 52)(15, 45)(16, 41)(17, 43)(18, 51)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.108
Graph:: simple bipartite
	v = 15 e = 36 f = 15
	degree seq :: [ 4^9, 6^6 ]

E4.111 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 3})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y3^-1 * Y1 * Y2^-1 * Y1 * Y2 ]
Map:: polytopal non-degenerate
	R = (1, 19, 2, 20)(3, 21, 11, 29)(4, 22, 10, 28)(5, 23, 15, 33)(6, 24, 8, 26)(7, 25, 13, 31)(9, 27, 14, 32)(12, 30, 17, 35)(16, 34, 18, 36)(37, 55, 39, 57, 41, 59)(38, 56, 43, 61, 45, 63)(40, 58, 48, 66, 50, 68)(42, 60, 49, 67, 52, 70)(44, 62, 53, 71, 51, 69)(46, 64, 47, 65, 54, 72)
	L = (1, 40)(2, 44)(3, 48)(4, 42)(5, 50)(6, 37)(7, 53)(8, 46)(9, 51)(10, 38)(11, 43)(12, 49)(13, 39)(14, 52)(15, 54)(16, 41)(17, 47)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 15 e = 36 f = 15
	degree seq :: [ 4^9, 6^6 ]

E4.112 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 3, 3})
Quotient :: dipole
Aut^+ = (C3 x C3) : C2 (small group id <18, 4>)
Aut   = C2 x ((C3 x C3) : C2) (small group id <36, 13>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y2^3, Y3^3, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2 ]
Map:: polytopal 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, 42)(5, 49)(6, 37)(7, 51)(8, 46)(9, 53)(10, 38)(11, 48)(12, 39)(13, 50)(14, 41)(15, 52)(16, 43)(17, 54)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible selfdual
Graph:: simple bipartite
	v = 15 e = 36 f = 15
	degree seq :: [ 4^9, 6^6 ]

E4.113 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 6, 6})
Quotient :: edge
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^6 ]
Map:: non-degenerate
	R = (1, 3, 9, 15, 11, 5)(2, 6, 12, 17, 13, 7)(4, 8, 14, 18, 16, 10)(19, 20, 22)(21, 26, 24)(23, 28, 25)(27, 30, 32)(29, 31, 34)(33, 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) :: { ( 12^3 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.115
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 18 f = 3
	degree seq :: [ 3^6, 6^3 ]

E4.114 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 6, 6})
Quotient :: edge
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (T2 * T1^-1)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^6, (T2^-1 * T1^-1)^6 ]
Map:: non-degenerate
	R = (1, 3, 9, 14, 13, 5)(2, 6, 15, 12, 16, 7)(4, 10, 18, 8, 17, 11)(19, 20, 22)(21, 26, 25)(23, 28, 30)(24, 32, 29)(27, 33, 36)(31, 34, 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) :: { ( 12^3 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.116
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 18 f = 3
	degree seq :: [ 3^6, 6^3 ]

E4.115 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 6, 6})
Quotient :: loop
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^6 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 9, 27, 15, 33, 11, 29, 5, 23)(2, 20, 6, 24, 12, 30, 17, 35, 13, 31, 7, 25)(4, 22, 8, 26, 14, 32, 18, 36, 16, 34, 10, 28)
	L = (1, 20)(2, 22)(3, 26)(4, 19)(5, 28)(6, 21)(7, 23)(8, 24)(9, 30)(10, 25)(11, 31)(12, 32)(13, 34)(14, 27)(15, 36)(16, 29)(17, 33)(18, 35)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.113
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 18 f = 9
	degree seq :: [ 12^3 ]

E4.116 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 6, 6})
Quotient :: loop
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (T2 * T1^-1)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1^-1, T2^6, (T2^-1 * T1^-1)^6 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 9, 27, 14, 32, 13, 31, 5, 23)(2, 20, 6, 24, 15, 33, 12, 30, 16, 34, 7, 25)(4, 22, 10, 28, 18, 36, 8, 26, 17, 35, 11, 29)
	L = (1, 20)(2, 22)(3, 26)(4, 19)(5, 28)(6, 32)(7, 21)(8, 25)(9, 33)(10, 30)(11, 24)(12, 23)(13, 34)(14, 29)(15, 36)(16, 35)(17, 31)(18, 27)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.114
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 18 f = 9
	degree seq :: [ 12^3 ]

E4.117 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|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, Y2^6, (Y2^-1 * Y1)^6 ]
Map::
	R = (1, 19, 2, 20, 4, 22)(3, 21, 8, 26, 6, 24)(5, 23, 10, 28, 7, 25)(9, 27, 12, 30, 14, 32)(11, 29, 13, 31, 16, 34)(15, 33, 18, 36, 17, 35)(37, 55, 39, 57, 45, 63, 51, 69, 47, 65, 41, 59)(38, 56, 42, 60, 48, 66, 53, 71, 49, 67, 43, 61)(40, 58, 44, 62, 50, 68, 54, 72, 52, 70, 46, 64)
	L = (1, 40)(2, 37)(3, 42)(4, 38)(5, 43)(6, 44)(7, 46)(8, 39)(9, 50)(10, 41)(11, 52)(12, 45)(13, 47)(14, 48)(15, 53)(16, 49)(17, 54)(18, 51)(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, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.119
Graph:: bipartite
	v = 9 e = 36 f = 21
	degree seq :: [ 6^6, 12^3 ]

E4.118 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^2 * Y3^-1, Y2 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2^-1, Y2^6, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 19, 2, 20, 4, 22)(3, 21, 8, 26, 7, 25)(5, 23, 10, 28, 12, 30)(6, 24, 14, 32, 11, 29)(9, 27, 15, 33, 18, 36)(13, 31, 16, 34, 17, 35)(37, 55, 39, 57, 45, 63, 50, 68, 49, 67, 41, 59)(38, 56, 42, 60, 51, 69, 48, 66, 52, 70, 43, 61)(40, 58, 46, 64, 54, 72, 44, 62, 53, 71, 47, 65)
	L = (1, 40)(2, 37)(3, 43)(4, 38)(5, 48)(6, 47)(7, 44)(8, 39)(9, 54)(10, 41)(11, 50)(12, 46)(13, 53)(14, 42)(15, 45)(16, 49)(17, 52)(18, 51)(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, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.120
Graph:: bipartite
	v = 9 e = 36 f = 21
	degree seq :: [ 6^6, 12^3 ]

E4.119 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^3 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 12, 30, 11, 29, 4, 22)(3, 21, 8, 26, 13, 31, 18, 36, 15, 33, 9, 27)(5, 23, 7, 25, 14, 32, 17, 35, 16, 34, 10, 28)(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, 46)(5, 37)(6, 49)(7, 44)(8, 38)(9, 40)(10, 45)(11, 51)(12, 53)(13, 50)(14, 42)(15, 52)(16, 47)(17, 54)(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, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.117
Graph:: simple bipartite
	v = 21 e = 36 f = 9
	degree seq :: [ 2^18, 12^3 ]

E4.120 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C3 x S3 (small group id <18, 3>)
Aut   = S3 x S3 (small group id <36, 10>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y1^-3, Y3 * Y1 * Y3 * Y1^3, (Y3 * Y2^-1)^3 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 14, 32, 11, 29, 4, 22)(3, 21, 9, 27, 15, 33, 12, 30, 18, 36, 8, 26)(5, 23, 10, 28, 16, 34, 7, 25, 17, 35, 13, 31)(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, 46)(5, 37)(6, 51)(7, 44)(8, 38)(9, 50)(10, 48)(11, 54)(12, 40)(13, 45)(14, 49)(15, 52)(16, 42)(17, 47)(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) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.118
Graph:: simple bipartite
	v = 21 e = 36 f = 9
	degree seq :: [ 2^18, 12^3 ]

E4.121 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 6, 6})
Quotient :: edge
Aut^+ = C6 x C3 (small group id <18, 5>)
Aut   = C2 x ((C3 x C3) : C2) (small group id <36, 13>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^6 ]
Map:: non-degenerate
	R = (1, 3, 8, 14, 11, 5)(2, 6, 12, 17, 13, 7)(4, 9, 15, 18, 16, 10)(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) :: { ( 12^3 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.122
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 18 f = 3
	degree seq :: [ 3^6, 6^3 ]

E4.122 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 6, 6})
Quotient :: loop
Aut^+ = C6 x C3 (small group id <18, 5>)
Aut   = C2 x ((C3 x C3) : C2) (small group id <36, 13>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^6 ]
Map:: non-degenerate
	R = (1, 19, 3, 21, 8, 26, 14, 32, 11, 29, 5, 23)(2, 20, 6, 24, 12, 30, 17, 35, 13, 31, 7, 25)(4, 22, 9, 27, 15, 33, 18, 36, 16, 34, 10, 28)
	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, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.121
Transitivity :: ET+ VT+ AT
Graph::
	v = 3 e = 18 f = 9
	degree seq :: [ 12^3 ]

E4.123 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C6 x C3 (small group id <18, 5>)
Aut   = C2 x ((C3 x C3) : C2) (small group id <36, 13>)
|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), Y3^6, Y2^6 ]
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, 47, 65, 41, 59)(38, 56, 42, 60, 48, 66, 53, 71, 49, 67, 43, 61)(40, 58, 45, 63, 51, 69, 54, 72, 52, 70, 46, 64)
	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, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.124
Graph:: bipartite
	v = 9 e = 36 f = 21
	degree seq :: [ 6^6, 12^3 ]

E4.124 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 6, 6})
Quotient :: dipole
Aut^+ = C6 x C3 (small group id <18, 5>)
Aut   = C2 x ((C3 x C3) : C2) (small group id <36, 13>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-6, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^6 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 12, 30, 10, 28, 4, 22)(3, 21, 7, 25, 13, 31, 17, 35, 15, 33, 9, 27)(5, 23, 8, 26, 14, 32, 18, 36, 16, 34, 11, 29)(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, 53)(13, 50)(14, 42)(15, 52)(16, 46)(17, 54)(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, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.123
Graph:: simple bipartite
	v = 21 e = 36 f = 9
	degree seq :: [ 2^18, 12^3 ]

E4.125 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 9, 18})
Quotient :: regular
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-9 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 15, 11, 7, 3, 6, 10, 14, 18, 16, 12, 8, 4)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 17)
	local type(s) :: { ( 9^18 ) }
Outer automorphisms :: reflexible
Dual of E4.126
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 1 e = 9 f = 2
	degree seq :: [ 18 ]

E4.126 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 9, 18})
Quotient :: regular
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^9 ]
Map::
	R = (1, 2, 5, 9, 13, 16, 12, 8, 4)(3, 6, 10, 14, 17, 18, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 17)(16, 18)
	local type(s) :: { ( 18^9 ) }
Outer automorphisms :: reflexible
Dual of E4.125
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 9 f = 1
	degree seq :: [ 9^2 ]

E4.127 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^9 ]
Map::
	R = (1, 3, 7, 11, 15, 16, 12, 8, 4)(2, 5, 9, 13, 17, 18, 14, 10, 6)(19, 20)(21, 23)(22, 24)(25, 27)(26, 28)(29, 31)(30, 32)(33, 35)(34, 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, 36 ), ( 36^9 ) }
Outer automorphisms :: reflexible
Dual of E4.131
Transitivity :: ET+
Graph:: simple bipartite
	v = 11 e = 18 f = 1
	degree seq :: [ 2^9, 9^2 ]

E4.128 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^2 * T2^-1 * T1 * T2^-3, T2^-2 * T1^7 ]
Map:: non-degenerate
	R = (1, 3, 9, 13, 17, 16, 11, 8, 2, 7, 4, 10, 14, 18, 15, 12, 6, 5)(19, 20, 24, 29, 33, 35, 32, 27, 22)(21, 25, 23, 26, 30, 34, 36, 31, 28)
	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) :: { ( 4^9 ), ( 4^18 ) }
Outer automorphisms :: reflexible
Dual of E4.132
Transitivity :: ET+
Graph:: bipartite
	v = 3 e = 18 f = 9
	degree seq :: [ 9^2, 18 ]

E4.129 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 9, 18})
Quotient :: edge
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-9 ]
Map::
	R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 17)(19, 20, 23, 27, 31, 35, 33, 29, 25, 21, 24, 28, 32, 36, 34, 30, 26, 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) :: { ( 18, 18 ), ( 18^18 ) }
Outer automorphisms :: reflexible
Dual of E4.130
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 18 f = 2
	degree seq :: [ 2^9, 18 ]

E4.130 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^9 ]
Map::
	R = (1, 19, 3, 21, 7, 25, 11, 29, 15, 33, 16, 34, 12, 30, 8, 26, 4, 22)(2, 20, 5, 23, 9, 27, 13, 31, 17, 35, 18, 36, 14, 32, 10, 28, 6, 24)
	L = (1, 20)(2, 19)(3, 23)(4, 24)(5, 21)(6, 22)(7, 27)(8, 28)(9, 25)(10, 26)(11, 31)(12, 32)(13, 29)(14, 30)(15, 35)(16, 36)(17, 33)(18, 34)
	local type(s) :: { ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18 ) }
Outer automorphisms :: reflexible
Dual of E4.129
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 18 f = 10
	degree seq :: [ 18^2 ]

E4.131 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ F^2, (T2, T1^-1), T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^2 * T2^-1 * T1 * T2^-3, T2^-2 * T1^7 ]
Map::
	R = (1, 19, 3, 21, 9, 27, 13, 31, 17, 35, 16, 34, 11, 29, 8, 26, 2, 20, 7, 25, 4, 22, 10, 28, 14, 32, 18, 36, 15, 33, 12, 30, 6, 24, 5, 23)
	L = (1, 20)(2, 24)(3, 25)(4, 19)(5, 26)(6, 29)(7, 23)(8, 30)(9, 22)(10, 21)(11, 33)(12, 34)(13, 28)(14, 27)(15, 35)(16, 36)(17, 32)(18, 31)
	local type(s) :: { ( 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9, 2, 9 ) }
Outer automorphisms :: reflexible
Dual of E4.127
Transitivity :: ET+ VT+ AT
Graph::
	v = 1 e = 18 f = 11
	degree seq :: [ 36 ]

E4.132 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 9, 18})
Quotient :: loop
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-9 ]
Map:: non-degenerate
	R = (1, 19, 3, 21)(2, 20, 6, 24)(4, 22, 7, 25)(5, 23, 10, 28)(8, 26, 11, 29)(9, 27, 14, 32)(12, 30, 15, 33)(13, 31, 18, 36)(16, 34, 17, 35)
	L = (1, 20)(2, 23)(3, 24)(4, 19)(5, 27)(6, 28)(7, 21)(8, 22)(9, 31)(10, 32)(11, 25)(12, 26)(13, 35)(14, 36)(15, 29)(16, 30)(17, 33)(18, 34)
	local type(s) :: { ( 9, 18, 9, 18 ) }
Outer automorphisms :: reflexible
Dual of E4.128
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 18 f = 3
	degree seq :: [ 4^9 ]

E4.133 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 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, Y2^9, (Y3 * Y2^-1)^18 ]
Map::
	R = (1, 19, 2, 20)(3, 21, 5, 23)(4, 22, 6, 24)(7, 25, 9, 27)(8, 26, 10, 28)(11, 29, 13, 31)(12, 30, 14, 32)(15, 33, 17, 35)(16, 34, 18, 36)(37, 55, 39, 57, 43, 61, 47, 65, 51, 69, 52, 70, 48, 66, 44, 62, 40, 58)(38, 56, 41, 59, 45, 63, 49, 67, 53, 71, 54, 72, 50, 68, 46, 64, 42, 60)
	L = (1, 38)(2, 37)(3, 41)(4, 42)(5, 39)(6, 40)(7, 45)(8, 46)(9, 43)(10, 44)(11, 49)(12, 50)(13, 47)(14, 48)(15, 53)(16, 54)(17, 51)(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) :: { ( 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 E4.136
Graph:: bipartite
	v = 11 e = 36 f = 19
	degree seq :: [ 4^9, 18^2 ]

E4.134 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 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 * Y2^8, Y1^9 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 14, 32, 9, 27, 4, 22)(3, 21, 7, 25, 5, 23, 8, 26, 12, 30, 16, 34, 18, 36, 13, 31, 10, 28)(37, 55, 39, 57, 45, 63, 49, 67, 53, 71, 52, 70, 47, 65, 44, 62, 38, 56, 43, 61, 40, 58, 46, 64, 50, 68, 54, 72, 51, 69, 48, 66, 42, 60, 41, 59)
	L = (1, 39)(2, 43)(3, 45)(4, 46)(5, 37)(6, 41)(7, 40)(8, 38)(9, 49)(10, 50)(11, 44)(12, 42)(13, 53)(14, 54)(15, 48)(16, 47)(17, 52)(18, 51)(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, 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 E4.135
Graph:: bipartite
	v = 3 e = 36 f = 27
	degree seq :: [ 18^2, 36 ]

E4.135 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 4>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^9 * 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)(39, 57, 41, 59)(40, 58, 42, 60)(43, 61, 45, 63)(44, 62, 46, 64)(47, 65, 49, 67)(48, 66, 50, 68)(51, 69, 53, 71)(52, 70, 54, 72)
	L = (1, 39)(2, 41)(3, 43)(4, 37)(5, 45)(6, 38)(7, 47)(8, 40)(9, 49)(10, 42)(11, 51)(12, 44)(13, 53)(14, 46)(15, 54)(16, 48)(17, 52)(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) :: { ( 18, 36 ), ( 18, 36, 18, 36 ) }
Outer automorphisms :: reflexible
Dual of E4.134
Graph:: simple bipartite
	v = 27 e = 36 f = 3
	degree seq :: [ 2^18, 4^9 ]

E4.136 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 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^-9 ]
Map::
	R = (1, 19, 2, 20, 5, 23, 9, 27, 13, 31, 17, 35, 15, 33, 11, 29, 7, 25, 3, 21, 6, 24, 10, 28, 14, 32, 18, 36, 16, 34, 12, 30, 8, 26, 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, 42)(3, 37)(4, 43)(5, 46)(6, 38)(7, 40)(8, 47)(9, 50)(10, 41)(11, 44)(12, 51)(13, 54)(14, 45)(15, 48)(16, 53)(17, 52)(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) :: { ( 4, 18 ), ( 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 4, 18, 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 E4.133
Graph:: bipartite
	v = 19 e = 36 f = 11
	degree seq :: [ 2^18, 36 ]

E4.137 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 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, Y2^9 * Y1, (Y3 * Y2^-1)^9 ]
Map::
	R = (1, 19, 2, 20)(3, 21, 5, 23)(4, 22, 6, 24)(7, 25, 9, 27)(8, 26, 10, 28)(11, 29, 13, 31)(12, 30, 14, 32)(15, 33, 17, 35)(16, 34, 18, 36)(37, 55, 39, 57, 43, 61, 47, 65, 51, 69, 54, 72, 50, 68, 46, 64, 42, 60, 38, 56, 41, 59, 45, 63, 49, 67, 53, 71, 52, 70, 48, 66, 44, 62, 40, 58)
	L = (1, 38)(2, 37)(3, 41)(4, 42)(5, 39)(6, 40)(7, 45)(8, 46)(9, 43)(10, 44)(11, 49)(12, 50)(13, 47)(14, 48)(15, 53)(16, 54)(17, 51)(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) :: { ( 2, 18, 2, 18 ), ( 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 2, 18, 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 E4.138
Graph:: bipartite
	v = 10 e = 36 f = 20
	degree seq :: [ 4^9, 36 ]

E4.138 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 9, 18})
Quotient :: dipole
Aut^+ = C18 (small group id <18, 2>)
Aut   = D36 (small group id <36, 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 * Y3^8, Y1^2 * Y3^-1 * Y1^2 * Y3^-3 * Y1, Y1^9, (Y3 * Y2^-1)^18 ]
Map::
	R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 14, 32, 9, 27, 4, 22)(3, 21, 7, 25, 5, 23, 8, 26, 12, 30, 16, 34, 18, 36, 13, 31, 10, 28)(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, 45)(4, 46)(5, 37)(6, 41)(7, 40)(8, 38)(9, 49)(10, 50)(11, 44)(12, 42)(13, 53)(14, 54)(15, 48)(16, 47)(17, 52)(18, 51)(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, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) }
Outer automorphisms :: reflexible
Dual of E4.137
Graph:: simple bipartite
	v = 20 e = 36 f = 10
	degree seq :: [ 2^18, 18^2 ]

E4.139 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 5})
Quotient :: dipole
Aut^+ = D20 (small group id <20, 4>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3 * Y1)^5 ]
Map:: polytopal non-degenerate
	R = (1, 21, 2, 22)(3, 23, 5, 25)(4, 24, 8, 28)(6, 26, 10, 30)(7, 27, 11, 31)(9, 29, 13, 33)(12, 32, 16, 36)(14, 34, 18, 38)(15, 35, 19, 39)(17, 37, 20, 40)(41, 61, 43, 63)(42, 62, 45, 65)(44, 64, 47, 67)(46, 66, 49, 69)(48, 68, 51, 71)(50, 70, 53, 73)(52, 72, 55, 75)(54, 74, 57, 77)(56, 76, 59, 79)(58, 78, 60, 80)
	L = (1, 44)(2, 46)(3, 47)(4, 41)(5, 49)(6, 42)(7, 43)(8, 52)(9, 45)(10, 54)(11, 55)(12, 48)(13, 57)(14, 50)(15, 51)(16, 58)(17, 53)(18, 56)(19, 60)(20, 59)(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) :: { ( 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.140
Graph:: simple bipartite
	v = 20 e = 40 f = 14
	degree seq :: [ 4^20 ]

E4.140 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 5})
Quotient :: dipole
Aut^+ = D20 (small group id <20, 4>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^5 ]
Map:: polytopal non-degenerate
	R = (1, 21, 2, 22, 6, 26, 12, 32, 5, 25)(3, 23, 9, 29, 16, 36, 13, 33, 7, 27)(4, 24, 11, 31, 18, 38, 14, 34, 8, 28)(10, 30, 15, 35, 19, 39, 20, 40, 17, 37)(41, 61, 43, 63)(42, 62, 47, 67)(44, 64, 50, 70)(45, 65, 49, 69)(46, 66, 53, 73)(48, 68, 55, 75)(51, 71, 57, 77)(52, 72, 56, 76)(54, 74, 59, 79)(58, 78, 60, 80)
	L = (1, 44)(2, 48)(3, 50)(4, 41)(5, 51)(6, 54)(7, 55)(8, 42)(9, 57)(10, 43)(11, 45)(12, 58)(13, 59)(14, 46)(15, 47)(16, 60)(17, 49)(18, 52)(19, 53)(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) :: { ( 4^4 ), ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E4.139
Graph:: simple bipartite
	v = 14 e = 40 f = 20
	degree seq :: [ 4^10, 10^4 ]

E4.141 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {4, 4, 5})
Quotient :: edge
Aut^+ = C5 : C4 (small group id <20, 1>)
Aut   = (C10 x C2) : C2 (small group id <40, 8>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^5 ]
Map:: non-degenerate
	R = (1, 3, 9, 12, 5)(2, 7, 15, 16, 8)(4, 11, 18, 17, 10)(6, 13, 19, 20, 14)(21, 22, 26, 24)(23, 28, 33, 30)(25, 27, 34, 31)(29, 36, 39, 37)(32, 35, 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) :: { ( 8^4 ), ( 8^5 ) }
Outer automorphisms :: reflexible
Dual of E4.142
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 20 f = 5
	degree seq :: [ 4^5, 5^4 ]

E4.142 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {4, 4, 5})
Quotient :: loop
Aut^+ = C5 : C4 (small group id <20, 1>)
Aut   = (C10 x C2) : C2 (small group id <40, 8>)
|r| :: 2
Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^5 ]
Map:: non-degenerate
	R = (1, 21, 3, 23, 6, 26, 5, 25)(2, 22, 7, 27, 4, 24, 8, 28)(9, 29, 13, 33, 10, 30, 14, 34)(11, 31, 15, 35, 12, 32, 16, 36)(17, 37, 20, 40, 18, 38, 19, 39)
	L = (1, 22)(2, 26)(3, 29)(4, 21)(5, 30)(6, 24)(7, 31)(8, 32)(9, 25)(10, 23)(11, 28)(12, 27)(13, 37)(14, 38)(15, 39)(16, 40)(17, 34)(18, 33)(19, 36)(20, 35)
	local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.141
Transitivity :: ET+ VT+ AT
Graph::
	v = 5 e = 20 f = 9
	degree seq :: [ 8^5 ]

E4.143 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 5})
Quotient :: dipole
Aut^+ = C5 : C4 (small group id <20, 1>)
Aut   = (C10 x C2) : C2 (small group id <40, 8>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, Y2^5, (Y3^-1 * Y1^-1)^4 ]
Map::
	R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 8, 28, 13, 33, 10, 30)(5, 25, 7, 27, 14, 34, 11, 31)(9, 29, 16, 36, 19, 39, 17, 37)(12, 32, 15, 35, 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, 51, 71, 58, 78, 57, 77, 50, 70)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74)
	L = (1, 43)(2, 47)(3, 49)(4, 51)(5, 41)(6, 53)(7, 55)(8, 42)(9, 52)(10, 44)(11, 58)(12, 45)(13, 59)(14, 46)(15, 56)(16, 48)(17, 50)(18, 57)(19, 60)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.144
Graph:: bipartite
	v = 9 e = 40 f = 25
	degree seq :: [ 8^5, 10^4 ]

E4.144 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {4, 4, 5})
Quotient :: dipole
Aut^+ = C5 : C4 (small group id <20, 1>)
Aut   = (C10 x C2) : C2 (small group id <40, 8>)
|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)^5 ]
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, 48, 68, 53, 73, 50, 70)(45, 65, 47, 67, 54, 74, 51, 71)(49, 69, 56, 76, 59, 79, 57, 77)(52, 72, 55, 75, 60, 80, 58, 78)
	L = (1, 43)(2, 47)(3, 49)(4, 51)(5, 41)(6, 53)(7, 55)(8, 42)(9, 52)(10, 44)(11, 58)(12, 45)(13, 59)(14, 46)(15, 56)(16, 48)(17, 50)(18, 57)(19, 60)(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) :: { ( 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.143
Graph:: simple bipartite
	v = 25 e = 40 f = 9
	degree seq :: [ 2^20, 8^5 ]

E4.145 :: Family: { 5 } :: Oriented family(ies): { E3a }
Signature :: (0; {4, 4, 5})
Quotient :: edge
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C5 : C4 (small group id <20, 3>)
|r| :: 1
Presentation :: [ X1^4, X2^5, X1 * X2^2 * X1^-1 * X2^-1, X1 * X2 * X1^-1 * X2^2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 6, 4)(3, 9, 18, 11)(5, 14, 17, 15)(7, 19, 13, 16)(8, 20, 12, 10)(21, 23, 30, 36, 25)(22, 27, 29, 34, 28)(24, 32, 35, 31, 33)(26, 37, 39, 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) :: { ( 8^4 ), ( 8^5 ) }
Outer automorphisms :: chiral
Transitivity :: ET+
Graph:: simple bipartite
	v = 9 e = 20 f = 5
	degree seq :: [ 4^5, 5^4 ]

E4.146 :: Family: { 5* } :: Oriented family(ies): { E3*a }
Signature :: (0; {4, 4, 5})
Quotient :: loop
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C5 : C4 (small group id <20, 3>)
|r| :: 1
Presentation :: [ (X2 * X1^-1)^2, X1^4, X2^4, X2^-1 * X1^2 * X2^-1 * X1^-1 * X2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 9, 29, 18, 38, 8, 28)(5, 25, 11, 31, 19, 39, 13, 33)(7, 27, 16, 36, 10, 30, 15, 35)(12, 32, 14, 34, 20, 40, 17, 37)
	L = (1, 23)(2, 27)(3, 30)(4, 31)(5, 21)(6, 34)(7, 37)(8, 22)(9, 39)(10, 25)(11, 38)(12, 24)(13, 35)(14, 33)(15, 26)(16, 29)(17, 28)(18, 32)(19, 40)(20, 36)
	local type(s) :: { ( 4, 5, 4, 5, 4, 5, 4, 5 ) }
Outer automorphisms :: chiral
Transitivity :: ET+ VT+
Graph::
	v = 5 e = 20 f = 9
	degree seq :: [ 8^5 ]

E4.147 :: Family: { 2*ex } :: Oriented family(ies): { E3c }
Signature :: (0; {4, 4, 5})
Quotient :: loop
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ F^2, F * T2 * F * T1, (T1^-1 * T2)^2, T2^4, T1^4, T2^-2 * T1 * T2 * T1^-2, (T2^-1 * T1^-1)^5 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 5)(2, 7, 17, 8)(4, 11, 18, 12)(6, 14, 13, 15)(9, 19, 20, 16)(21, 22, 26, 24)(23, 29, 38, 28)(25, 31, 39, 33)(27, 36, 30, 35)(32, 34, 40, 37)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.148
Transitivity :: ET+ VT AT
Graph:: simple bipartite
	v = 10 e = 20 f = 4
	degree seq :: [ 4^10 ]

E4.148 :: Family: { 2ex } :: Oriented family(ies): { E3*c }
Signature :: (0; {4, 4, 5})
Quotient :: edge
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, T1^4, F * T1 * T2 * F * T1^-1, T1 * T2^2 * T1^-1 * T2^-1, T2^5, T1 * T2 * T1^-1 * T2^2 ]
Map:: polytopal non-degenerate
	R = (1, 21, 3, 23, 10, 30, 16, 36, 5, 25)(2, 22, 7, 27, 9, 29, 14, 34, 8, 28)(4, 24, 12, 32, 15, 35, 11, 31, 13, 33)(6, 26, 17, 37, 19, 39, 20, 40, 18, 38)
	L = (1, 22)(2, 26)(3, 29)(4, 21)(5, 34)(6, 24)(7, 39)(8, 40)(9, 38)(10, 28)(11, 23)(12, 30)(13, 36)(14, 37)(15, 25)(16, 27)(17, 35)(18, 31)(19, 33)(20, 32)
	local type(s) :: { ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E4.147
Transitivity :: ET+ VT+
Graph:: bipartite
	v = 4 e = 20 f = 10
	degree seq :: [ 10^4 ]

E4.149 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 5})
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, Y1^-1 * Y3^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3 * Y2^-1 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3^-2, Y1^-1 * Y2^-1 * Y3^3 ]
Map:: polytopal non-degenerate
	R = (1, 21, 4, 24, 16, 36, 12, 32, 7, 27)(2, 22, 9, 29, 6, 26, 19, 39, 11, 31)(3, 23, 5, 25, 18, 38, 15, 35, 14, 34)(8, 28, 13, 33, 10, 30, 20, 40, 17, 37)(41, 42, 48, 45)(43, 52, 49, 50)(44, 46, 57, 54)(47, 59, 53, 55)(51, 60, 58, 56)(61, 63, 73, 66)(62, 67, 78, 70)(64, 75, 68, 71)(65, 77, 69, 76)(72, 74, 80, 79)
	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) :: { ( 4^4 ), ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E4.152
Graph:: simple bipartite
	v = 14 e = 40 f = 20
	degree seq :: [ 4^10, 10^4 ]

E4.150 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {4, 4, 5})
Quotient :: edge^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ Y3, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1 * Y2)^2, Y2^4, Y1^4, Y2^2 * Y1^-2 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^5 ]
Map:: polytopal
	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, 42, 46, 44)(43, 49, 58, 48)(45, 51, 59, 53)(47, 56, 50, 55)(52, 54, 60, 57)(61, 63, 70, 65)(62, 67, 77, 68)(64, 71, 78, 72)(66, 74, 73, 75)(69, 79, 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) :: { ( 20, 20 ), ( 20^4 ) }
Outer automorphisms :: reflexible
Dual of E4.151
Graph:: simple bipartite
	v = 30 e = 40 f = 4
	degree seq :: [ 2^20, 4^10 ]

E4.151 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 5})
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, Y1^-1 * Y3^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3 * Y2^-1 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3^-2, Y1^-1 * Y2^-1 * Y3^3 ]
Map::
	R = (1, 21, 41, 61, 4, 24, 44, 64, 16, 36, 56, 76, 12, 32, 52, 72, 7, 27, 47, 67)(2, 22, 42, 62, 9, 29, 49, 69, 6, 26, 46, 66, 19, 39, 59, 79, 11, 31, 51, 71)(3, 23, 43, 63, 5, 25, 45, 65, 18, 38, 58, 78, 15, 35, 55, 75, 14, 34, 54, 74)(8, 28, 48, 68, 13, 33, 53, 73, 10, 30, 50, 70, 20, 40, 60, 80, 17, 37, 57, 77)
	L = (1, 22)(2, 28)(3, 32)(4, 26)(5, 21)(6, 37)(7, 39)(8, 25)(9, 30)(10, 23)(11, 40)(12, 29)(13, 35)(14, 24)(15, 27)(16, 31)(17, 34)(18, 36)(19, 33)(20, 38)(41, 63)(42, 67)(43, 73)(44, 75)(45, 77)(46, 61)(47, 78)(48, 71)(49, 76)(50, 62)(51, 64)(52, 74)(53, 66)(54, 80)(55, 68)(56, 65)(57, 69)(58, 70)(59, 72)(60, 79)
	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 E4.150
Transitivity :: VT+
Graph:: bipartite
	v = 4 e = 40 f = 30
	degree seq :: [ 20^4 ]

E4.152 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {4, 4, 5})
Quotient :: loop^2
Aut^+ = C5 : C4 (small group id <20, 3>)
Aut   = C2 x (C5 : C4) (small group id <40, 12>)
|r| :: 2
Presentation :: [ Y3, R^2, (R * Y3)^2, R * Y1 * R * Y2, (Y1^-1 * Y2)^2, Y2^4, Y1^4, Y2^2 * Y1^-2 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^5 ]
Map:: polytopal non-degenerate
	R = (1, 21, 41, 61)(2, 22, 42, 62)(3, 23, 43, 63)(4, 24, 44, 64)(5, 25, 45, 65)(6, 26, 46, 66)(7, 27, 47, 67)(8, 28, 48, 68)(9, 29, 49, 69)(10, 30, 50, 70)(11, 31, 51, 71)(12, 32, 52, 72)(13, 33, 53, 73)(14, 34, 54, 74)(15, 35, 55, 75)(16, 36, 56, 76)(17, 37, 57, 77)(18, 38, 58, 78)(19, 39, 59, 79)(20, 40, 60, 80)
	L = (1, 22)(2, 26)(3, 29)(4, 21)(5, 31)(6, 24)(7, 36)(8, 23)(9, 38)(10, 35)(11, 39)(12, 34)(13, 25)(14, 40)(15, 27)(16, 30)(17, 32)(18, 28)(19, 33)(20, 37)(41, 63)(42, 67)(43, 70)(44, 71)(45, 61)(46, 74)(47, 77)(48, 62)(49, 79)(50, 65)(51, 78)(52, 64)(53, 75)(54, 73)(55, 66)(56, 69)(57, 68)(58, 72)(59, 80)(60, 76)
	local type(s) :: { ( 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.149
Transitivity :: VT+
Graph:: simple bipartite
	v = 20 e = 40 f = 14
	degree seq :: [ 4^20 ]

E4.153 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 10, 10})
Quotient :: regular
Aut^+ = C10 x C2 (small group id <20, 5>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T1^10 ]
Map::
	R = (1, 2, 5, 9, 13, 17, 16, 12, 8, 4)(3, 6, 10, 14, 18, 20, 19, 15, 11, 7)
	L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 20)
	local type(s) :: { ( 10^10 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 10 f = 2
	degree seq :: [ 10^2 ]

E4.154 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 10, 10})
Quotient :: edge
Aut^+ = C10 x C2 (small group id <20, 5>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^10 ]
Map::
	R = (1, 3, 7, 11, 15, 19, 16, 12, 8, 4)(2, 5, 9, 13, 17, 20, 18, 14, 10, 6)(21, 22)(23, 25)(24, 26)(27, 29)(28, 30)(31, 33)(32, 34)(35, 37)(36, 38)(39, 40)
	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) :: { ( 20, 20 ), ( 20^10 ) }
Outer automorphisms :: reflexible
Dual of E4.155
Transitivity :: ET+
Graph:: simple bipartite
	v = 12 e = 20 f = 2
	degree seq :: [ 2^10, 10^2 ]

E4.155 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 10, 10})
Quotient :: loop
Aut^+ = C10 x C2 (small group id <20, 5>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^10 ]
Map::
	R = (1, 21, 3, 23, 7, 27, 11, 31, 15, 35, 19, 39, 16, 36, 12, 32, 8, 28, 4, 24)(2, 22, 5, 25, 9, 29, 13, 33, 17, 37, 20, 40, 18, 38, 14, 34, 10, 30, 6, 26)
	L = (1, 22)(2, 21)(3, 25)(4, 26)(5, 23)(6, 24)(7, 29)(8, 30)(9, 27)(10, 28)(11, 33)(12, 34)(13, 31)(14, 32)(15, 37)(16, 38)(17, 35)(18, 36)(19, 40)(20, 39)
	local type(s) :: { ( 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 E4.154
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 20 f = 12
	degree seq :: [ 20^2 ]

E4.156 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 10})
Quotient :: dipole
Aut^+ = C10 x C2 (small group id <20, 5>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|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, Y2^10, (Y3 * Y2^-1)^10 ]
Map::
	R = (1, 21, 2, 22)(3, 23, 5, 25)(4, 24, 6, 26)(7, 27, 9, 29)(8, 28, 10, 30)(11, 31, 13, 33)(12, 32, 14, 34)(15, 35, 17, 37)(16, 36, 18, 38)(19, 39, 20, 40)(41, 61, 43, 63, 47, 67, 51, 71, 55, 75, 59, 79, 56, 76, 52, 72, 48, 68, 44, 64)(42, 62, 45, 65, 49, 69, 53, 73, 57, 77, 60, 80, 58, 78, 54, 74, 50, 70, 46, 66)
	L = (1, 42)(2, 41)(3, 45)(4, 46)(5, 43)(6, 44)(7, 49)(8, 50)(9, 47)(10, 48)(11, 53)(12, 54)(13, 51)(14, 52)(15, 57)(16, 58)(17, 55)(18, 56)(19, 60)(20, 59)(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, 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 E4.157
Graph:: bipartite
	v = 12 e = 40 f = 22
	degree seq :: [ 4^10, 20^2 ]

E4.157 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 10, 10})
Quotient :: dipole
Aut^+ = C10 x C2 (small group id <20, 5>)
Aut   = C2 x C2 x D10 (small group id <40, 13>)
|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^-10, Y1^10 ]
Map::
	R = (1, 21, 2, 22, 5, 25, 9, 29, 13, 33, 17, 37, 16, 36, 12, 32, 8, 28, 4, 24)(3, 23, 6, 26, 10, 30, 14, 34, 18, 38, 20, 40, 19, 39, 15, 35, 11, 31, 7, 27)(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, 46)(3, 41)(4, 47)(5, 50)(6, 42)(7, 44)(8, 51)(9, 54)(10, 45)(11, 48)(12, 55)(13, 58)(14, 49)(15, 52)(16, 59)(17, 60)(18, 53)(19, 56)(20, 57)(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) :: { ( 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 E4.156
Graph:: simple bipartite
	v = 22 e = 40 f = 12
	degree seq :: [ 2^20, 20^2 ]

E4.158 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3 * Y2)^2, (Y3 * Y1)^3, (Y2 * Y1)^3, (Y1 * Y3 * Y2)^4 ]
Map:: polytopal non-degenerate
	R = (1, 26, 2, 25)(3, 31, 7, 27)(4, 33, 9, 28)(5, 34, 10, 29)(6, 36, 12, 30)(8, 38, 14, 32)(11, 41, 17, 35)(13, 43, 19, 37)(15, 44, 20, 39)(16, 45, 21, 40)(18, 46, 22, 42)(23, 48, 24, 47)
	L = (1, 3)(2, 5)(4, 8)(6, 11)(7, 10)(9, 15)(12, 18)(13, 16)(14, 20)(17, 22)(19, 23)(21, 24)(25, 28)(26, 30)(27, 32)(29, 35)(31, 37)(33, 36)(34, 40)(38, 43)(39, 42)(41, 45)(44, 47)(46, 48)
	local type(s) :: { ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E4.159
Transitivity :: VT+ AT
Graph:: simple
	v = 12 e = 24 f = 6
	degree seq :: [ 4^12 ]

E4.159 :: Family: { 2P } :: Oriented family(ies): { E2 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: halfedge^2
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y2^2, Y3^2, R^2, (R * Y1)^2, R * Y2 * R * Y3, Y1^4, (Y3 * Y2)^2, (Y1^-1 * Y3 * Y2)^2, Y2 * Y1 * Y2 * Y1^-1 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y1 * Y3 * Y1^-1, (Y2 * Y1^-1)^3, Y1^-1 * Y3 * Y1^-2 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 26, 2, 30, 6, 29, 5, 25)(3, 33, 9, 41, 17, 35, 11, 27)(4, 36, 12, 40, 16, 37, 13, 28)(7, 42, 18, 39, 15, 44, 20, 31)(8, 45, 21, 38, 14, 46, 22, 32)(10, 47, 23, 48, 24, 43, 19, 34)
	L = (1, 3)(2, 7)(4, 10)(5, 14)(6, 16)(8, 19)(9, 21)(11, 18)(12, 22)(13, 20)(15, 23)(17, 24)(25, 28)(26, 32)(27, 34)(29, 39)(30, 41)(31, 43)(33, 44)(35, 46)(36, 42)(37, 45)(38, 47)(40, 48)
	local type(s) :: { ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E4.158
Transitivity :: VT+ AT
Graph::
	v = 6 e = 24 f = 12
	degree seq :: [ 8^6 ]

E4.160 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1)^3, (Y3 * Y2)^3 ]
Map:: polytopal
	R = (1, 25, 4, 28)(2, 26, 6, 30)(3, 27, 7, 31)(5, 29, 10, 34)(8, 32, 11, 35)(9, 33, 14, 38)(12, 36, 17, 41)(13, 37, 16, 40)(15, 39, 20, 44)(18, 42, 22, 46)(19, 43, 23, 47)(21, 45, 24, 48)(49, 50)(51, 53)(52, 56)(54, 59)(55, 61)(57, 63)(58, 64)(60, 66)(62, 67)(65, 69)(68, 71)(70, 72)(73, 75)(74, 77)(76, 81)(78, 84)(79, 86)(80, 87)(82, 89)(83, 90)(85, 91)(88, 93)(92, 94)(95, 96)
	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 ), ( 16^4 ) }
Outer automorphisms :: reflexible
Dual of E4.163
Graph:: simple bipartite
	v = 36 e = 48 f = 6
	degree seq :: [ 2^24, 4^12 ]

E4.161 :: Family: { 4 } :: Oriented family(ies): { E4 }
Signature :: (0; {2, 2, 2, 4})
Quotient :: edge^2
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, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y3^-2 * Y1, Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 ]
Map:: polytopal
	R = (1, 25, 4, 28, 13, 37, 5, 29)(2, 26, 7, 31, 20, 44, 8, 32)(3, 27, 9, 33, 23, 47, 10, 34)(6, 30, 16, 40, 24, 48, 17, 41)(11, 35, 21, 45, 15, 39, 19, 43)(12, 36, 18, 42, 14, 38, 22, 46)(49, 50)(51, 54)(52, 59)(53, 62)(55, 66)(56, 69)(57, 70)(58, 67)(60, 65)(61, 71)(63, 64)(68, 72)(73, 75)(74, 78)(76, 84)(77, 87)(79, 91)(80, 94)(81, 93)(82, 90)(83, 89)(85, 92)(86, 88)(95, 96)
	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 ), ( 8^8 ) }
Outer automorphisms :: reflexible
Dual of E4.162
Graph:: simple bipartite
	v = 30 e = 48 f = 12
	degree seq :: [ 2^24, 8^6 ]

E4.162 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
Aut^+ = S4 (small group id <24, 12>)
Aut   = C2 x S4 (small group id <48, 48>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (Y1 * Y2)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1)^3, (Y3 * Y2)^3 ]
Map::
	R = (1, 25, 49, 73, 4, 28, 52, 76)(2, 26, 50, 74, 6, 30, 54, 78)(3, 27, 51, 75, 7, 31, 55, 79)(5, 29, 53, 77, 10, 34, 58, 82)(8, 32, 56, 80, 11, 35, 59, 83)(9, 33, 57, 81, 14, 38, 62, 86)(12, 36, 60, 84, 17, 41, 65, 89)(13, 37, 61, 85, 16, 40, 64, 88)(15, 39, 63, 87, 20, 44, 68, 92)(18, 42, 66, 90, 22, 46, 70, 94)(19, 43, 67, 91, 23, 47, 71, 95)(21, 45, 69, 93, 24, 48, 72, 96)
	L = (1, 26)(2, 25)(3, 29)(4, 32)(5, 27)(6, 35)(7, 37)(8, 28)(9, 39)(10, 40)(11, 30)(12, 42)(13, 31)(14, 43)(15, 33)(16, 34)(17, 45)(18, 36)(19, 38)(20, 47)(21, 41)(22, 48)(23, 44)(24, 46)(49, 75)(50, 77)(51, 73)(52, 81)(53, 74)(54, 84)(55, 86)(56, 87)(57, 76)(58, 89)(59, 90)(60, 78)(61, 91)(62, 79)(63, 80)(64, 93)(65, 82)(66, 83)(67, 85)(68, 94)(69, 88)(70, 92)(71, 96)(72, 95)
	local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.161
Transitivity :: VT+
Graph::
	v = 12 e = 48 f = 30
	degree seq :: [ 8^12 ]

E4.163 :: Family: { 4* } :: Oriented family(ies): { E4* }
Signature :: (0; {2, 2, 2, 4})
Quotient :: loop^2
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, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1)^2, Y3^4, Y3^2 * Y2 * Y3^-2 * Y1, Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2 ]
Map::
	R = (1, 25, 49, 73, 4, 28, 52, 76, 13, 37, 61, 85, 5, 29, 53, 77)(2, 26, 50, 74, 7, 31, 55, 79, 20, 44, 68, 92, 8, 32, 56, 80)(3, 27, 51, 75, 9, 33, 57, 81, 23, 47, 71, 95, 10, 34, 58, 82)(6, 30, 54, 78, 16, 40, 64, 88, 24, 48, 72, 96, 17, 41, 65, 89)(11, 35, 59, 83, 21, 45, 69, 93, 15, 39, 63, 87, 19, 43, 67, 91)(12, 36, 60, 84, 18, 42, 66, 90, 14, 38, 62, 86, 22, 46, 70, 94)
	L = (1, 26)(2, 25)(3, 30)(4, 35)(5, 38)(6, 27)(7, 42)(8, 45)(9, 46)(10, 43)(11, 28)(12, 41)(13, 47)(14, 29)(15, 40)(16, 39)(17, 36)(18, 31)(19, 34)(20, 48)(21, 32)(22, 33)(23, 37)(24, 44)(49, 75)(50, 78)(51, 73)(52, 84)(53, 87)(54, 74)(55, 91)(56, 94)(57, 93)(58, 90)(59, 89)(60, 76)(61, 92)(62, 88)(63, 77)(64, 86)(65, 83)(66, 82)(67, 79)(68, 85)(69, 81)(70, 80)(71, 96)(72, 95)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.160
Transitivity :: VT+
Graph::
	v = 6 e = 48 f = 36
	degree seq :: [ 16^6 ]

E4.164 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 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, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^3, (Y3 * Y1)^4, Y1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 10, 34)(6, 30, 12, 36)(8, 32, 14, 38)(11, 35, 18, 42)(13, 37, 21, 45)(15, 39, 22, 46)(16, 40, 20, 44)(17, 41, 24, 48)(19, 43, 23, 47)(49, 73, 51, 75)(50, 74, 53, 77)(52, 76, 56, 80)(54, 78, 59, 83)(55, 79, 58, 82)(57, 81, 63, 87)(60, 84, 67, 91)(61, 85, 65, 89)(62, 86, 70, 94)(64, 88, 72, 96)(66, 90, 71, 95)(68, 92, 69, 93)
	L = (1, 52)(2, 54)(3, 56)(4, 49)(5, 59)(6, 50)(7, 61)(8, 51)(9, 64)(10, 65)(11, 53)(12, 68)(13, 55)(14, 71)(15, 72)(16, 57)(17, 58)(18, 70)(19, 69)(20, 60)(21, 67)(22, 66)(23, 62)(24, 63)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.165
Graph:: simple bipartite
	v = 24 e = 48 f = 18
	degree seq :: [ 4^24 ]

E4.165 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 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 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2 * Y1^-1)^3, Y2 * Y1^-1 * Y2 * Y1 * Y3 * Y2 * Y1 ]
Map:: polytopal non-degenerate
	R = (1, 25, 2, 26, 6, 30, 5, 29)(3, 27, 9, 33, 19, 43, 11, 35)(4, 28, 12, 36, 15, 39, 8, 32)(7, 31, 16, 40, 23, 47, 18, 42)(10, 34, 22, 46, 14, 38, 21, 45)(13, 37, 24, 48, 17, 41, 20, 44)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 58, 82)(53, 77, 61, 85)(54, 78, 62, 86)(56, 80, 65, 89)(57, 81, 68, 92)(59, 83, 64, 88)(60, 84, 71, 95)(63, 87, 67, 91)(66, 90, 69, 93)(70, 94, 72, 96)
	L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 60)(6, 63)(7, 65)(8, 50)(9, 69)(10, 51)(11, 70)(12, 53)(13, 71)(14, 67)(15, 54)(16, 72)(17, 55)(18, 68)(19, 62)(20, 66)(21, 57)(22, 59)(23, 61)(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) :: { ( 4^4 ), ( 4^8 ) }
Outer automorphisms :: reflexible
Dual of E4.164
Graph:: simple bipartite
	v = 18 e = 48 f = 24
	degree seq :: [ 4^12, 8^6 ]

E4.166 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 4, 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, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2^-2 * T1^-1 * T2^-2, (T2 * T1^-1)^3 ]
Map:: non-degenerate
	R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 13, 21)(10, 18, 14, 15)(17, 24, 19, 23)(25, 26, 28)(27, 32, 34)(29, 37, 38)(30, 39, 41)(31, 42, 43)(33, 40, 46)(35, 47, 44)(36, 48, 45)
	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) :: { ( 12^3 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E4.170
Transitivity :: ET+
Graph:: simple bipartite
	v = 14 e = 24 f = 4
	degree seq :: [ 3^8, 4^6 ]

E4.167 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 4, 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^-2 * T2^3, T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 6, 16, 5)(2, 7, 13, 4, 12, 8)(9, 19, 22, 11, 20, 21)(14, 23, 17, 15, 24, 18)(25, 26, 30, 28)(27, 33, 40, 35)(29, 38, 34, 39)(31, 41, 36, 42)(32, 43, 37, 44)(45, 48, 46, 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) :: { ( 6^4 ), ( 6^6 ) }
Outer automorphisms :: reflexible
Dual of E4.171
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 24 f = 8
	degree seq :: [ 4^6, 6^4 ]

E4.168 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2, T1^6, (T2 * T1^-1)^3 ]
Map:: non-degenerate
	R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 9)(10, 19, 21)(12, 15, 23)(14, 20, 22)(16, 24, 18)(25, 26, 30, 40, 36, 28)(27, 33, 44, 48, 37, 34)(29, 38, 31, 42, 45, 39)(32, 43, 41, 47, 46, 35)
	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) :: { ( 8^3 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E4.169
Transitivity :: ET+
Graph:: simple bipartite
	v = 12 e = 24 f = 6
	degree seq :: [ 3^8, 6^4 ]

E4.169 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 4, 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, T1^3, (F * T1)^2, (F * T2)^2, T2^4, T1 * T2^-2 * T1^-1 * T2^-2, (T2 * T1^-1)^3 ]
Map:: non-degenerate
	R = (1, 25, 3, 27, 9, 33, 5, 29)(2, 26, 6, 30, 16, 40, 7, 31)(4, 28, 11, 35, 22, 46, 12, 36)(8, 32, 20, 44, 13, 37, 21, 45)(10, 34, 18, 42, 14, 38, 15, 39)(17, 41, 24, 48, 19, 43, 23, 47)
	L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 37)(6, 39)(7, 42)(8, 34)(9, 40)(10, 27)(11, 47)(12, 48)(13, 38)(14, 29)(15, 41)(16, 46)(17, 30)(18, 43)(19, 31)(20, 35)(21, 36)(22, 33)(23, 44)(24, 45)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.168
Transitivity :: ET+ VT+ AT
Graph::
	v = 6 e = 24 f = 12
	degree seq :: [ 8^6 ]

E4.170 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 4, 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^-2 * T2^3, T1 * T2^-1 * T1^-1 * T2^-1 * T1 * 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, 19, 43, 22, 46, 11, 35, 20, 44, 21, 45)(14, 38, 23, 47, 17, 41, 15, 39, 24, 48, 18, 42)
	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, 48)(22, 47)(23, 45)(24, 46)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.166
Transitivity :: ET+ VT+ AT
Graph::
	v = 4 e = 24 f = 14
	degree seq :: [ 12^4 ]

E4.171 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 4, 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, T2^3, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^-2 * T2, T1^6, (T2 * T1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 25, 3, 27, 5, 29)(2, 26, 7, 31, 8, 32)(4, 28, 11, 35, 13, 37)(6, 30, 17, 41, 9, 33)(10, 34, 19, 43, 21, 45)(12, 36, 15, 39, 23, 47)(14, 38, 20, 44, 22, 46)(16, 40, 24, 48, 18, 42)
	L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 38)(6, 40)(7, 42)(8, 43)(9, 44)(10, 27)(11, 32)(12, 28)(13, 34)(14, 31)(15, 29)(16, 36)(17, 47)(18, 45)(19, 41)(20, 48)(21, 39)(22, 35)(23, 46)(24, 37)
	local type(s) :: { ( 4, 6, 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.167
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 8 e = 24 f = 10
	degree seq :: [ 6^8 ]

E4.172 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 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, Y3 * Y1, Y1^2 * Y3^-1, Y2^4, (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 ]
Map::
	R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 10, 34)(5, 29, 13, 37, 14, 38)(6, 30, 15, 39, 17, 41)(7, 31, 18, 42, 19, 43)(9, 33, 16, 40, 22, 46)(11, 35, 23, 47, 20, 44)(12, 36, 24, 48, 21, 45)(49, 73, 51, 75, 57, 81, 53, 77)(50, 74, 54, 78, 64, 88, 55, 79)(52, 76, 59, 83, 70, 94, 60, 84)(56, 80, 68, 92, 61, 85, 69, 93)(58, 82, 66, 90, 62, 86, 63, 87)(65, 89, 72, 96, 67, 91, 71, 95)
	L = (1, 52)(2, 49)(3, 58)(4, 50)(5, 62)(6, 65)(7, 67)(8, 51)(9, 70)(10, 56)(11, 68)(12, 69)(13, 53)(14, 61)(15, 54)(16, 57)(17, 63)(18, 55)(19, 66)(20, 71)(21, 72)(22, 64)(23, 59)(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) :: { ( 2, 12, 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.175
Graph:: bipartite
	v = 14 e = 48 f = 28
	degree seq :: [ 6^8, 8^6 ]

E4.173 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 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, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^3 * Y1^-1, (Y1 * Y2)^3, (Y3^-1 * Y1^-1)^3 ]
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, 24, 48, 22, 46, 23, 47)(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, 67, 91, 70, 94, 59, 83, 68, 92, 69, 93)(62, 86, 71, 95, 65, 89, 63, 87, 72, 96, 66, 90)
	L = (1, 51)(2, 55)(3, 58)(4, 60)(5, 49)(6, 64)(7, 61)(8, 50)(9, 67)(10, 54)(11, 68)(12, 56)(13, 52)(14, 71)(15, 72)(16, 53)(17, 63)(18, 62)(19, 70)(20, 69)(21, 57)(22, 59)(23, 65)(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) :: { ( 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 E4.174
Graph:: bipartite
	v = 10 e = 48 f = 32
	degree seq :: [ 8^6, 12^4 ]

E4.174 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 6})
Quotient :: dipole
Aut^+ = SL(2,3) (small group id <24, 3>)
Aut   = GL(2,3) (small group id <48, 29>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, R * Y2 * Y3 * R * Y2^-1, Y3^2 * Y2 * Y3^-1 * Y2, Y3^6, (Y2^-1 * Y3^-1)^3, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	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, 52, 76)(51, 75, 56, 80, 58, 82)(53, 77, 61, 85, 62, 86)(54, 78, 64, 88, 65, 89)(55, 79, 63, 87, 66, 90)(57, 81, 59, 83, 70, 94)(60, 84, 67, 91, 68, 92)(69, 93, 71, 95, 72, 96)
	L = (1, 51)(2, 54)(3, 57)(4, 59)(5, 49)(6, 58)(7, 50)(8, 68)(9, 69)(10, 71)(11, 65)(12, 52)(13, 60)(14, 56)(15, 53)(16, 62)(17, 72)(18, 64)(19, 55)(20, 70)(21, 63)(22, 66)(23, 67)(24, 61)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.173
Graph:: simple bipartite
	v = 32 e = 48 f = 10
	degree seq :: [ 2^24, 6^8 ]

E4.175 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 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, Y3^3, (R * Y3)^2, (R * Y1)^2, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y1^-1)^3, (Y3 * Y2^-1)^3 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 16, 40, 12, 36, 4, 28)(3, 27, 9, 33, 20, 44, 24, 48, 13, 37, 10, 34)(5, 29, 14, 38, 7, 31, 18, 42, 21, 45, 15, 39)(8, 32, 19, 43, 17, 41, 23, 47, 22, 46, 11, 35)(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, 59)(5, 49)(6, 65)(7, 56)(8, 50)(9, 54)(10, 67)(11, 61)(12, 63)(13, 52)(14, 68)(15, 71)(16, 72)(17, 57)(18, 64)(19, 69)(20, 70)(21, 58)(22, 62)(23, 60)(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, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.172
Graph:: simple bipartite
	v = 28 e = 48 f = 14
	degree seq :: [ 2^24, 12^4 ]

E4.176 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 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, Y3 * Y1, Y1^3, Y3^2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y1^-1 * Y2, Y1 * Y2^-2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y2^6, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^4 ]
Map::
	R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 10, 34)(5, 29, 13, 37, 14, 38)(6, 30, 9, 33, 17, 41)(7, 31, 18, 42, 19, 43)(11, 35, 16, 40, 22, 46)(12, 36, 23, 47, 15, 39)(20, 44, 21, 45, 24, 48)(49, 73, 51, 75, 57, 81, 69, 93, 63, 87, 53, 77)(50, 74, 54, 78, 64, 88, 72, 96, 62, 86, 55, 79)(52, 76, 59, 83, 56, 80, 68, 92, 67, 91, 60, 84)(58, 82, 66, 90, 65, 89, 71, 95, 70, 94, 61, 85)
	L = (1, 52)(2, 49)(3, 58)(4, 50)(5, 62)(6, 65)(7, 67)(8, 51)(9, 54)(10, 56)(11, 70)(12, 63)(13, 53)(14, 61)(15, 71)(16, 59)(17, 57)(18, 55)(19, 66)(20, 72)(21, 68)(22, 64)(23, 60)(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) :: { ( 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.177
Graph:: bipartite
	v = 12 e = 48 f = 30
	degree seq :: [ 6^8, 12^4 ]

E4.177 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 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 * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y3^3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y1 * Y3)^3, (Y3 * Y2^-1)^6 ]
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, 24, 48, 22, 46, 23, 47)(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, 64)(7, 61)(8, 50)(9, 67)(10, 54)(11, 68)(12, 56)(13, 52)(14, 71)(15, 72)(16, 53)(17, 63)(18, 62)(19, 70)(20, 69)(21, 57)(22, 59)(23, 65)(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, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.176
Graph:: simple bipartite
	v = 30 e = 48 f = 12
	degree seq :: [ 2^24, 8^6 ]

E4.178 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 12})
Quotient :: regular
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T1^-2 * T2 * T1^-1)^2, (T2 * T1^-1 * T2 * T1)^2 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 16, 24, 15, 23, 19, 10, 4)(3, 7, 12, 22, 18, 9, 14, 6, 13, 21, 17, 8)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 20)(19, 22)
	local type(s) :: { ( 6^12 ) }
Outer automorphisms :: reflexible
Dual of E4.179
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 12 f = 4
	degree seq :: [ 12^2 ]

E4.179 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 12})
Quotient :: regular
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1^-2 * T2 * T1, T1^6, (T2 * T1^-1 * T2 * T1)^2, (T2 * T1^-3)^4 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 21, 24, 23, 16, 22)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 23)(20, 24)
	local type(s) :: { ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.178
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 4 e = 12 f = 2
	degree seq :: [ 6^4 ]

E4.180 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 12})
Quotient :: edge
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1 * T2 * T1)^2, (T1 * T2^-3)^4 ]
Map::
	R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 23, 18, 9, 16)(11, 19, 24, 22, 13, 20)(25, 26)(27, 31)(28, 33)(29, 35)(30, 37)(32, 36)(34, 38)(39, 43)(40, 44)(41, 47)(42, 46)(45, 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) :: { ( 24, 24 ), ( 24^6 ) }
Outer automorphisms :: reflexible
Dual of E4.184
Transitivity :: ET+
Graph:: simple bipartite
	v = 16 e = 24 f = 2
	degree seq :: [ 2^12, 6^4 ]

E4.181 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 12})
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 * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-2, T1 * T2^-4 * T1, T2^-1 * T1 * T2^-1 * T1^-3, T1^6, (T2^2 * T1^-1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 6, 17, 24, 20, 13, 21, 15, 5)(2, 7, 19, 11, 16, 14, 23, 9, 4, 12, 22, 8)(25, 26, 30, 40, 37, 28)(27, 33, 41, 32, 45, 35)(29, 38, 42, 36, 44, 31)(34, 43, 48, 47, 39, 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) :: { ( 4^6 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E4.185
Transitivity :: ET+
Graph:: bipartite
	v = 6 e = 24 f = 12
	degree seq :: [ 6^4, 12^2 ]

E4.182 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 12})
Quotient :: edge
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|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)^2, (T2 * T1^-1 * T2 * T1)^2 ]
Map::
	R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 20)(19, 22)(25, 26, 29, 35, 44, 40, 48, 39, 47, 43, 34, 28)(27, 31, 36, 46, 42, 33, 38, 30, 37, 45, 41, 32)
	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, 12 ), ( 12^12 ) }
Outer automorphisms :: reflexible
Dual of E4.183
Transitivity :: ET+
Graph:: simple bipartite
	v = 14 e = 24 f = 4
	degree seq :: [ 2^12, 12^2 ]

E4.183 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 12})
Quotient :: loop
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1 * T2 * T1)^2, (T1 * T2^-3)^4 ]
Map::
	R = (1, 25, 3, 27, 8, 32, 17, 41, 10, 34, 4, 28)(2, 26, 5, 29, 12, 36, 21, 45, 14, 38, 6, 30)(7, 31, 15, 39, 23, 47, 18, 42, 9, 33, 16, 40)(11, 35, 19, 43, 24, 48, 22, 46, 13, 37, 20, 44)
	L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 35)(6, 37)(7, 27)(8, 36)(9, 28)(10, 38)(11, 29)(12, 32)(13, 30)(14, 34)(15, 43)(16, 44)(17, 47)(18, 46)(19, 39)(20, 40)(21, 48)(22, 42)(23, 41)(24, 45)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.182
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 24 f = 14
	degree seq :: [ 12^4 ]

E4.184 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 12})
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 * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-2, T1 * T2^-4 * T1, T2^-1 * T1 * T2^-1 * T1^-3, T1^6, (T2^2 * T1^-1)^2 ]
Map::
	R = (1, 25, 3, 27, 10, 34, 18, 42, 6, 30, 17, 41, 24, 48, 20, 44, 13, 37, 21, 45, 15, 39, 5, 29)(2, 26, 7, 31, 19, 43, 11, 35, 16, 40, 14, 38, 23, 47, 9, 33, 4, 28, 12, 36, 22, 46, 8, 32)
	L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 38)(6, 40)(7, 29)(8, 45)(9, 41)(10, 43)(11, 27)(12, 44)(13, 28)(14, 42)(15, 46)(16, 37)(17, 32)(18, 36)(19, 48)(20, 31)(21, 35)(22, 34)(23, 39)(24, 47)
	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 E4.180
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 24 f = 16
	degree seq :: [ 24^2 ]

E4.185 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 12})
Quotient :: loop
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|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)^2, (T2 * T1^-1 * T2 * T1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 25, 3, 27)(2, 26, 6, 30)(4, 28, 9, 33)(5, 29, 12, 36)(7, 31, 15, 39)(8, 32, 16, 40)(10, 34, 17, 41)(11, 35, 21, 45)(13, 37, 23, 47)(14, 38, 24, 48)(18, 42, 20, 44)(19, 43, 22, 46)
	L = (1, 26)(2, 29)(3, 31)(4, 25)(5, 35)(6, 37)(7, 36)(8, 27)(9, 38)(10, 28)(11, 44)(12, 46)(13, 45)(14, 30)(15, 47)(16, 48)(17, 32)(18, 33)(19, 34)(20, 40)(21, 41)(22, 42)(23, 43)(24, 39)
	local type(s) :: { ( 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.181
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 12 e = 24 f = 6
	degree seq :: [ 4^12 ]

E4.186 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
Quotient :: dipole
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^6, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * Y1 * Y2 * Y1)^2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 11, 35)(6, 30, 13, 37)(8, 32, 12, 36)(10, 34, 14, 38)(15, 39, 19, 43)(16, 40, 20, 44)(17, 41, 23, 47)(18, 42, 22, 46)(21, 45, 24, 48)(49, 73, 51, 75, 56, 80, 65, 89, 58, 82, 52, 76)(50, 74, 53, 77, 60, 84, 69, 93, 62, 86, 54, 78)(55, 79, 63, 87, 71, 95, 66, 90, 57, 81, 64, 88)(59, 83, 67, 91, 72, 96, 70, 94, 61, 85, 68, 92)
	L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 60)(9, 52)(10, 62)(11, 53)(12, 56)(13, 54)(14, 58)(15, 67)(16, 68)(17, 71)(18, 70)(19, 63)(20, 64)(21, 72)(22, 66)(23, 65)(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) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.189
Graph:: bipartite
	v = 16 e = 48 f = 26
	degree seq :: [ 4^12, 12^4 ]

E4.187 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
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, Y2 * Y3^-1, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^2 * Y1^-1)^2, Y1^-1 * Y2^4 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y1^6, Y2^2 * Y1 * Y2^-2 * Y1^-1 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 16, 40, 13, 37, 4, 28)(3, 27, 9, 33, 17, 41, 8, 32, 21, 45, 11, 35)(5, 29, 14, 38, 18, 42, 12, 36, 20, 44, 7, 31)(10, 34, 19, 43, 24, 48, 23, 47, 15, 39, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 54, 78, 65, 89, 72, 96, 68, 92, 61, 85, 69, 93, 63, 87, 53, 77)(50, 74, 55, 79, 67, 91, 59, 83, 64, 88, 62, 86, 71, 95, 57, 81, 52, 76, 60, 84, 70, 94, 56, 80)
	L = (1, 51)(2, 55)(3, 58)(4, 60)(5, 49)(6, 65)(7, 67)(8, 50)(9, 52)(10, 66)(11, 64)(12, 70)(13, 69)(14, 71)(15, 53)(16, 62)(17, 72)(18, 54)(19, 59)(20, 61)(21, 63)(22, 56)(23, 57)(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) :: { ( 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 E4.188
Graph:: bipartite
	v = 6 e = 48 f = 36
	degree seq :: [ 12^4, 24^2 ]

E4.188 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
Quotient :: dipole
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2 * Y3^-2, (Y3 * Y2 * Y3^2)^2, (Y3^-1 * Y2 * Y3 * Y2)^2, (Y3^-1 * Y1^-1)^12 ]
Map:: polytopal
	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)(51, 75, 55, 79)(52, 76, 57, 81)(53, 77, 59, 83)(54, 78, 61, 85)(56, 80, 60, 84)(58, 82, 62, 86)(63, 87, 68, 92)(64, 88, 69, 93)(65, 89, 72, 96)(66, 90, 71, 95)(67, 91, 70, 94)
	L = (1, 51)(2, 53)(3, 56)(4, 49)(5, 60)(6, 50)(7, 63)(8, 65)(9, 64)(10, 52)(11, 68)(12, 70)(13, 69)(14, 54)(15, 72)(16, 55)(17, 71)(18, 57)(19, 58)(20, 67)(21, 59)(22, 66)(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) :: { ( 12, 24 ), ( 12, 24, 12, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.187
Graph:: simple bipartite
	v = 36 e = 48 f = 6
	degree seq :: [ 2^24, 4^12 ]

E4.189 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
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, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3^-1 * Y1^-1 * Y3^-2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^2 * Y3^-1 * Y1 * Y3^-1 * Y1^3 ]
Map::
	R = (1, 25, 2, 26, 5, 29, 11, 35, 20, 44, 16, 40, 24, 48, 15, 39, 23, 47, 19, 43, 10, 34, 4, 28)(3, 27, 7, 31, 12, 36, 22, 46, 18, 42, 9, 33, 14, 38, 6, 30, 13, 37, 21, 45, 17, 41, 8, 32)(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, 57)(5, 60)(6, 50)(7, 63)(8, 64)(9, 52)(10, 65)(11, 69)(12, 53)(13, 71)(14, 72)(15, 55)(16, 56)(17, 58)(18, 68)(19, 70)(20, 66)(21, 59)(22, 67)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.186
Graph:: simple bipartite
	v = 26 e = 48 f = 16
	degree seq :: [ 2^24, 24^2 ]

E4.190 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
Quotient :: dipole
Aut^+ = C3 x D8 (small group id <24, 10>)
Aut   = D8 x S3 (small group id <48, 38>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * Y1 * Y2 * Y1)^2, (Y2 * Y1 * Y2^2)^2, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 11, 35)(6, 30, 13, 37)(8, 32, 12, 36)(10, 34, 14, 38)(15, 39, 20, 44)(16, 40, 21, 45)(17, 41, 24, 48)(18, 42, 23, 47)(19, 43, 22, 46)(49, 73, 51, 75, 56, 80, 65, 89, 71, 95, 61, 85, 69, 93, 59, 83, 68, 92, 67, 91, 58, 82, 52, 76)(50, 74, 53, 77, 60, 84, 70, 94, 66, 90, 57, 81, 64, 88, 55, 79, 63, 87, 72, 96, 62, 86, 54, 78)
	L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 60)(9, 52)(10, 62)(11, 53)(12, 56)(13, 54)(14, 58)(15, 68)(16, 69)(17, 72)(18, 71)(19, 70)(20, 63)(21, 64)(22, 67)(23, 66)(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) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 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 E4.191
Graph:: bipartite
	v = 14 e = 48 f = 28
	degree seq :: [ 4^12, 24^2 ]

E4.191 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 12})
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, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^2, (Y3^-2 * Y1)^2, Y1^6, Y3^4 * Y1^-2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 25, 2, 26, 6, 30, 16, 40, 13, 37, 4, 28)(3, 27, 9, 33, 17, 41, 8, 32, 21, 45, 11, 35)(5, 29, 14, 38, 18, 42, 12, 36, 20, 44, 7, 31)(10, 34, 19, 43, 24, 48, 23, 47, 15, 39, 22, 46)(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, 65)(7, 67)(8, 50)(9, 52)(10, 66)(11, 64)(12, 70)(13, 69)(14, 71)(15, 53)(16, 62)(17, 72)(18, 54)(19, 59)(20, 61)(21, 63)(22, 56)(23, 57)(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, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.190
Graph:: simple bipartite
	v = 28 e = 48 f = 14
	degree seq :: [ 2^24, 12^4 ]

E4.192 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 16})
Quotient :: regular
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T2 * T1^2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, T2 * T1^-1 * T2 * T1^7 ]
Map:: non-degenerate
	R = (1, 2, 5, 11, 20, 29, 26, 16, 23, 17, 24, 32, 28, 19, 10, 4)(3, 7, 15, 25, 31, 21, 14, 6, 13, 9, 18, 27, 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, 29)(28, 31)
	local type(s) :: { ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E4.193
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 2 e = 16 f = 8
	degree seq :: [ 16^2 ]

E4.193 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 16})
Quotient :: regular
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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^-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, 32, 30, 31)
	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)
	local type(s) :: { ( 16^4 ) }
Outer automorphisms :: reflexible
Dual of E4.192
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 8 e = 16 f = 2
	degree seq :: [ 4^8 ]

E4.194 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 16})
Quotient :: edge
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 ]
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, 34)(35, 39)(36, 41)(37, 42)(38, 44)(40, 43)(45, 49)(46, 50)(47, 51)(48, 52)(53, 57)(54, 58)(55, 59)(56, 60)(61, 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 ), ( 32^4 ) }
Outer automorphisms :: reflexible
Dual of E4.198
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 32 f = 2
	degree seq :: [ 2^16, 4^8 ]

E4.195 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 16})
Quotient :: edge
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^7 * T1 * T2^-1 * T1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 30, 22, 14, 6, 13, 21, 29, 28, 20, 12, 5)(2, 7, 15, 23, 31, 25, 17, 9, 4, 11, 19, 27, 32, 24, 16, 8)(33, 34, 38, 36)(35, 41, 45, 40)(37, 43, 46, 39)(42, 48, 53, 49)(44, 47, 54, 51)(50, 57, 61, 56)(52, 59, 62, 55)(58, 64, 60, 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) :: { ( 4^4 ), ( 4^16 ) }
Outer automorphisms :: reflexible
Dual of E4.199
Transitivity :: ET+
Graph:: bipartite
	v = 10 e = 32 f = 16
	degree seq :: [ 4^8, 16^2 ]

E4.196 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 16})
Quotient :: edge
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^7 ]
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, 29)(28, 31)(33, 34, 37, 43, 52, 61, 58, 48, 55, 49, 56, 64, 60, 51, 42, 36)(35, 39, 47, 57, 63, 53, 46, 38, 45, 41, 50, 59, 62, 54, 44, 40)
	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) :: { ( 8, 8 ), ( 8^16 ) }
Outer automorphisms :: reflexible
Dual of E4.197
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 32 f = 8
	degree seq :: [ 2^16, 16^2 ]

E4.197 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 16})
Quotient :: loop
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 ]
Map::
	R = (1, 33, 3, 35, 8, 40, 4, 36)(2, 34, 5, 37, 11, 43, 6, 38)(7, 39, 13, 45, 9, 41, 14, 46)(10, 42, 15, 47, 12, 44, 16, 48)(17, 49, 21, 53, 18, 50, 22, 54)(19, 51, 23, 55, 20, 52, 24, 56)(25, 57, 29, 61, 26, 58, 30, 62)(27, 59, 31, 63, 28, 60, 32, 64)
	L = (1, 34)(2, 33)(3, 39)(4, 41)(5, 42)(6, 44)(7, 35)(8, 43)(9, 36)(10, 37)(11, 40)(12, 38)(13, 49)(14, 50)(15, 51)(16, 52)(17, 45)(18, 46)(19, 47)(20, 48)(21, 57)(22, 58)(23, 59)(24, 60)(25, 53)(26, 54)(27, 55)(28, 56)(29, 64)(30, 63)(31, 62)(32, 61)
	local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ) }
Outer automorphisms :: reflexible
Dual of E4.196
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 8 e = 32 f = 18
	degree seq :: [ 8^8 ]

E4.198 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 16})
Quotient :: loop
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^7 * T1 * T2^-1 * T1^-1 ]
Map::
	R = (1, 33, 3, 35, 10, 42, 18, 50, 26, 58, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 25, 57, 17, 49, 9, 41, 4, 36, 11, 43, 19, 51, 27, 59, 32, 64, 24, 56, 16, 48, 8, 40)
	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, 54)(16, 53)(17, 42)(18, 57)(19, 44)(20, 59)(21, 49)(22, 51)(23, 52)(24, 50)(25, 61)(26, 64)(27, 62)(28, 63)(29, 56)(30, 55)(31, 58)(32, 60)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.194
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 2 e = 32 f = 24
	degree seq :: [ 32^2 ]

E4.199 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 16})
Quotient :: loop
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T2 * T1^-1 * T2 * T1^7 ]
Map:: polytopal non-degenerate
	R = (1, 33, 3, 35)(2, 34, 6, 38)(4, 36, 9, 41)(5, 37, 12, 44)(7, 39, 16, 48)(8, 40, 17, 49)(10, 42, 15, 47)(11, 43, 21, 53)(13, 45, 23, 55)(14, 46, 24, 56)(18, 50, 26, 58)(19, 51, 27, 59)(20, 52, 30, 62)(22, 54, 32, 64)(25, 57, 29, 61)(28, 60, 31, 63)
	L = (1, 34)(2, 37)(3, 39)(4, 33)(5, 43)(6, 45)(7, 47)(8, 35)(9, 50)(10, 36)(11, 52)(12, 40)(13, 41)(14, 38)(15, 57)(16, 55)(17, 56)(18, 59)(19, 42)(20, 61)(21, 46)(22, 44)(23, 49)(24, 64)(25, 63)(26, 48)(27, 62)(28, 51)(29, 58)(30, 54)(31, 53)(32, 60)
	local type(s) :: { ( 4, 16, 4, 16 ) }
Outer automorphisms :: reflexible
Dual of E4.195
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 16 e = 32 f = 10
	degree seq :: [ 4^16 ]

E4.200 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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 * R * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 10, 42)(6, 38, 12, 44)(8, 40, 11, 43)(13, 45, 17, 49)(14, 46, 18, 50)(15, 47, 19, 51)(16, 48, 20, 52)(21, 53, 25, 57)(22, 54, 26, 58)(23, 55, 27, 59)(24, 56, 28, 60)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 72, 104, 68, 100)(66, 98, 69, 101, 75, 107, 70, 102)(71, 103, 77, 109, 73, 105, 78, 110)(74, 106, 79, 111, 76, 108, 80, 112)(81, 113, 85, 117, 82, 114, 86, 118)(83, 115, 87, 119, 84, 116, 88, 120)(89, 121, 93, 125, 90, 122, 94, 126)(91, 123, 95, 127, 92, 124, 96, 128)
	L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 74)(6, 76)(7, 67)(8, 75)(9, 68)(10, 69)(11, 72)(12, 70)(13, 81)(14, 82)(15, 83)(16, 84)(17, 77)(18, 78)(19, 79)(20, 80)(21, 89)(22, 90)(23, 91)(24, 92)(25, 85)(26, 86)(27, 87)(28, 88)(29, 96)(30, 95)(31, 94)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 2, 32, 2, 32 ), ( 2, 32, 2, 32, 2, 32, 2, 32 ) }
Outer automorphisms :: reflexible
Dual of E4.203
Graph:: bipartite
	v = 24 e = 64 f = 34
	degree seq :: [ 4^16, 8^8 ]

E4.201 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y2^-1 * Y1)^2, Y1^-1 * Y2^-8 * Y1^-1 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 13, 45, 8, 40)(5, 37, 11, 43, 14, 46, 7, 39)(10, 42, 16, 48, 21, 53, 17, 49)(12, 44, 15, 47, 22, 54, 19, 51)(18, 50, 25, 57, 29, 61, 24, 56)(20, 52, 27, 59, 30, 62, 23, 55)(26, 58, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 89, 121, 81, 113, 73, 105, 68, 100, 75, 107, 83, 115, 91, 123, 96, 128, 88, 120, 80, 112, 72, 104)
	L = (1, 67)(2, 71)(3, 74)(4, 75)(5, 65)(6, 77)(7, 79)(8, 66)(9, 68)(10, 82)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 73)(18, 90)(19, 91)(20, 76)(21, 93)(22, 78)(23, 95)(24, 80)(25, 81)(26, 94)(27, 96)(28, 84)(29, 92)(30, 86)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.202
Graph:: bipartite
	v = 10 e = 64 f = 48
	degree seq :: [ 8^8, 32^2 ]

E4.202 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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, Y3^5 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^16 ]
Map:: polytopal
	R = (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)(65, 97, 66, 98)(67, 99, 71, 103)(68, 100, 73, 105)(69, 101, 75, 107)(70, 102, 77, 109)(72, 104, 78, 110)(74, 106, 76, 108)(79, 111, 84, 116)(80, 112, 87, 119)(81, 113, 89, 121)(82, 114, 85, 117)(83, 115, 91, 123)(86, 118, 93, 125)(88, 120, 95, 127)(90, 122, 96, 128)(92, 124, 94, 126)
	L = (1, 67)(2, 69)(3, 72)(4, 65)(5, 76)(6, 66)(7, 79)(8, 81)(9, 82)(10, 68)(11, 84)(12, 86)(13, 87)(14, 70)(15, 73)(16, 71)(17, 90)(18, 91)(19, 74)(20, 77)(21, 75)(22, 94)(23, 95)(24, 78)(25, 80)(26, 93)(27, 96)(28, 83)(29, 85)(30, 89)(31, 92)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 8, 32 ), ( 8, 32, 8, 32 ) }
Outer automorphisms :: reflexible
Dual of E4.201
Graph:: simple bipartite
	v = 48 e = 64 f = 10
	degree seq :: [ 2^32, 4^16 ]

E4.203 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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^-1 * Y3 * Y1^7, Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-3 ]
Map::
	R = (1, 33, 2, 34, 5, 37, 11, 43, 20, 52, 29, 61, 26, 58, 16, 48, 23, 55, 17, 49, 24, 56, 32, 64, 28, 60, 19, 51, 10, 42, 4, 36)(3, 35, 7, 39, 15, 47, 25, 57, 31, 63, 21, 53, 14, 46, 6, 38, 13, 45, 9, 41, 18, 50, 27, 59, 30, 62, 22, 54, 12, 44, 8, 40)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128)
	L = (1, 67)(2, 70)(3, 65)(4, 73)(5, 76)(6, 66)(7, 80)(8, 81)(9, 68)(10, 79)(11, 85)(12, 69)(13, 87)(14, 88)(15, 74)(16, 71)(17, 72)(18, 90)(19, 91)(20, 94)(21, 75)(22, 96)(23, 77)(24, 78)(25, 93)(26, 82)(27, 83)(28, 95)(29, 89)(30, 84)(31, 92)(32, 86)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.200
Graph:: simple bipartite
	v = 34 e = 64 f = 24
	degree seq :: [ 2^32, 32^2 ]

E4.204 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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^-5 * Y1 ]
Map::
	R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 14, 46)(10, 42, 12, 44)(15, 47, 20, 52)(16, 48, 23, 55)(17, 49, 25, 57)(18, 50, 21, 53)(19, 51, 27, 59)(22, 54, 29, 61)(24, 56, 31, 63)(26, 58, 32, 64)(28, 60, 30, 62)(65, 97, 67, 99, 72, 104, 81, 113, 90, 122, 93, 125, 85, 117, 75, 107, 84, 116, 77, 109, 87, 119, 95, 127, 92, 124, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 94, 126, 89, 121, 80, 112, 71, 103, 79, 111, 73, 105, 82, 114, 91, 123, 96, 128, 88, 120, 78, 110, 70, 102)
	L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 75)(6, 77)(7, 67)(8, 78)(9, 68)(10, 76)(11, 69)(12, 74)(13, 70)(14, 72)(15, 84)(16, 87)(17, 89)(18, 85)(19, 91)(20, 79)(21, 82)(22, 93)(23, 80)(24, 95)(25, 81)(26, 96)(27, 83)(28, 94)(29, 86)(30, 92)(31, 88)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.205
Graph:: bipartite
	v = 18 e = 64 f = 40
	degree seq :: [ 4^16, 32^2 ]

E4.205 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 16})
Quotient :: dipole
Aut^+ = QD32 (small group id <32, 19>)
Aut   = (C2 x D16) : C2 (small group id <64, 190>)
|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^-8 * Y1^-1, (Y3 * Y2^-1)^16 ]
Map::
	R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 13, 45, 8, 40)(5, 37, 11, 43, 14, 46, 7, 39)(10, 42, 16, 48, 21, 53, 17, 49)(12, 44, 15, 47, 22, 54, 19, 51)(18, 50, 25, 57, 29, 61, 24, 56)(20, 52, 27, 59, 30, 62, 23, 55)(26, 58, 32, 64, 28, 60, 31, 63)(65, 97)(66, 98)(67, 99)(68, 100)(69, 101)(70, 102)(71, 103)(72, 104)(73, 105)(74, 106)(75, 107)(76, 108)(77, 109)(78, 110)(79, 111)(80, 112)(81, 113)(82, 114)(83, 115)(84, 116)(85, 117)(86, 118)(87, 119)(88, 120)(89, 121)(90, 122)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128)
	L = (1, 67)(2, 71)(3, 74)(4, 75)(5, 65)(6, 77)(7, 79)(8, 66)(9, 68)(10, 82)(11, 83)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 73)(18, 90)(19, 91)(20, 76)(21, 93)(22, 78)(23, 95)(24, 80)(25, 81)(26, 94)(27, 96)(28, 84)(29, 92)(30, 86)(31, 89)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)
	local type(s) :: { ( 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) }
Outer automorphisms :: reflexible
Dual of E4.204
Graph:: simple bipartite
	v = 40 e = 64 f = 18
	degree seq :: [ 2^32, 8^8 ]

E4.206 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 3})
Quotient :: dipole
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^3, (Y2 * Y1 * Y3 * Y2 * Y1)^2 ]
Map:: polytopal non-degenerate
	R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 10, 46)(6, 42, 12, 48)(8, 44, 15, 51)(11, 47, 19, 55)(13, 49, 21, 57)(14, 50, 23, 59)(16, 52, 25, 61)(17, 53, 26, 62)(18, 54, 28, 64)(20, 56, 30, 66)(22, 58, 29, 65)(24, 60, 27, 63)(31, 67, 34, 70)(32, 68, 36, 72)(33, 69, 35, 71)(73, 109, 75, 111)(74, 110, 77, 113)(76, 112, 80, 116)(78, 114, 83, 119)(79, 115, 85, 121)(81, 117, 88, 124)(82, 118, 89, 125)(84, 120, 92, 128)(86, 122, 94, 130)(87, 123, 96, 132)(90, 126, 99, 135)(91, 127, 101, 137)(93, 129, 103, 139)(95, 131, 105, 141)(97, 133, 104, 140)(98, 134, 106, 142)(100, 136, 108, 144)(102, 138, 107, 143)
	L = (1, 76)(2, 78)(3, 80)(4, 73)(5, 83)(6, 74)(7, 86)(8, 75)(9, 84)(10, 90)(11, 77)(12, 81)(13, 94)(14, 79)(15, 95)(16, 92)(17, 99)(18, 82)(19, 100)(20, 88)(21, 104)(22, 85)(23, 87)(24, 105)(25, 103)(26, 107)(27, 89)(28, 91)(29, 108)(30, 106)(31, 97)(32, 93)(33, 96)(34, 102)(35, 98)(36, 101)(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, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.207
Graph:: simple bipartite
	v = 36 e = 72 f = 30
	degree seq :: [ 4^36 ]

E4.207 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 2, 2, 3})
Quotient :: dipole
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 ]
Map:: polytopal non-degenerate
	R = (1, 37, 2, 38, 5, 41)(3, 39, 8, 44, 10, 46)(4, 40, 11, 47, 7, 43)(6, 42, 13, 49, 15, 51)(9, 45, 18, 54, 17, 53)(12, 48, 21, 57, 22, 58)(14, 50, 25, 61, 24, 60)(16, 52, 23, 59, 28, 64)(19, 55, 26, 62, 30, 66)(20, 56, 31, 67, 32, 68)(27, 63, 35, 71, 33, 69)(29, 65, 36, 72, 34, 70)(73, 109, 75, 111)(74, 110, 78, 114)(76, 112, 81, 117)(77, 113, 84, 120)(79, 115, 86, 122)(80, 116, 88, 124)(82, 118, 91, 127)(83, 119, 92, 128)(85, 121, 95, 131)(87, 123, 98, 134)(89, 125, 99, 135)(90, 126, 101, 137)(93, 129, 100, 136)(94, 130, 102, 138)(96, 132, 105, 141)(97, 133, 106, 142)(103, 139, 108, 144)(104, 140, 107, 143)
	L = (1, 76)(2, 79)(3, 81)(4, 73)(5, 83)(6, 86)(7, 74)(8, 89)(9, 75)(10, 90)(11, 77)(12, 92)(13, 96)(14, 78)(15, 97)(16, 99)(17, 80)(18, 82)(19, 101)(20, 84)(21, 104)(22, 103)(23, 105)(24, 85)(25, 87)(26, 106)(27, 88)(28, 107)(29, 91)(30, 108)(31, 94)(32, 93)(33, 95)(34, 98)(35, 100)(36, 102)(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 ), ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E4.206
Graph:: simple bipartite
	v = 30 e = 72 f = 36
	degree seq :: [ 4^18, 6^12 ]

E4.208 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 4, 4})
Quotient :: edge
Aut^+ = (C3 x C3) : C4 (small group id <36, 9>)
Aut   = (S3 x S3) : C2 (small group id <72, 40>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, (T2^-2 * T1^-1)^2, (T2 * T1 * T2 * T1^-1)^2, (T1^-1, T2^-1, T1^-1) ]
Map:: polytopal non-degenerate
	R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 22, 12)(8, 20, 14, 21)(10, 23, 13, 24)(15, 29, 19, 30)(17, 31, 18, 32)(25, 33, 28, 34)(26, 35, 27, 36)(37, 38, 40)(39, 44, 46)(41, 49, 50)(42, 51, 53)(43, 54, 55)(45, 58, 52)(47, 61, 62)(48, 63, 64)(56, 69, 65)(57, 66, 70)(59, 71, 67)(60, 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) :: { ( 8^3 ), ( 8^4 ) }
Outer automorphisms :: reflexible
Dual of E4.209
Transitivity :: ET+
Graph:: simple bipartite
	v = 21 e = 36 f = 9
	degree seq :: [ 3^12, 4^9 ]

E4.209 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 4, 4})
Quotient :: loop
Aut^+ = (C3 x C3) : C4 (small group id <36, 9>)
Aut   = (S3 x S3) : C2 (small group id <72, 40>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, (T2^-2 * T1^-1)^2, (T2 * T1 * T2 * T1^-1)^2, (T1^-1, T2^-1, T1^-1) ]
Map:: polytopal non-degenerate
	R = (1, 37, 3, 39, 9, 45, 5, 41)(2, 38, 6, 42, 16, 52, 7, 43)(4, 40, 11, 47, 22, 58, 12, 48)(8, 44, 20, 56, 14, 50, 21, 57)(10, 46, 23, 59, 13, 49, 24, 60)(15, 51, 29, 65, 19, 55, 30, 66)(17, 53, 31, 67, 18, 54, 32, 68)(25, 61, 33, 69, 28, 64, 34, 70)(26, 62, 35, 71, 27, 63, 36, 72)
	L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 49)(6, 51)(7, 54)(8, 46)(9, 58)(10, 39)(11, 61)(12, 63)(13, 50)(14, 41)(15, 53)(16, 45)(17, 42)(18, 55)(19, 43)(20, 69)(21, 66)(22, 52)(23, 71)(24, 68)(25, 62)(26, 47)(27, 64)(28, 48)(29, 56)(30, 70)(31, 59)(32, 72)(33, 65)(34, 57)(35, 67)(36, 60)
	local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.208
Transitivity :: ET+ VT+ AT
Graph::
	v = 9 e = 36 f = 21
	degree seq :: [ 8^9 ]

E4.210 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4})
Quotient :: dipole
Aut^+ = (C3 x C3) : C4 (small group id <36, 9>)
Aut   = (S3 x S3) : C2 (small group id <72, 40>)
|r| :: 2
Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y2^-2 * Y1^-1 * Y2^-2, (Y3 * Y2 * Y1 * Y2)^2, (Y1^-1, Y2^-1, Y1^-1), Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 ]
Map::
	R = (1, 37, 2, 38, 4, 40)(3, 39, 8, 44, 10, 46)(5, 41, 13, 49, 14, 50)(6, 42, 15, 51, 17, 53)(7, 43, 18, 54, 19, 55)(9, 45, 22, 58, 16, 52)(11, 47, 25, 61, 26, 62)(12, 48, 27, 63, 28, 64)(20, 56, 33, 69, 29, 65)(21, 57, 30, 66, 34, 70)(23, 59, 35, 71, 31, 67)(24, 60, 32, 68, 36, 72)(73, 109, 75, 111, 81, 117, 77, 113)(74, 110, 78, 114, 88, 124, 79, 115)(76, 112, 83, 119, 94, 130, 84, 120)(80, 116, 92, 128, 86, 122, 93, 129)(82, 118, 95, 131, 85, 121, 96, 132)(87, 123, 101, 137, 91, 127, 102, 138)(89, 125, 103, 139, 90, 126, 104, 140)(97, 133, 105, 141, 100, 136, 106, 142)(98, 134, 107, 143, 99, 135, 108, 144)
	L = (1, 76)(2, 73)(3, 82)(4, 74)(5, 86)(6, 89)(7, 91)(8, 75)(9, 88)(10, 80)(11, 98)(12, 100)(13, 77)(14, 85)(15, 78)(16, 94)(17, 87)(18, 79)(19, 90)(20, 101)(21, 106)(22, 81)(23, 103)(24, 108)(25, 83)(26, 97)(27, 84)(28, 99)(29, 105)(30, 93)(31, 107)(32, 96)(33, 92)(34, 102)(35, 95)(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, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.211
Graph:: bipartite
	v = 21 e = 72 f = 45
	degree seq :: [ 6^12, 8^9 ]

E4.211 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 4, 4})
Quotient :: dipole
Aut^+ = (C3 x C3) : C4 (small group id <36, 9>)
Aut   = (S3 x S3) : C2 (small group id <72, 40>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1 * Y1)^2, (Y3 * Y2^-1)^3, Y3 * Y1 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4 ]
Map:: polytopal
	R = (1, 37, 2, 38, 6, 42, 4, 40)(3, 39, 9, 45, 16, 52, 10, 46)(5, 41, 13, 49, 15, 51, 14, 50)(7, 43, 17, 53, 12, 48, 18, 54)(8, 44, 19, 55, 11, 47, 20, 56)(21, 57, 30, 66, 24, 60, 31, 67)(22, 58, 34, 70, 23, 59, 35, 71)(25, 61, 29, 65, 28, 64, 32, 68)(26, 62, 33, 69, 27, 63, 36, 72)(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, 79)(3, 77)(4, 83)(5, 73)(6, 87)(7, 80)(8, 74)(9, 93)(10, 95)(11, 84)(12, 76)(13, 97)(14, 99)(15, 88)(16, 78)(17, 101)(18, 103)(19, 105)(20, 107)(21, 94)(22, 81)(23, 96)(24, 82)(25, 98)(26, 85)(27, 100)(28, 86)(29, 102)(30, 89)(31, 104)(32, 90)(33, 106)(34, 91)(35, 108)(36, 92)(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) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.210
Graph:: simple bipartite
	v = 45 e = 72 f = 21
	degree seq :: [ 2^36, 8^9 ]

E4.212 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {3, 3, 6})
Quotient :: edge
Aut^+ = C3 x A4 (small group id <36, 11>)
Aut   = (C3 x A4) : C2 (small group id <72, 43>)
|r| :: 2
Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^3, T2^6, T2^2 * T1 * T2^-2 * T1^-1, (T2 * T1^-1)^3 ]
Map:: polytopal non-degenerate
	R = (1, 3, 9, 24, 15, 5)(2, 6, 17, 32, 21, 7)(4, 11, 25, 35, 30, 12)(8, 22, 34, 28, 13, 23)(10, 19, 31, 16, 14, 26)(18, 29, 36, 27, 20, 33)(37, 38, 40)(39, 44, 46)(41, 49, 50)(42, 52, 54)(43, 55, 56)(45, 53, 61)(47, 63, 64)(48, 65, 58)(51, 57, 66)(59, 71, 69)(60, 70, 67)(62, 72, 68)
	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) :: { ( 6^3 ), ( 6^6 ) }
Outer automorphisms :: reflexible
Dual of E4.213
Transitivity :: ET+
Graph:: simple bipartite
	v = 18 e = 36 f = 12
	degree seq :: [ 3^12, 6^6 ]

E4.213 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {3, 3, 6})
Quotient :: loop
Aut^+ = C3 x A4 (small group id <36, 11>)
Aut   = (C3 x A4) : C2 (small group id <72, 43>)
|r| :: 2
Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, (T1 * T2^-1)^3, (T2^-1, T1^-1)^2, (T2^-1 * T1^-1)^6 ]
Map:: polytopal non-degenerate
	R = (1, 37, 3, 39, 5, 41)(2, 38, 6, 42, 7, 43)(4, 40, 10, 46, 11, 47)(8, 44, 18, 54, 19, 55)(9, 45, 16, 52, 20, 56)(12, 48, 25, 61, 22, 58)(13, 49, 26, 62, 27, 63)(14, 50, 28, 64, 29, 65)(15, 51, 23, 59, 30, 66)(17, 53, 31, 67, 32, 68)(21, 57, 33, 69, 34, 70)(24, 60, 35, 71, 36, 72)
	L = (1, 38)(2, 40)(3, 44)(4, 37)(5, 48)(6, 50)(7, 52)(8, 45)(9, 39)(10, 57)(11, 59)(12, 49)(13, 41)(14, 51)(15, 42)(16, 53)(17, 43)(18, 64)(19, 62)(20, 70)(21, 58)(22, 46)(23, 60)(24, 47)(25, 65)(26, 66)(27, 68)(28, 69)(29, 67)(30, 55)(31, 61)(32, 72)(33, 54)(34, 71)(35, 56)(36, 63)
	local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.212
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 12 e = 36 f = 18
	degree seq :: [ 6^12 ]

E4.214 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 6})
Quotient :: dipole
Aut^+ = C3 x A4 (small group id <36, 11>)
Aut   = (C3 x A4) : C2 (small group id <72, 43>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^6, (Y3^-1 * Y1^-1)^3, Y2^2 * Y1 * Y2^-2 * Y1^-1, (Y2 * Y1^-1)^3 ]
Map::
	R = (1, 37, 2, 38, 4, 40)(3, 39, 8, 44, 10, 46)(5, 41, 13, 49, 14, 50)(6, 42, 16, 52, 18, 54)(7, 43, 19, 55, 20, 56)(9, 45, 17, 53, 25, 61)(11, 47, 27, 63, 28, 64)(12, 48, 29, 65, 22, 58)(15, 51, 21, 57, 30, 66)(23, 59, 35, 71, 33, 69)(24, 60, 34, 70, 31, 67)(26, 62, 36, 72, 32, 68)(73, 109, 75, 111, 81, 117, 96, 132, 87, 123, 77, 113)(74, 110, 78, 114, 89, 125, 104, 140, 93, 129, 79, 115)(76, 112, 83, 119, 97, 133, 107, 143, 102, 138, 84, 120)(80, 116, 94, 130, 106, 142, 100, 136, 85, 121, 95, 131)(82, 118, 91, 127, 103, 139, 88, 124, 86, 122, 98, 134)(90, 126, 101, 137, 108, 144, 99, 135, 92, 128, 105, 141)
	L = (1, 75)(2, 78)(3, 81)(4, 83)(5, 73)(6, 89)(7, 74)(8, 94)(9, 96)(10, 91)(11, 97)(12, 76)(13, 95)(14, 98)(15, 77)(16, 86)(17, 104)(18, 101)(19, 103)(20, 105)(21, 79)(22, 106)(23, 80)(24, 87)(25, 107)(26, 82)(27, 92)(28, 85)(29, 108)(30, 84)(31, 88)(32, 93)(33, 90)(34, 100)(35, 102)(36, 99)(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, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.215
Graph:: bipartite
	v = 18 e = 72 f = 48
	degree seq :: [ 6^12, 12^6 ]

E4.215 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {3, 3, 6})
Quotient :: dipole
Aut^+ = C3 x A4 (small group id <36, 11>)
Aut   = (C3 x A4) : C2 (small group id <72, 43>)
|r| :: 2
Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y2 * Y3^2 * Y2^-1 * Y3^-1, (Y2^-1 * Y3^-1)^3, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	R = (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)(73, 109, 74, 110, 76, 112)(75, 111, 80, 116, 82, 118)(77, 113, 85, 121, 86, 122)(78, 114, 88, 124, 90, 126)(79, 115, 91, 127, 92, 128)(81, 117, 89, 125, 97, 133)(83, 119, 99, 135, 100, 136)(84, 120, 101, 137, 94, 130)(87, 123, 93, 129, 102, 138)(95, 131, 107, 143, 105, 141)(96, 132, 106, 142, 103, 139)(98, 134, 108, 144, 104, 140)
	L = (1, 75)(2, 78)(3, 81)(4, 83)(5, 73)(6, 89)(7, 74)(8, 94)(9, 96)(10, 91)(11, 97)(12, 76)(13, 95)(14, 98)(15, 77)(16, 86)(17, 104)(18, 101)(19, 103)(20, 105)(21, 79)(22, 106)(23, 80)(24, 87)(25, 107)(26, 82)(27, 92)(28, 85)(29, 108)(30, 84)(31, 88)(32, 93)(33, 90)(34, 100)(35, 102)(36, 99)(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) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.214
Graph:: simple bipartite
	v = 48 e = 72 f = 18
	degree seq :: [ 2^36, 6^12 ]

E4.216 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 6})
Quotient :: regular
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^6, (T2 * T1^-3)^2, T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ]
Map:: polytopal 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, 26, 33, 32, 36, 30)(17, 27, 34, 29, 35, 31)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 29)(18, 32)(19, 30)(20, 31)(23, 33)(24, 34)(25, 35)(28, 36)
	local type(s) :: { ( 6^6 ) }
Outer automorphisms :: reflexible
Dual of E4.217
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 6 e = 18 f = 6
	degree seq :: [ 6^6 ]

E4.217 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 6})
Quotient :: regular
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^6, (T1^-1 * T2)^6 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 34, 33, 36, 32, 35)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)
	local type(s) :: { ( 6^6 ) }
Outer automorphisms :: reflexible
Dual of E4.216
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 6 e = 18 f = 6
	degree seq :: [ 6^6 ]

E4.218 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 6, 6})
Quotient :: regular
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2 * T1)^2, T1^6, T1 * T2 * T1 * 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, 35, 32, 36, 33, 34)
	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)
	local type(s) :: { ( 6^6 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 6 e = 18 f = 6
	degree seq :: [ 6^6 ]

E4.219 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 6})
Quotient :: edge
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, (T2^-1 * T1 * T2^-2)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
Map:: polytopal
	R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 25, 14, 6)(7, 15, 29, 21, 30, 16)(9, 19, 32, 17, 31, 20)(11, 22, 33, 28, 34, 23)(13, 26, 36, 24, 35, 27)(37, 38)(39, 43)(40, 45)(41, 47)(42, 49)(44, 53)(46, 57)(48, 60)(50, 64)(51, 58)(52, 62)(54, 61)(55, 59)(56, 63)(65, 71)(66, 70)(67, 69)(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) :: { ( 12, 12 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.224
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 36 f = 6
	degree seq :: [ 2^18, 6^6 ]

E4.220 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 6})
Quotient :: edge
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1)^6 ]
Map:: polytopal
	R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 24, 18, 9, 16)(11, 19, 28, 22, 13, 20)(23, 31, 26, 33, 25, 32)(27, 34, 30, 36, 29, 35)(37, 38)(39, 43)(40, 45)(41, 47)(42, 49)(44, 48)(46, 50)(51, 59)(52, 61)(53, 60)(54, 62)(55, 63)(56, 65)(57, 64)(58, 66)(67, 70)(68, 71)(69, 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) :: { ( 12, 12 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.223
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 36 f = 6
	degree seq :: [ 2^18, 6^6 ]

E4.221 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 6})
Quotient :: edge
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^6 ]
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, 38)(39, 43)(40, 45)(41, 47)(42, 49)(44, 50)(46, 48)(51, 59)(52, 60)(53, 61)(54, 62)(55, 63)(56, 64)(57, 65)(58, 66)(67, 71)(68, 70)(69, 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) :: { ( 12, 12 ), ( 12^6 ) }
Outer automorphisms :: reflexible
Dual of E4.225
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 36 f = 6
	degree seq :: [ 2^18, 6^6 ]

E4.222 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 6, 6})
Quotient :: edge
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2 * T1^-1 * T2^3 * T1^-1, T2^-3 * T1^-1 * T2 * T1^-1, T1^6, T2^6 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 21, 15, 5)(2, 7, 19, 11, 22, 8)(4, 12, 25, 14, 24, 9)(6, 17, 30, 20, 32, 18)(13, 27, 34, 23, 33, 26)(16, 28, 35, 31, 36, 29)(37, 38, 42, 52, 49, 40)(39, 45, 59, 64, 54, 47)(41, 50, 63, 65, 56, 43)(44, 57, 48, 62, 67, 53)(46, 55, 66, 71, 70, 61)(51, 58, 68, 72, 69, 60)
	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) :: { ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E4.226
Transitivity :: ET+
Graph:: simple bipartite
	v = 12 e = 36 f = 18
	degree seq :: [ 6^12 ]

E4.223 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 6})
Quotient :: loop
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, (T2^-1 * T1 * T2^-2)^2, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 37, 3, 39, 8, 44, 18, 54, 10, 46, 4, 40)(2, 38, 5, 41, 12, 48, 25, 61, 14, 50, 6, 42)(7, 43, 15, 51, 29, 65, 21, 57, 30, 66, 16, 52)(9, 45, 19, 55, 32, 68, 17, 53, 31, 67, 20, 56)(11, 47, 22, 58, 33, 69, 28, 64, 34, 70, 23, 59)(13, 49, 26, 62, 36, 72, 24, 60, 35, 71, 27, 63)
	L = (1, 38)(2, 37)(3, 43)(4, 45)(5, 47)(6, 49)(7, 39)(8, 53)(9, 40)(10, 57)(11, 41)(12, 60)(13, 42)(14, 64)(15, 58)(16, 62)(17, 44)(18, 61)(19, 59)(20, 63)(21, 46)(22, 51)(23, 55)(24, 48)(25, 54)(26, 52)(27, 56)(28, 50)(29, 71)(30, 70)(31, 69)(32, 72)(33, 67)(34, 66)(35, 65)(36, 68)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.220
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 36 f = 24
	degree seq :: [ 12^6 ]

E4.224 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 6})
Quotient :: loop
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^6, (T2^-1 * T1)^6 ]
Map::
	R = (1, 37, 3, 39, 8, 44, 17, 53, 10, 46, 4, 40)(2, 38, 5, 41, 12, 48, 21, 57, 14, 50, 6, 42)(7, 43, 15, 51, 24, 60, 18, 54, 9, 45, 16, 52)(11, 47, 19, 55, 28, 64, 22, 58, 13, 49, 20, 56)(23, 59, 31, 67, 26, 62, 33, 69, 25, 61, 32, 68)(27, 63, 34, 70, 30, 66, 36, 72, 29, 65, 35, 71)
	L = (1, 38)(2, 37)(3, 43)(4, 45)(5, 47)(6, 49)(7, 39)(8, 48)(9, 40)(10, 50)(11, 41)(12, 44)(13, 42)(14, 46)(15, 59)(16, 61)(17, 60)(18, 62)(19, 63)(20, 65)(21, 64)(22, 66)(23, 51)(24, 53)(25, 52)(26, 54)(27, 55)(28, 57)(29, 56)(30, 58)(31, 70)(32, 71)(33, 72)(34, 67)(35, 68)(36, 69)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.219
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 36 f = 24
	degree seq :: [ 12^6 ]

E4.225 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 6})
Quotient :: loop
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^6 ]
Map::
	R = (1, 37, 3, 39, 8, 44, 17, 53, 10, 46, 4, 40)(2, 38, 5, 41, 12, 48, 21, 57, 14, 50, 6, 42)(7, 43, 15, 51, 9, 45, 18, 54, 25, 61, 16, 52)(11, 47, 19, 55, 13, 49, 22, 58, 29, 65, 20, 56)(23, 59, 31, 67, 24, 60, 33, 69, 26, 62, 32, 68)(27, 63, 34, 70, 28, 64, 36, 72, 30, 66, 35, 71)
	L = (1, 38)(2, 37)(3, 43)(4, 45)(5, 47)(6, 49)(7, 39)(8, 50)(9, 40)(10, 48)(11, 41)(12, 46)(13, 42)(14, 44)(15, 59)(16, 60)(17, 61)(18, 62)(19, 63)(20, 64)(21, 65)(22, 66)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(29, 57)(30, 58)(31, 71)(32, 70)(33, 72)(34, 68)(35, 67)(36, 69)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.221
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 6 e = 36 f = 24
	degree seq :: [ 12^6 ]

E4.226 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 6, 6})
Quotient :: loop
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-3)^2, T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 37, 3, 39)(2, 38, 6, 42)(4, 40, 9, 45)(5, 41, 12, 48)(7, 43, 16, 52)(8, 44, 17, 53)(10, 46, 21, 57)(11, 47, 22, 58)(13, 49, 26, 62)(14, 50, 27, 63)(15, 51, 29, 65)(18, 54, 32, 68)(19, 55, 30, 66)(20, 56, 31, 67)(23, 59, 33, 69)(24, 60, 34, 70)(25, 61, 35, 71)(28, 64, 36, 72)
	L = (1, 38)(2, 41)(3, 43)(4, 37)(5, 47)(6, 49)(7, 51)(8, 39)(9, 55)(10, 40)(11, 46)(12, 59)(13, 61)(14, 42)(15, 58)(16, 62)(17, 63)(18, 44)(19, 60)(20, 45)(21, 64)(22, 54)(23, 56)(24, 48)(25, 57)(26, 69)(27, 70)(28, 50)(29, 71)(30, 52)(31, 53)(32, 72)(33, 68)(34, 65)(35, 67)(36, 66)
	local type(s) :: { ( 6^4 ) }
Outer automorphisms :: reflexible
Dual of E4.222
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 18 e = 36 f = 12
	degree seq :: [ 4^18 ]

E4.227 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y2^-3 * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^6 ]
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, 24, 60)(14, 50, 28, 64)(15, 51, 22, 58)(16, 52, 26, 62)(18, 54, 25, 61)(19, 55, 23, 59)(20, 56, 27, 63)(29, 65, 35, 71)(30, 66, 34, 70)(31, 67, 33, 69)(32, 68, 36, 72)(73, 109, 75, 111, 80, 116, 90, 126, 82, 118, 76, 112)(74, 110, 77, 113, 84, 120, 97, 133, 86, 122, 78, 114)(79, 115, 87, 123, 101, 137, 93, 129, 102, 138, 88, 124)(81, 117, 91, 127, 104, 140, 89, 125, 103, 139, 92, 128)(83, 119, 94, 130, 105, 141, 100, 136, 106, 142, 95, 131)(85, 121, 98, 134, 108, 144, 96, 132, 107, 143, 99, 135)
	L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 89)(9, 76)(10, 93)(11, 77)(12, 96)(13, 78)(14, 100)(15, 94)(16, 98)(17, 80)(18, 97)(19, 95)(20, 99)(21, 82)(22, 87)(23, 91)(24, 84)(25, 90)(26, 88)(27, 92)(28, 86)(29, 107)(30, 106)(31, 105)(32, 108)(33, 103)(34, 102)(35, 101)(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, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.232
Graph:: bipartite
	v = 24 e = 72 f = 42
	degree seq :: [ 4^18, 12^6 ]

E4.228 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|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, Y2^6, (Y3 * Y2^-1)^6 ]
Map::
	R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 11, 47)(6, 42, 13, 49)(8, 44, 12, 48)(10, 46, 14, 50)(15, 51, 23, 59)(16, 52, 25, 61)(17, 53, 24, 60)(18, 54, 26, 62)(19, 55, 27, 63)(20, 56, 29, 65)(21, 57, 28, 64)(22, 58, 30, 66)(31, 67, 34, 70)(32, 68, 35, 71)(33, 69, 36, 72)(73, 109, 75, 111, 80, 116, 89, 125, 82, 118, 76, 112)(74, 110, 77, 113, 84, 120, 93, 129, 86, 122, 78, 114)(79, 115, 87, 123, 96, 132, 90, 126, 81, 117, 88, 124)(83, 119, 91, 127, 100, 136, 94, 130, 85, 121, 92, 128)(95, 131, 103, 139, 98, 134, 105, 141, 97, 133, 104, 140)(99, 135, 106, 142, 102, 138, 108, 144, 101, 137, 107, 143)
	L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 84)(9, 76)(10, 86)(11, 77)(12, 80)(13, 78)(14, 82)(15, 95)(16, 97)(17, 96)(18, 98)(19, 99)(20, 101)(21, 100)(22, 102)(23, 87)(24, 89)(25, 88)(26, 90)(27, 91)(28, 93)(29, 92)(30, 94)(31, 106)(32, 107)(33, 108)(34, 103)(35, 104)(36, 105)(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, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.233
Graph:: bipartite
	v = 24 e = 72 f = 42
	degree seq :: [ 4^18, 12^6 ]

E4.229 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|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)^6 ]
Map::
	R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 9, 45)(5, 41, 11, 47)(6, 42, 13, 49)(8, 44, 14, 50)(10, 46, 12, 48)(15, 51, 23, 59)(16, 52, 24, 60)(17, 53, 25, 61)(18, 54, 26, 62)(19, 55, 27, 63)(20, 56, 28, 64)(21, 57, 29, 65)(22, 58, 30, 66)(31, 67, 35, 71)(32, 68, 34, 70)(33, 69, 36, 72)(73, 109, 75, 111, 80, 116, 89, 125, 82, 118, 76, 112)(74, 110, 77, 113, 84, 120, 93, 129, 86, 122, 78, 114)(79, 115, 87, 123, 81, 117, 90, 126, 97, 133, 88, 124)(83, 119, 91, 127, 85, 121, 94, 130, 101, 137, 92, 128)(95, 131, 103, 139, 96, 132, 105, 141, 98, 134, 104, 140)(99, 135, 106, 142, 100, 136, 108, 144, 102, 138, 107, 143)
	L = (1, 74)(2, 73)(3, 79)(4, 81)(5, 83)(6, 85)(7, 75)(8, 86)(9, 76)(10, 84)(11, 77)(12, 82)(13, 78)(14, 80)(15, 95)(16, 96)(17, 97)(18, 98)(19, 99)(20, 100)(21, 101)(22, 102)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 107)(32, 106)(33, 108)(34, 104)(35, 103)(36, 105)(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, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.234
Graph:: bipartite
	v = 24 e = 72 f = 42
	degree seq :: [ 4^18, 12^6 ]

E4.230 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-3, Y2^6, Y1^6, (Y2^2 * Y1^-1)^2 ]
Map::
	R = (1, 37, 2, 38, 6, 42, 16, 52, 13, 49, 4, 40)(3, 39, 9, 45, 17, 53, 8, 44, 21, 57, 11, 47)(5, 41, 14, 50, 18, 54, 12, 48, 20, 56, 7, 43)(10, 46, 24, 60, 28, 64, 23, 59, 32, 68, 22, 58)(15, 51, 26, 62, 29, 65, 19, 55, 30, 66, 27, 63)(25, 61, 31, 67, 35, 71, 34, 70, 36, 72, 33, 69)(73, 109, 75, 111, 82, 118, 97, 133, 87, 123, 77, 113)(74, 110, 79, 115, 91, 127, 103, 139, 94, 130, 80, 116)(76, 112, 84, 120, 98, 134, 105, 141, 95, 131, 81, 117)(78, 114, 89, 125, 100, 136, 107, 143, 101, 137, 90, 126)(83, 119, 88, 124, 86, 122, 99, 135, 106, 142, 96, 132)(85, 121, 93, 129, 104, 140, 108, 144, 102, 138, 92, 128)
	L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 89)(7, 91)(8, 74)(9, 76)(10, 97)(11, 88)(12, 98)(13, 93)(14, 99)(15, 77)(16, 86)(17, 100)(18, 78)(19, 103)(20, 85)(21, 104)(22, 80)(23, 81)(24, 83)(25, 87)(26, 105)(27, 106)(28, 107)(29, 90)(30, 92)(31, 94)(32, 108)(33, 95)(34, 96)(35, 101)(36, 102)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.231
Graph:: bipartite
	v = 12 e = 72 f = 54
	degree seq :: [ 12^12 ]

E4.231 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^6, (Y3^-3 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	R = (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)(73, 109, 74, 110)(75, 111, 79, 115)(76, 112, 81, 117)(77, 113, 83, 119)(78, 114, 85, 121)(80, 116, 89, 125)(82, 118, 93, 129)(84, 120, 96, 132)(86, 122, 100, 136)(87, 123, 94, 130)(88, 124, 98, 134)(90, 126, 97, 133)(91, 127, 95, 131)(92, 128, 99, 135)(101, 137, 107, 143)(102, 138, 106, 142)(103, 139, 105, 141)(104, 140, 108, 144)
	L = (1, 75)(2, 77)(3, 80)(4, 73)(5, 84)(6, 74)(7, 87)(8, 90)(9, 91)(10, 76)(11, 94)(12, 97)(13, 98)(14, 78)(15, 101)(16, 79)(17, 103)(18, 82)(19, 104)(20, 81)(21, 102)(22, 105)(23, 83)(24, 107)(25, 86)(26, 108)(27, 85)(28, 106)(29, 93)(30, 88)(31, 92)(32, 89)(33, 100)(34, 95)(35, 99)(36, 96)(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) :: { ( 12, 12 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E4.230
Graph:: simple bipartite
	v = 54 e = 72 f = 12
	degree seq :: [ 2^36, 4^18 ]

E4.232 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1^-1)^6 ]
Map:: polytopal
	R = (1, 37, 2, 38, 5, 41, 11, 47, 10, 46, 4, 40)(3, 39, 7, 43, 12, 48, 20, 56, 17, 53, 8, 44)(6, 42, 13, 49, 19, 55, 18, 54, 9, 45, 14, 50)(15, 51, 23, 59, 27, 63, 25, 61, 16, 52, 24, 60)(21, 57, 28, 64, 26, 62, 30, 66, 22, 58, 29, 65)(31, 67, 34, 70, 33, 69, 36, 72, 32, 68, 35, 71)(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, 87)(8, 88)(9, 76)(10, 89)(11, 91)(12, 77)(13, 93)(14, 94)(15, 79)(16, 80)(17, 82)(18, 98)(19, 83)(20, 99)(21, 85)(22, 86)(23, 103)(24, 104)(25, 105)(26, 90)(27, 92)(28, 106)(29, 107)(30, 108)(31, 95)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.227
Graph:: simple bipartite
	v = 42 e = 72 f = 24
	degree seq :: [ 2^36, 12^6 ]

E4.233 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = C6 x S3 (small group id <36, 12>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3 * Y1^-3 * Y3^-1 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1)^6 ]
Map:: polytopal
	R = (1, 37, 2, 38, 5, 41, 11, 47, 10, 46, 4, 40)(3, 39, 7, 43, 15, 51, 22, 58, 18, 54, 8, 44)(6, 42, 13, 49, 25, 61, 21, 57, 28, 64, 14, 50)(9, 45, 19, 55, 24, 60, 12, 48, 23, 59, 20, 56)(16, 52, 26, 62, 33, 69, 32, 68, 36, 72, 30, 66)(17, 53, 27, 63, 34, 70, 29, 65, 35, 71, 31, 67)(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, 94)(12, 77)(13, 98)(14, 99)(15, 101)(16, 79)(17, 80)(18, 104)(19, 102)(20, 103)(21, 82)(22, 83)(23, 105)(24, 106)(25, 107)(26, 85)(27, 86)(28, 108)(29, 87)(30, 91)(31, 92)(32, 90)(33, 95)(34, 96)(35, 97)(36, 100)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.228
Graph:: simple bipartite
	v = 42 e = 72 f = 24
	degree seq :: [ 2^36, 12^6 ]

E4.234 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 6, 6})
Quotient :: dipole
Aut^+ = S3 x S3 (small group id <36, 10>)
Aut   = C2 x S3 x S3 (small group id <72, 46>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^6 ]
Map:: polytopal
	R = (1, 37, 2, 38, 5, 41, 11, 47, 10, 46, 4, 40)(3, 39, 7, 43, 15, 51, 20, 56, 12, 48, 8, 44)(6, 42, 13, 49, 9, 45, 18, 54, 19, 55, 14, 50)(16, 52, 23, 59, 17, 53, 25, 61, 27, 63, 24, 60)(21, 57, 28, 64, 22, 58, 30, 66, 26, 62, 29, 65)(31, 67, 35, 71, 32, 68, 36, 72, 33, 69, 34, 70)(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, 87)(11, 91)(12, 77)(13, 93)(14, 94)(15, 82)(16, 79)(17, 80)(18, 98)(19, 83)(20, 99)(21, 85)(22, 86)(23, 103)(24, 104)(25, 105)(26, 90)(27, 92)(28, 106)(29, 107)(30, 108)(31, 95)(32, 96)(33, 97)(34, 100)(35, 101)(36, 102)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.229
Graph:: simple bipartite
	v = 42 e = 72 f = 24
	degree seq :: [ 2^36, 12^6 ]

E4.235 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 10})
Quotient :: regular
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T2 * T1^-2)^2, (T1 * T2)^4, T1^10 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 20, 29, 28, 19, 10, 4)(3, 7, 15, 25, 33, 37, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 36, 31, 21, 14)(16, 23, 17, 24, 32, 38, 40, 39, 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, 36)(31, 38)(35, 39)(37, 40)
	local type(s) :: { ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E4.236
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 4 e = 20 f = 10
	degree seq :: [ 10^4 ]

E4.236 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 10})
Quotient :: regular
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^10 ]
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, 40, 38, 39)
	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)
	local type(s) :: { ( 10^4 ) }
Outer automorphisms :: reflexible
Dual of E4.235
Transitivity :: ET+ VT+ AT+ REG+
Graph:: bipartite
	v = 10 e = 20 f = 4
	degree seq :: [ 4^10 ]

E4.237 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 10})
Quotient :: edge
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^10 ]
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, 42)(43, 47)(44, 49)(45, 50)(46, 52)(48, 51)(53, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(69, 73)(70, 74)(71, 75)(72, 76)(77, 80)(78, 79)
	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) :: { ( 20, 20 ), ( 20^4 ) }
Outer automorphisms :: reflexible
Dual of E4.241
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 40 f = 4
	degree seq :: [ 2^20, 4^10 ]

E4.238 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 10})
Quotient :: edge
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^10 ]
Map:: polytopal non-degenerate
	R = (1, 3, 10, 18, 26, 34, 28, 20, 12, 5)(2, 7, 15, 23, 31, 38, 32, 24, 16, 8)(4, 11, 19, 27, 35, 39, 33, 25, 17, 9)(6, 13, 21, 29, 36, 40, 37, 30, 22, 14)(41, 42, 46, 44)(43, 49, 53, 48)(45, 51, 54, 47)(50, 56, 61, 57)(52, 55, 62, 59)(58, 65, 69, 64)(60, 67, 70, 63)(66, 72, 76, 73)(68, 71, 77, 75)(74, 79, 80, 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) :: { ( 4^4 ), ( 4^10 ) }
Outer automorphisms :: reflexible
Dual of E4.242
Transitivity :: ET+
Graph:: simple bipartite
	v = 14 e = 40 f = 20
	degree seq :: [ 4^10, 10^4 ]

E4.239 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 10})
Quotient :: edge
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^10 ]
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, 36)(31, 38)(35, 39)(37, 40)(41, 42, 45, 51, 60, 69, 68, 59, 50, 44)(43, 47, 55, 65, 73, 77, 70, 62, 52, 48)(46, 53, 49, 58, 67, 75, 76, 71, 61, 54)(56, 63, 57, 64, 72, 78, 80, 79, 74, 66)
	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, 8 ), ( 8^10 ) }
Outer automorphisms :: reflexible
Dual of E4.240
Transitivity :: ET+
Graph:: simple bipartite
	v = 24 e = 40 f = 10
	degree seq :: [ 2^20, 10^4 ]

E4.240 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 10})
Quotient :: loop
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^10 ]
Map::
	R = (1, 41, 3, 43, 8, 48, 4, 44)(2, 42, 5, 45, 11, 51, 6, 46)(7, 47, 13, 53, 9, 49, 14, 54)(10, 50, 15, 55, 12, 52, 16, 56)(17, 57, 21, 61, 18, 58, 22, 62)(19, 59, 23, 63, 20, 60, 24, 64)(25, 65, 29, 69, 26, 66, 30, 70)(27, 67, 31, 71, 28, 68, 32, 72)(33, 73, 37, 77, 34, 74, 38, 78)(35, 75, 39, 79, 36, 76, 40, 80)
	L = (1, 42)(2, 41)(3, 47)(4, 49)(5, 50)(6, 52)(7, 43)(8, 51)(9, 44)(10, 45)(11, 48)(12, 46)(13, 57)(14, 58)(15, 59)(16, 60)(17, 53)(18, 54)(19, 55)(20, 56)(21, 65)(22, 66)(23, 67)(24, 68)(25, 61)(26, 62)(27, 63)(28, 64)(29, 73)(30, 74)(31, 75)(32, 76)(33, 69)(34, 70)(35, 71)(36, 72)(37, 80)(38, 79)(39, 78)(40, 77)
	local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.239
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 10 e = 40 f = 24
	degree seq :: [ 8^10 ]

E4.241 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 10})
Quotient :: loop
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^10 ]
Map::
	R = (1, 41, 3, 43, 10, 50, 18, 58, 26, 66, 34, 74, 28, 68, 20, 60, 12, 52, 5, 45)(2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 38, 78, 32, 72, 24, 64, 16, 56, 8, 48)(4, 44, 11, 51, 19, 59, 27, 67, 35, 75, 39, 79, 33, 73, 25, 65, 17, 57, 9, 49)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54)
	L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 51)(6, 44)(7, 45)(8, 43)(9, 53)(10, 56)(11, 54)(12, 55)(13, 48)(14, 47)(15, 62)(16, 61)(17, 50)(18, 65)(19, 52)(20, 67)(21, 57)(22, 59)(23, 60)(24, 58)(25, 69)(26, 72)(27, 70)(28, 71)(29, 64)(30, 63)(31, 77)(32, 76)(33, 66)(34, 79)(35, 68)(36, 73)(37, 75)(38, 74)(39, 80)(40, 78)
	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 E4.237
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 4 e = 40 f = 30
	degree seq :: [ 20^4 ]

E4.242 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 10})
Quotient :: loop
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^10 ]
Map:: polytopal non-degenerate
	R = (1, 41, 3, 43)(2, 42, 6, 46)(4, 44, 9, 49)(5, 45, 12, 52)(7, 47, 16, 56)(8, 48, 17, 57)(10, 50, 15, 55)(11, 51, 21, 61)(13, 53, 23, 63)(14, 54, 24, 64)(18, 58, 26, 66)(19, 59, 27, 67)(20, 60, 30, 70)(22, 62, 32, 72)(25, 65, 34, 74)(28, 68, 33, 73)(29, 69, 36, 76)(31, 71, 38, 78)(35, 75, 39, 79)(37, 77, 40, 80)
	L = (1, 42)(2, 45)(3, 47)(4, 41)(5, 51)(6, 53)(7, 55)(8, 43)(9, 58)(10, 44)(11, 60)(12, 48)(13, 49)(14, 46)(15, 65)(16, 63)(17, 64)(18, 67)(19, 50)(20, 69)(21, 54)(22, 52)(23, 57)(24, 72)(25, 73)(26, 56)(27, 75)(28, 59)(29, 68)(30, 62)(31, 61)(32, 78)(33, 77)(34, 66)(35, 76)(36, 71)(37, 70)(38, 80)(39, 74)(40, 79)
	local type(s) :: { ( 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.238
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 20 e = 40 f = 14
	degree seq :: [ 4^20 ]

E4.243 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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)^10 ]
Map::
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 9, 49)(5, 45, 10, 50)(6, 46, 12, 52)(8, 48, 11, 51)(13, 53, 17, 57)(14, 54, 18, 58)(15, 55, 19, 59)(16, 56, 20, 60)(21, 61, 25, 65)(22, 62, 26, 66)(23, 63, 27, 67)(24, 64, 28, 68)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 88, 128, 84, 124)(82, 122, 85, 125, 91, 131, 86, 126)(87, 127, 93, 133, 89, 129, 94, 134)(90, 130, 95, 135, 92, 132, 96, 136)(97, 137, 101, 141, 98, 138, 102, 142)(99, 139, 103, 143, 100, 140, 104, 144)(105, 145, 109, 149, 106, 146, 110, 150)(107, 147, 111, 151, 108, 148, 112, 152)(113, 153, 117, 157, 114, 154, 118, 158)(115, 155, 119, 159, 116, 156, 120, 160)
	L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 90)(6, 92)(7, 83)(8, 91)(9, 84)(10, 85)(11, 88)(12, 86)(13, 97)(14, 98)(15, 99)(16, 100)(17, 93)(18, 94)(19, 95)(20, 96)(21, 105)(22, 106)(23, 107)(24, 108)(25, 101)(26, 102)(27, 103)(28, 104)(29, 113)(30, 114)(31, 115)(32, 116)(33, 109)(34, 110)(35, 111)(36, 112)(37, 120)(38, 119)(39, 118)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.246
Graph:: bipartite
	v = 30 e = 80 f = 44
	degree seq :: [ 4^20, 8^10 ]

E4.244 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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, Y2^10 ]
Map::
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 8, 48)(5, 45, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 36, 76, 33, 73)(28, 68, 31, 71, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 91, 131, 99, 139, 107, 147, 115, 155, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134)
	L = (1, 83)(2, 87)(3, 90)(4, 91)(5, 81)(6, 93)(7, 95)(8, 82)(9, 84)(10, 98)(11, 99)(12, 85)(13, 101)(14, 86)(15, 103)(16, 88)(17, 89)(18, 106)(19, 107)(20, 92)(21, 109)(22, 94)(23, 111)(24, 96)(25, 97)(26, 114)(27, 115)(28, 100)(29, 116)(30, 102)(31, 118)(32, 104)(33, 105)(34, 108)(35, 119)(36, 120)(37, 110)(38, 112)(39, 113)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	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 E4.245
Graph:: bipartite
	v = 14 e = 80 f = 60
	degree seq :: [ 8^10, 20^4 ]

E4.245 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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)^10 ]
Map:: polytopal
	R = (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)(81, 121, 82, 122)(83, 123, 87, 127)(84, 124, 89, 129)(85, 125, 91, 131)(86, 126, 93, 133)(88, 128, 94, 134)(90, 130, 92, 132)(95, 135, 100, 140)(96, 136, 103, 143)(97, 137, 105, 145)(98, 138, 101, 141)(99, 139, 107, 147)(102, 142, 109, 149)(104, 144, 111, 151)(106, 146, 112, 152)(108, 148, 110, 150)(113, 153, 118, 158)(114, 154, 119, 159)(115, 155, 116, 156)(117, 157, 120, 160)
	L = (1, 83)(2, 85)(3, 88)(4, 81)(5, 92)(6, 82)(7, 95)(8, 97)(9, 98)(10, 84)(11, 100)(12, 102)(13, 103)(14, 86)(15, 89)(16, 87)(17, 106)(18, 107)(19, 90)(20, 93)(21, 91)(22, 110)(23, 111)(24, 94)(25, 96)(26, 114)(27, 115)(28, 99)(29, 101)(30, 117)(31, 118)(32, 104)(33, 105)(34, 108)(35, 119)(36, 109)(37, 112)(38, 120)(39, 113)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 8, 20 ), ( 8, 20, 8, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.244
Graph:: simple bipartite
	v = 60 e = 80 f = 14
	degree seq :: [ 2^40, 4^20 ]

E4.246 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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, Y1^10 ]
Map:: polytopal
	R = (1, 41, 2, 42, 5, 45, 11, 51, 20, 60, 29, 69, 28, 68, 19, 59, 10, 50, 4, 44)(3, 43, 7, 47, 15, 55, 25, 65, 33, 73, 37, 77, 30, 70, 22, 62, 12, 52, 8, 48)(6, 46, 13, 53, 9, 49, 18, 58, 27, 67, 35, 75, 36, 76, 31, 71, 21, 61, 14, 54)(16, 56, 23, 63, 17, 57, 24, 64, 32, 72, 38, 78, 40, 80, 39, 79, 34, 74, 26, 66)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160)
	L = (1, 83)(2, 86)(3, 81)(4, 89)(5, 92)(6, 82)(7, 96)(8, 97)(9, 84)(10, 95)(11, 101)(12, 85)(13, 103)(14, 104)(15, 90)(16, 87)(17, 88)(18, 106)(19, 107)(20, 110)(21, 91)(22, 112)(23, 93)(24, 94)(25, 114)(26, 98)(27, 99)(28, 113)(29, 116)(30, 100)(31, 118)(32, 102)(33, 108)(34, 105)(35, 119)(36, 109)(37, 120)(38, 111)(39, 115)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.243
Graph:: simple bipartite
	v = 44 e = 80 f = 30
	degree seq :: [ 2^40, 20^4 ]

E4.247 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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, Y2^10 ]
Map::
	R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 9, 49)(5, 45, 11, 51)(6, 46, 13, 53)(8, 48, 14, 54)(10, 50, 12, 52)(15, 55, 20, 60)(16, 56, 23, 63)(17, 57, 25, 65)(18, 58, 21, 61)(19, 59, 27, 67)(22, 62, 29, 69)(24, 64, 31, 71)(26, 66, 32, 72)(28, 68, 30, 70)(33, 73, 38, 78)(34, 74, 39, 79)(35, 75, 36, 76)(37, 77, 40, 80)(81, 121, 83, 123, 88, 128, 97, 137, 106, 146, 114, 154, 108, 148, 99, 139, 90, 130, 84, 124)(82, 122, 85, 125, 92, 132, 102, 142, 110, 150, 117, 157, 112, 152, 104, 144, 94, 134, 86, 126)(87, 127, 95, 135, 89, 129, 98, 138, 107, 147, 115, 155, 119, 159, 113, 153, 105, 145, 96, 136)(91, 131, 100, 140, 93, 133, 103, 143, 111, 151, 118, 158, 120, 160, 116, 156, 109, 149, 101, 141)
	L = (1, 82)(2, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 94)(9, 84)(10, 92)(11, 85)(12, 90)(13, 86)(14, 88)(15, 100)(16, 103)(17, 105)(18, 101)(19, 107)(20, 95)(21, 98)(22, 109)(23, 96)(24, 111)(25, 97)(26, 112)(27, 99)(28, 110)(29, 102)(30, 108)(31, 104)(32, 106)(33, 118)(34, 119)(35, 116)(36, 115)(37, 120)(38, 113)(39, 114)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.248
Graph:: bipartite
	v = 24 e = 80 f = 50
	degree seq :: [ 4^20, 20^4 ]

E4.248 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 10})
Quotient :: dipole
Aut^+ = (C10 x C2) : C2 (small group id <40, 8>)
Aut   = D8 x D10 (small group id <80, 39>)
|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)^10 ]
Map:: polytopal
	R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 9, 49, 13, 53, 8, 48)(5, 45, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 36, 76, 33, 73)(28, 68, 31, 71, 37, 77, 35, 75)(34, 74, 39, 79, 40, 80, 38, 78)(81, 121)(82, 122)(83, 123)(84, 124)(85, 125)(86, 126)(87, 127)(88, 128)(89, 129)(90, 130)(91, 131)(92, 132)(93, 133)(94, 134)(95, 135)(96, 136)(97, 137)(98, 138)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160)
	L = (1, 83)(2, 87)(3, 90)(4, 91)(5, 81)(6, 93)(7, 95)(8, 82)(9, 84)(10, 98)(11, 99)(12, 85)(13, 101)(14, 86)(15, 103)(16, 88)(17, 89)(18, 106)(19, 107)(20, 92)(21, 109)(22, 94)(23, 111)(24, 96)(25, 97)(26, 114)(27, 115)(28, 100)(29, 116)(30, 102)(31, 118)(32, 104)(33, 105)(34, 108)(35, 119)(36, 120)(37, 110)(38, 112)(39, 113)(40, 117)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160)
	local type(s) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20 ) }
Outer automorphisms :: reflexible
Dual of E4.247
Graph:: simple bipartite
	v = 50 e = 80 f = 24
	degree seq :: [ 2^40, 8^10 ]

E4.249 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 5, 5})
Quotient :: regular
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^5, (T1^2 * T2)^3, (T2 * T1 * T2 * T1^-2)^2, (T1^-1 * T2)^5 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 33, 36, 19)(11, 21, 32, 41, 22)(15, 28, 47, 40, 29)(16, 30, 50, 52, 31)(20, 37, 46, 27, 38)(24, 42, 57, 55, 43)(25, 44, 34, 53, 45)(35, 54, 39, 56, 48)(49, 59, 51, 60, 58)
	L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 32)(18, 34)(19, 35)(21, 39)(22, 40)(23, 36)(26, 46)(28, 48)(29, 49)(30, 51)(31, 42)(33, 41)(37, 50)(38, 55)(43, 58)(44, 59)(45, 56)(47, 52)(53, 57)(54, 60)
	local type(s) :: { ( 5^5 ) }
Outer automorphisms :: reflexible selfdual
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 12 e = 30 f = 12
	degree seq :: [ 5^12 ]

E4.250 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 5, 5})
Quotient :: edge
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, (T1 * T2^2)^3, (T1 * T2^-2)^3, (T2^-1 * T1)^5, (T2 * T1 * T2^-2 * T1)^2, (T2 * T1 * T2^-1 * T1)^3 ]
Map:: polytopal
	R = (1, 3, 8, 10, 4)(2, 5, 12, 14, 6)(7, 15, 28, 30, 16)(9, 18, 34, 36, 19)(11, 21, 40, 42, 22)(13, 24, 45, 47, 25)(17, 31, 26, 48, 32)(20, 37, 43, 23, 38)(27, 46, 60, 55, 49)(29, 50, 33, 53, 51)(35, 54, 52, 56, 39)(41, 57, 44, 59, 58)(61, 62)(63, 67)(64, 69)(65, 71)(66, 73)(68, 77)(70, 80)(72, 83)(74, 86)(75, 87)(76, 89)(78, 93)(79, 95)(81, 99)(82, 101)(84, 104)(85, 106)(88, 96)(90, 103)(91, 112)(92, 102)(94, 108)(97, 105)(98, 115)(100, 107)(109, 118)(110, 117)(111, 116)(113, 120)(114, 119)
	L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(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) :: { ( 10, 10 ), ( 10^5 ) }
Outer automorphisms :: reflexible
Dual of E4.251
Transitivity :: ET+
Graph:: simple bipartite
	v = 42 e = 60 f = 12
	degree seq :: [ 2^30, 5^12 ]

E4.251 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 5, 5})
Quotient :: loop
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^5, (T1 * T2^2)^3, (T1 * T2^-2)^3, (T2^-1 * T1)^5, (T2 * T1 * T2^-2 * T1)^2, (T2 * T1 * T2^-1 * T1)^3 ]
Map::
	R = (1, 61, 3, 63, 8, 68, 10, 70, 4, 64)(2, 62, 5, 65, 12, 72, 14, 74, 6, 66)(7, 67, 15, 75, 28, 88, 30, 90, 16, 76)(9, 69, 18, 78, 34, 94, 36, 96, 19, 79)(11, 71, 21, 81, 40, 100, 42, 102, 22, 82)(13, 73, 24, 84, 45, 105, 47, 107, 25, 85)(17, 77, 31, 91, 26, 86, 48, 108, 32, 92)(20, 80, 37, 97, 43, 103, 23, 83, 38, 98)(27, 87, 46, 106, 60, 120, 55, 115, 49, 109)(29, 89, 50, 110, 33, 93, 53, 113, 51, 111)(35, 95, 54, 114, 52, 112, 56, 116, 39, 99)(41, 101, 57, 117, 44, 104, 59, 119, 58, 118)
	L = (1, 62)(2, 61)(3, 67)(4, 69)(5, 71)(6, 73)(7, 63)(8, 77)(9, 64)(10, 80)(11, 65)(12, 83)(13, 66)(14, 86)(15, 87)(16, 89)(17, 68)(18, 93)(19, 95)(20, 70)(21, 99)(22, 101)(23, 72)(24, 104)(25, 106)(26, 74)(27, 75)(28, 96)(29, 76)(30, 103)(31, 112)(32, 102)(33, 78)(34, 108)(35, 79)(36, 88)(37, 105)(38, 115)(39, 81)(40, 107)(41, 82)(42, 92)(43, 90)(44, 84)(45, 97)(46, 85)(47, 100)(48, 94)(49, 118)(50, 117)(51, 116)(52, 91)(53, 120)(54, 119)(55, 98)(56, 111)(57, 110)(58, 109)(59, 114)(60, 113)
	local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.250
Transitivity :: ET+ VT+ AT
Graph::
	v = 12 e = 60 f = 42
	degree seq :: [ 10^12 ]

E4.252 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5})
Quotient :: dipole
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, (Y2 * Y1 * Y2)^3, (Y1 * Y2^-2)^3, (Y2^2 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^5, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1)^2 ]
Map::
	R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 11, 71)(6, 66, 13, 73)(8, 68, 17, 77)(10, 70, 20, 80)(12, 72, 23, 83)(14, 74, 26, 86)(15, 75, 27, 87)(16, 76, 29, 89)(18, 78, 33, 93)(19, 79, 35, 95)(21, 81, 39, 99)(22, 82, 41, 101)(24, 84, 44, 104)(25, 85, 46, 106)(28, 88, 36, 96)(30, 90, 43, 103)(31, 91, 52, 112)(32, 92, 42, 102)(34, 94, 48, 108)(37, 97, 45, 105)(38, 98, 55, 115)(40, 100, 47, 107)(49, 109, 58, 118)(50, 110, 57, 117)(51, 111, 56, 116)(53, 113, 60, 120)(54, 114, 59, 119)(121, 181, 123, 183, 128, 188, 130, 190, 124, 184)(122, 182, 125, 185, 132, 192, 134, 194, 126, 186)(127, 187, 135, 195, 148, 208, 150, 210, 136, 196)(129, 189, 138, 198, 154, 214, 156, 216, 139, 199)(131, 191, 141, 201, 160, 220, 162, 222, 142, 202)(133, 193, 144, 204, 165, 225, 167, 227, 145, 205)(137, 197, 151, 211, 146, 206, 168, 228, 152, 212)(140, 200, 157, 217, 163, 223, 143, 203, 158, 218)(147, 207, 166, 226, 180, 240, 175, 235, 169, 229)(149, 209, 170, 230, 153, 213, 173, 233, 171, 231)(155, 215, 174, 234, 172, 232, 176, 236, 159, 219)(161, 221, 177, 237, 164, 224, 179, 239, 178, 238)
	L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 137)(9, 124)(10, 140)(11, 125)(12, 143)(13, 126)(14, 146)(15, 147)(16, 149)(17, 128)(18, 153)(19, 155)(20, 130)(21, 159)(22, 161)(23, 132)(24, 164)(25, 166)(26, 134)(27, 135)(28, 156)(29, 136)(30, 163)(31, 172)(32, 162)(33, 138)(34, 168)(35, 139)(36, 148)(37, 165)(38, 175)(39, 141)(40, 167)(41, 142)(42, 152)(43, 150)(44, 144)(45, 157)(46, 145)(47, 160)(48, 154)(49, 178)(50, 177)(51, 176)(52, 151)(53, 180)(54, 179)(55, 158)(56, 171)(57, 170)(58, 169)(59, 174)(60, 173)(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) :: { ( 2, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.253
Graph:: bipartite
	v = 42 e = 120 f = 72
	degree seq :: [ 4^30, 10^12 ]

E4.253 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 5, 5})
Quotient :: dipole
Aut^+ = A5 (small group id <60, 5>)
Aut   = C2 x A5 (small group id <120, 35>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^5, (Y1^2 * Y3)^3, (Y3 * Y1^-1)^5, (Y3 * Y1^2 * Y3 * Y1^-1)^2 ]
Map:: polytopal
	R = (1, 61, 2, 62, 5, 65, 10, 70, 4, 64)(3, 63, 7, 67, 14, 74, 17, 77, 8, 68)(6, 66, 12, 72, 23, 83, 26, 86, 13, 73)(9, 69, 18, 78, 33, 93, 36, 96, 19, 79)(11, 71, 21, 81, 32, 92, 41, 101, 22, 82)(15, 75, 28, 88, 47, 107, 40, 100, 29, 89)(16, 76, 30, 90, 50, 110, 52, 112, 31, 91)(20, 80, 37, 97, 46, 106, 27, 87, 38, 98)(24, 84, 42, 102, 57, 117, 55, 115, 43, 103)(25, 85, 44, 104, 34, 94, 53, 113, 45, 105)(35, 95, 54, 114, 39, 99, 56, 116, 48, 108)(49, 109, 59, 119, 51, 111, 60, 120, 58, 118)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240)
	L = (1, 123)(2, 126)(3, 121)(4, 129)(5, 131)(6, 122)(7, 135)(8, 136)(9, 124)(10, 140)(11, 125)(12, 144)(13, 145)(14, 147)(15, 127)(16, 128)(17, 152)(18, 154)(19, 155)(20, 130)(21, 159)(22, 160)(23, 156)(24, 132)(25, 133)(26, 166)(27, 134)(28, 168)(29, 169)(30, 171)(31, 162)(32, 137)(33, 161)(34, 138)(35, 139)(36, 143)(37, 170)(38, 175)(39, 141)(40, 142)(41, 153)(42, 151)(43, 178)(44, 179)(45, 176)(46, 146)(47, 172)(48, 148)(49, 149)(50, 157)(51, 150)(52, 167)(53, 177)(54, 180)(55, 158)(56, 165)(57, 173)(58, 163)(59, 164)(60, 174)(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, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.252
Graph:: simple bipartite
	v = 72 e = 120 f = 42
	degree seq :: [ 2^60, 10^12 ]

E4.254 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 6})
Quotient :: regular
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, T1^6, (T1^-1 * T2)^4, (T2 * T1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 29, 18, 8)(6, 13, 25, 44, 28, 14)(9, 19, 34, 52, 35, 20)(12, 23, 40, 59, 43, 24)(16, 31, 49, 57, 41, 27)(17, 32, 50, 56, 42, 26)(21, 36, 53, 66, 54, 37)(22, 38, 55, 67, 58, 39)(30, 46, 60, 69, 64, 48)(33, 45, 61, 68, 65, 51)(47, 63, 71, 72, 70, 62)
	L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 30)(18, 33)(19, 32)(20, 31)(23, 41)(24, 42)(25, 45)(28, 46)(29, 47)(34, 51)(35, 48)(36, 49)(37, 50)(38, 56)(39, 57)(40, 60)(43, 61)(44, 62)(52, 63)(53, 64)(54, 65)(55, 68)(58, 69)(59, 70)(66, 71)(67, 72)
	local type(s) :: { ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E4.255
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 12 e = 36 f = 18
	degree seq :: [ 6^12 ]

E4.255 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 6})
Quotient :: regular
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2 * T1^-1 * T2 * T1)^2, (T1^-1 * T2)^6 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 27, 17)(10, 18, 29, 19)(14, 24, 34, 22)(15, 25, 38, 26)(21, 33, 44, 31)(23, 35, 49, 36)(28, 30, 43, 41)(32, 45, 60, 46)(37, 52, 64, 51)(39, 50, 62, 47)(40, 54, 66, 55)(42, 56, 67, 57)(48, 61, 69, 58)(53, 59, 68, 65)(63, 71, 72, 70)
	L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 25)(17, 28)(18, 30)(19, 31)(20, 32)(24, 37)(26, 39)(27, 40)(29, 42)(33, 47)(34, 48)(35, 50)(36, 51)(38, 53)(41, 52)(43, 58)(44, 59)(45, 61)(46, 62)(49, 63)(54, 64)(55, 65)(56, 68)(57, 69)(60, 70)(66, 71)(67, 72)
	local type(s) :: { ( 6^4 ) }
Outer automorphisms :: reflexible
Dual of E4.254
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 18 e = 36 f = 12
	degree seq :: [ 4^18 ]

E4.256 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T1 * T2^-1 * T1 * T2)^2, (T2^-1 * T1)^6 ]
Map:: polytopal
	R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 27, 17)(10, 18, 30, 19)(12, 21, 33, 22)(15, 25, 39, 26)(20, 31, 46, 32)(23, 35, 49, 36)(28, 38, 52, 41)(29, 42, 56, 43)(34, 45, 59, 48)(37, 50, 63, 51)(40, 54, 66, 55)(44, 57, 67, 58)(47, 61, 70, 62)(53, 64, 71, 65)(60, 68, 72, 69)(73, 74)(75, 79)(76, 81)(77, 82)(78, 84)(80, 87)(83, 92)(85, 95)(86, 91)(88, 93)(89, 100)(90, 101)(94, 106)(96, 109)(97, 110)(98, 108)(99, 112)(102, 116)(103, 117)(104, 115)(105, 119)(107, 120)(111, 125)(113, 114)(118, 132)(121, 133)(122, 129)(123, 131)(124, 130)(126, 128)(127, 134)(135, 141)(136, 142)(137, 139)(138, 140)(143, 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) :: { ( 12, 12 ), ( 12^4 ) }
Outer automorphisms :: reflexible
Dual of E4.260
Transitivity :: ET+
Graph:: simple bipartite
	v = 54 e = 72 f = 12
	degree seq :: [ 2^36, 4^18 ]

E4.257 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ F^2, T1^4, (T1 * T2)^2, (F * T2)^2, (F * T1)^2, T1^4, T2^6, T1^-1 * T2^-2 * T1^2 * T2^-2 * T1^-1, T2^2 * T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1 ]
Map:: polyhedral non-degenerate
	R = (1, 3, 10, 24, 14, 5)(2, 7, 17, 37, 20, 8)(4, 12, 27, 44, 22, 9)(6, 15, 32, 54, 35, 16)(11, 26, 48, 56, 34, 23)(13, 29, 33, 55, 52, 30)(18, 39, 60, 43, 21, 36)(19, 40, 28, 50, 63, 41)(25, 47, 66, 71, 65, 45)(31, 46, 61, 70, 62, 53)(38, 59, 49, 67, 51, 57)(42, 58, 68, 72, 69, 64)(73, 74, 78, 76)(75, 81, 93, 83)(77, 85, 90, 79)(80, 91, 105, 87)(82, 95, 107, 97)(84, 88, 106, 100)(86, 103, 104, 101)(89, 108, 94, 110)(92, 114, 99, 112)(96, 117, 132, 118)(98, 115, 137, 121)(102, 123, 133, 111)(109, 129, 124, 130)(113, 134, 140, 127)(116, 136, 120, 131)(119, 126, 125, 135)(122, 128, 141, 138)(139, 143, 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 ), ( 4^6 ) }
Outer automorphisms :: reflexible
Dual of E4.261
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 72 f = 36
	degree seq :: [ 4^18, 6^12 ]

E4.258 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 6})
Quotient :: edge
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ]
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, 33)(19, 32)(20, 31)(23, 41)(24, 42)(25, 45)(28, 46)(29, 47)(34, 51)(35, 48)(36, 49)(37, 50)(38, 56)(39, 57)(40, 60)(43, 61)(44, 62)(52, 63)(53, 64)(54, 65)(55, 68)(58, 69)(59, 70)(66, 71)(67, 72)(73, 74, 77, 83, 82, 76)(75, 79, 87, 101, 90, 80)(78, 85, 97, 116, 100, 86)(81, 91, 106, 124, 107, 92)(84, 95, 112, 131, 115, 96)(88, 103, 121, 129, 113, 99)(89, 104, 122, 128, 114, 98)(93, 108, 125, 138, 126, 109)(94, 110, 127, 139, 130, 111)(102, 118, 132, 141, 136, 120)(105, 117, 133, 140, 137, 123)(119, 135, 143, 144, 142, 134)
	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 ), ( 8^6 ) }
Outer automorphisms :: reflexible
Dual of E4.259
Transitivity :: ET+
Graph:: simple bipartite
	v = 48 e = 72 f = 18
	degree seq :: [ 2^36, 6^12 ]

E4.259 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T1 * T2^-1 * T1 * T2)^2, (T2^-1 * T1)^6 ]
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, 27, 99, 17, 89)(10, 82, 18, 90, 30, 102, 19, 91)(12, 84, 21, 93, 33, 105, 22, 94)(15, 87, 25, 97, 39, 111, 26, 98)(20, 92, 31, 103, 46, 118, 32, 104)(23, 95, 35, 107, 49, 121, 36, 108)(28, 100, 38, 110, 52, 124, 41, 113)(29, 101, 42, 114, 56, 128, 43, 115)(34, 106, 45, 117, 59, 131, 48, 120)(37, 109, 50, 122, 63, 135, 51, 123)(40, 112, 54, 126, 66, 138, 55, 127)(44, 116, 57, 129, 67, 139, 58, 130)(47, 119, 61, 133, 70, 142, 62, 134)(53, 125, 64, 136, 71, 143, 65, 137)(60, 132, 68, 140, 72, 144, 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, 91)(15, 80)(16, 93)(17, 100)(18, 101)(19, 86)(20, 83)(21, 88)(22, 106)(23, 85)(24, 109)(25, 110)(26, 108)(27, 112)(28, 89)(29, 90)(30, 116)(31, 117)(32, 115)(33, 119)(34, 94)(35, 120)(36, 98)(37, 96)(38, 97)(39, 125)(40, 99)(41, 114)(42, 113)(43, 104)(44, 102)(45, 103)(46, 132)(47, 105)(48, 107)(49, 133)(50, 129)(51, 131)(52, 130)(53, 111)(54, 128)(55, 134)(56, 126)(57, 122)(58, 124)(59, 123)(60, 118)(61, 121)(62, 127)(63, 141)(64, 142)(65, 139)(66, 140)(67, 137)(68, 138)(69, 135)(70, 136)(71, 144)(72, 143)
	local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.258
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 18 e = 72 f = 48
	degree seq :: [ 8^18 ]

E4.260 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ F^2, T1^4, (T1 * T2)^2, (F * T2)^2, (F * T1)^2, T1^4, T2^6, T1^-1 * T2^-2 * T1^2 * T2^-2 * T1^-1, T2^2 * T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1 ]
Map::
	R = (1, 73, 3, 75, 10, 82, 24, 96, 14, 86, 5, 77)(2, 74, 7, 79, 17, 89, 37, 109, 20, 92, 8, 80)(4, 76, 12, 84, 27, 99, 44, 116, 22, 94, 9, 81)(6, 78, 15, 87, 32, 104, 54, 126, 35, 107, 16, 88)(11, 83, 26, 98, 48, 120, 56, 128, 34, 106, 23, 95)(13, 85, 29, 101, 33, 105, 55, 127, 52, 124, 30, 102)(18, 90, 39, 111, 60, 132, 43, 115, 21, 93, 36, 108)(19, 91, 40, 112, 28, 100, 50, 122, 63, 135, 41, 113)(25, 97, 47, 119, 66, 138, 71, 143, 65, 137, 45, 117)(31, 103, 46, 118, 61, 133, 70, 142, 62, 134, 53, 125)(38, 110, 59, 131, 49, 121, 67, 139, 51, 123, 57, 129)(42, 114, 58, 130, 68, 140, 72, 144, 69, 141, 64, 136)
	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, 103)(15, 80)(16, 106)(17, 108)(18, 79)(19, 105)(20, 114)(21, 83)(22, 110)(23, 107)(24, 117)(25, 82)(26, 115)(27, 112)(28, 84)(29, 86)(30, 123)(31, 104)(32, 101)(33, 87)(34, 100)(35, 97)(36, 94)(37, 129)(38, 89)(39, 102)(40, 92)(41, 134)(42, 99)(43, 137)(44, 136)(45, 132)(46, 96)(47, 126)(48, 131)(49, 98)(50, 128)(51, 133)(52, 130)(53, 135)(54, 125)(55, 113)(56, 141)(57, 124)(58, 109)(59, 116)(60, 118)(61, 111)(62, 140)(63, 119)(64, 120)(65, 121)(66, 122)(67, 143)(68, 127)(69, 138)(70, 139)(71, 144)(72, 142)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.256
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 12 e = 72 f = 54
	degree seq :: [ 12^12 ]

E4.261 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 6})
Quotient :: loop
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-1)^2, T1^-2 * T2 * T1^-2 * T2 * T1^2 * T2 * T1^2 * T2 ]
Map:: polyhedral 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, 22, 94)(13, 85, 26, 98)(14, 86, 27, 99)(15, 87, 30, 102)(18, 90, 33, 105)(19, 91, 32, 104)(20, 92, 31, 103)(23, 95, 41, 113)(24, 96, 42, 114)(25, 97, 45, 117)(28, 100, 46, 118)(29, 101, 47, 119)(34, 106, 51, 123)(35, 107, 48, 120)(36, 108, 49, 121)(37, 109, 50, 122)(38, 110, 56, 128)(39, 111, 57, 129)(40, 112, 60, 132)(43, 115, 61, 133)(44, 116, 62, 134)(52, 124, 63, 135)(53, 125, 64, 136)(54, 126, 65, 137)(55, 127, 68, 140)(58, 130, 69, 141)(59, 131, 70, 142)(66, 138, 71, 143)(67, 139, 72, 144)
	L = (1, 74)(2, 77)(3, 79)(4, 73)(5, 83)(6, 85)(7, 87)(8, 75)(9, 91)(10, 76)(11, 82)(12, 95)(13, 97)(14, 78)(15, 101)(16, 103)(17, 104)(18, 80)(19, 106)(20, 81)(21, 108)(22, 110)(23, 112)(24, 84)(25, 116)(26, 89)(27, 88)(28, 86)(29, 90)(30, 118)(31, 121)(32, 122)(33, 117)(34, 124)(35, 92)(36, 125)(37, 93)(38, 127)(39, 94)(40, 131)(41, 99)(42, 98)(43, 96)(44, 100)(45, 133)(46, 132)(47, 135)(48, 102)(49, 129)(50, 128)(51, 105)(52, 107)(53, 138)(54, 109)(55, 139)(56, 114)(57, 113)(58, 111)(59, 115)(60, 141)(61, 140)(62, 119)(63, 143)(64, 120)(65, 123)(66, 126)(67, 130)(68, 137)(69, 136)(70, 134)(71, 144)(72, 142)
	local type(s) :: { ( 4, 6, 4, 6 ) }
Outer automorphisms :: reflexible
Dual of E4.257
Transitivity :: ET+ VT+ AT
Graph:: simple bipartite
	v = 36 e = 72 f = 30
	degree seq :: [ 4^36 ]

E4.262 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1 * Y1 * Y2)^2, (Y3 * Y2^-1)^6 ]
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, 19, 91)(16, 88, 21, 93)(17, 89, 28, 100)(18, 90, 29, 101)(22, 94, 34, 106)(24, 96, 37, 109)(25, 97, 38, 110)(26, 98, 36, 108)(27, 99, 40, 112)(30, 102, 44, 116)(31, 103, 45, 117)(32, 104, 43, 115)(33, 105, 47, 119)(35, 107, 48, 120)(39, 111, 53, 125)(41, 113, 42, 114)(46, 118, 60, 132)(49, 121, 61, 133)(50, 122, 57, 129)(51, 123, 59, 131)(52, 124, 58, 130)(54, 126, 56, 128)(55, 127, 62, 134)(63, 135, 69, 141)(64, 136, 70, 142)(65, 137, 67, 139)(66, 138, 68, 140)(71, 143, 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, 171, 243, 161, 233)(154, 226, 162, 234, 174, 246, 163, 235)(156, 228, 165, 237, 177, 249, 166, 238)(159, 231, 169, 241, 183, 255, 170, 242)(164, 236, 175, 247, 190, 262, 176, 248)(167, 239, 179, 251, 193, 265, 180, 252)(172, 244, 182, 254, 196, 268, 185, 257)(173, 245, 186, 258, 200, 272, 187, 259)(178, 250, 189, 261, 203, 275, 192, 264)(181, 253, 194, 266, 207, 279, 195, 267)(184, 256, 198, 270, 210, 282, 199, 271)(188, 260, 201, 273, 211, 283, 202, 274)(191, 263, 205, 277, 214, 286, 206, 278)(197, 269, 208, 280, 215, 287, 209, 281)(204, 276, 212, 284, 216, 288, 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, 163)(15, 152)(16, 165)(17, 172)(18, 173)(19, 158)(20, 155)(21, 160)(22, 178)(23, 157)(24, 181)(25, 182)(26, 180)(27, 184)(28, 161)(29, 162)(30, 188)(31, 189)(32, 187)(33, 191)(34, 166)(35, 192)(36, 170)(37, 168)(38, 169)(39, 197)(40, 171)(41, 186)(42, 185)(43, 176)(44, 174)(45, 175)(46, 204)(47, 177)(48, 179)(49, 205)(50, 201)(51, 203)(52, 202)(53, 183)(54, 200)(55, 206)(56, 198)(57, 194)(58, 196)(59, 195)(60, 190)(61, 193)(62, 199)(63, 213)(64, 214)(65, 211)(66, 212)(67, 209)(68, 210)(69, 207)(70, 208)(71, 216)(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, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.265
Graph:: bipartite
	v = 54 e = 144 f = 84
	degree seq :: [ 4^36, 8^18 ]

E4.263 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2 * Y1)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2^6, Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^2 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, (Y2^2 * Y1^-1 * Y2 * Y1^-1)^2 ]
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, 33, 105, 15, 87)(10, 82, 23, 95, 35, 107, 25, 97)(12, 84, 16, 88, 34, 106, 28, 100)(14, 86, 31, 103, 32, 104, 29, 101)(17, 89, 36, 108, 22, 94, 38, 110)(20, 92, 42, 114, 27, 99, 40, 112)(24, 96, 45, 117, 60, 132, 46, 118)(26, 98, 43, 115, 65, 137, 49, 121)(30, 102, 51, 123, 61, 133, 39, 111)(37, 109, 57, 129, 52, 124, 58, 130)(41, 113, 62, 134, 68, 140, 55, 127)(44, 116, 64, 136, 48, 120, 59, 131)(47, 119, 54, 126, 53, 125, 63, 135)(50, 122, 56, 128, 69, 141, 66, 138)(67, 139, 71, 143, 72, 144, 70, 142)(145, 217, 147, 219, 154, 226, 168, 240, 158, 230, 149, 221)(146, 218, 151, 223, 161, 233, 181, 253, 164, 236, 152, 224)(148, 220, 156, 228, 171, 243, 188, 260, 166, 238, 153, 225)(150, 222, 159, 231, 176, 248, 198, 270, 179, 251, 160, 232)(155, 227, 170, 242, 192, 264, 200, 272, 178, 250, 167, 239)(157, 229, 173, 245, 177, 249, 199, 271, 196, 268, 174, 246)(162, 234, 183, 255, 204, 276, 187, 259, 165, 237, 180, 252)(163, 235, 184, 256, 172, 244, 194, 266, 207, 279, 185, 257)(169, 241, 191, 263, 210, 282, 215, 287, 209, 281, 189, 261)(175, 247, 190, 262, 205, 277, 214, 286, 206, 278, 197, 269)(182, 254, 203, 275, 193, 265, 211, 283, 195, 267, 201, 273)(186, 258, 202, 274, 212, 284, 216, 288, 213, 285, 208, 280)
	L = (1, 147)(2, 151)(3, 154)(4, 156)(5, 145)(6, 159)(7, 161)(8, 146)(9, 148)(10, 168)(11, 170)(12, 171)(13, 173)(14, 149)(15, 176)(16, 150)(17, 181)(18, 183)(19, 184)(20, 152)(21, 180)(22, 153)(23, 155)(24, 158)(25, 191)(26, 192)(27, 188)(28, 194)(29, 177)(30, 157)(31, 190)(32, 198)(33, 199)(34, 167)(35, 160)(36, 162)(37, 164)(38, 203)(39, 204)(40, 172)(41, 163)(42, 202)(43, 165)(44, 166)(45, 169)(46, 205)(47, 210)(48, 200)(49, 211)(50, 207)(51, 201)(52, 174)(53, 175)(54, 179)(55, 196)(56, 178)(57, 182)(58, 212)(59, 193)(60, 187)(61, 214)(62, 197)(63, 185)(64, 186)(65, 189)(66, 215)(67, 195)(68, 216)(69, 208)(70, 206)(71, 209)(72, 213)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.264
Graph:: bipartite
	v = 30 e = 144 f = 108
	degree seq :: [ 8^18, 12^12 ]

E4.264 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3 * Y2 * Y3^-1 * Y2)^2, (Y3^-1 * Y1^-1)^6, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2 ]
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, 168, 240)(158, 230, 172, 244)(159, 231, 171, 243)(160, 232, 167, 239)(162, 234, 177, 249)(163, 235, 170, 242)(164, 236, 166, 238)(169, 241, 186, 258)(173, 245, 189, 261)(174, 246, 184, 256)(175, 247, 183, 255)(176, 248, 188, 260)(178, 250, 190, 262)(179, 251, 185, 257)(180, 252, 182, 254)(181, 253, 187, 259)(191, 263, 203, 275)(192, 264, 200, 272)(193, 265, 205, 277)(194, 266, 204, 276)(195, 267, 199, 271)(196, 268, 202, 274)(197, 269, 201, 273)(198, 270, 206, 278)(207, 279, 213, 285)(208, 280, 214, 286)(209, 281, 211, 283)(210, 282, 212, 284)(215, 287, 216, 288)
	L = (1, 147)(2, 149)(3, 152)(4, 145)(5, 156)(6, 146)(7, 159)(8, 162)(9, 163)(10, 148)(11, 166)(12, 169)(13, 170)(14, 150)(15, 173)(16, 151)(17, 175)(18, 154)(19, 178)(20, 153)(21, 180)(22, 182)(23, 155)(24, 184)(25, 158)(26, 187)(27, 157)(28, 189)(29, 191)(30, 160)(31, 192)(32, 161)(33, 194)(34, 196)(35, 164)(36, 197)(37, 165)(38, 199)(39, 167)(40, 200)(41, 168)(42, 202)(43, 204)(44, 171)(45, 205)(46, 172)(47, 174)(48, 207)(49, 176)(50, 208)(51, 177)(52, 179)(53, 210)(54, 181)(55, 183)(56, 211)(57, 185)(58, 212)(59, 186)(60, 188)(61, 214)(62, 190)(63, 193)(64, 215)(65, 195)(66, 198)(67, 201)(68, 216)(69, 203)(70, 206)(71, 209)(72, 213)(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, 12 ), ( 8, 12, 8, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.263
Graph:: simple bipartite
	v = 108 e = 144 f = 30
	degree seq :: [ 2^72, 4^36 ]

E4.265 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y1^6, (Y3^-1 * Y1 * Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1 * Y3^-1 * Y1^-1)^2, Y1^-2 * Y3 * Y1^-2 * Y3 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1 ]
Map:: polytopal
	R = (1, 73, 2, 74, 5, 77, 11, 83, 10, 82, 4, 76)(3, 75, 7, 79, 15, 87, 29, 101, 18, 90, 8, 80)(6, 78, 13, 85, 25, 97, 44, 116, 28, 100, 14, 86)(9, 81, 19, 91, 34, 106, 52, 124, 35, 107, 20, 92)(12, 84, 23, 95, 40, 112, 59, 131, 43, 115, 24, 96)(16, 88, 31, 103, 49, 121, 57, 129, 41, 113, 27, 99)(17, 89, 32, 104, 50, 122, 56, 128, 42, 114, 26, 98)(21, 93, 36, 108, 53, 125, 66, 138, 54, 126, 37, 109)(22, 94, 38, 110, 55, 127, 67, 139, 58, 130, 39, 111)(30, 102, 46, 118, 60, 132, 69, 141, 64, 136, 48, 120)(33, 105, 45, 117, 61, 133, 68, 140, 65, 137, 51, 123)(47, 119, 63, 135, 71, 143, 72, 144, 70, 142, 62, 134)(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, 166)(12, 149)(13, 170)(14, 171)(15, 174)(16, 151)(17, 152)(18, 177)(19, 176)(20, 175)(21, 154)(22, 155)(23, 185)(24, 186)(25, 189)(26, 157)(27, 158)(28, 190)(29, 191)(30, 159)(31, 164)(32, 163)(33, 162)(34, 195)(35, 192)(36, 193)(37, 194)(38, 200)(39, 201)(40, 204)(41, 167)(42, 168)(43, 205)(44, 206)(45, 169)(46, 172)(47, 173)(48, 179)(49, 180)(50, 181)(51, 178)(52, 207)(53, 208)(54, 209)(55, 212)(56, 182)(57, 183)(58, 213)(59, 214)(60, 184)(61, 187)(62, 188)(63, 196)(64, 197)(65, 198)(66, 215)(67, 216)(68, 199)(69, 202)(70, 203)(71, 210)(72, 211)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.262
Graph:: simple bipartite
	v = 84 e = 144 f = 54
	degree seq :: [ 2^72, 12^12 ]

E4.266 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y2 * Y1)^4, (Y2 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^4, Y2^2 * Y1 * Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 ]
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, 24, 96)(14, 86, 28, 100)(15, 87, 27, 99)(16, 88, 23, 95)(18, 90, 33, 105)(19, 91, 26, 98)(20, 92, 22, 94)(25, 97, 42, 114)(29, 101, 45, 117)(30, 102, 40, 112)(31, 103, 39, 111)(32, 104, 44, 116)(34, 106, 46, 118)(35, 107, 41, 113)(36, 108, 38, 110)(37, 109, 43, 115)(47, 119, 59, 131)(48, 120, 56, 128)(49, 121, 61, 133)(50, 122, 60, 132)(51, 123, 55, 127)(52, 124, 58, 130)(53, 125, 57, 129)(54, 126, 62, 134)(63, 135, 69, 141)(64, 136, 70, 142)(65, 137, 67, 139)(66, 138, 68, 140)(71, 143, 72, 144)(145, 217, 147, 219, 152, 224, 162, 234, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 169, 241, 158, 230, 150, 222)(151, 223, 159, 231, 173, 245, 191, 263, 174, 246, 160, 232)(153, 225, 163, 235, 178, 250, 196, 268, 179, 251, 164, 236)(155, 227, 166, 238, 182, 254, 199, 271, 183, 255, 167, 239)(157, 229, 170, 242, 187, 259, 204, 276, 188, 260, 171, 243)(161, 233, 175, 247, 192, 264, 207, 279, 193, 265, 176, 248)(165, 237, 180, 252, 197, 269, 210, 282, 198, 270, 181, 253)(168, 240, 184, 256, 200, 272, 211, 283, 201, 273, 185, 257)(172, 244, 189, 261, 205, 277, 214, 286, 206, 278, 190, 262)(177, 249, 194, 266, 208, 280, 215, 287, 209, 281, 195, 267)(186, 258, 202, 274, 212, 284, 216, 288, 213, 285, 203, 275)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 161)(9, 148)(10, 165)(11, 149)(12, 168)(13, 150)(14, 172)(15, 171)(16, 167)(17, 152)(18, 177)(19, 170)(20, 166)(21, 154)(22, 164)(23, 160)(24, 156)(25, 186)(26, 163)(27, 159)(28, 158)(29, 189)(30, 184)(31, 183)(32, 188)(33, 162)(34, 190)(35, 185)(36, 182)(37, 187)(38, 180)(39, 175)(40, 174)(41, 179)(42, 169)(43, 181)(44, 176)(45, 173)(46, 178)(47, 203)(48, 200)(49, 205)(50, 204)(51, 199)(52, 202)(53, 201)(54, 206)(55, 195)(56, 192)(57, 197)(58, 196)(59, 191)(60, 194)(61, 193)(62, 198)(63, 213)(64, 214)(65, 211)(66, 212)(67, 209)(68, 210)(69, 207)(70, 208)(71, 216)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) }
Outer automorphisms :: reflexible
Dual of E4.267
Graph:: bipartite
	v = 48 e = 144 f = 90
	degree seq :: [ 4^36, 12^12 ]

E4.267 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 6})
Quotient :: dipole
Aut^+ = (S3 x S3) : C2 (small group id <72, 40>)
Aut   = C2 x ((S3 x S3) : C2) (small group id <144, 186>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y1^2 * Y3^-2 * Y1^-1, Y3^2 * Y1^-1 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^6 ]
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, 33, 105, 15, 87)(10, 82, 23, 95, 35, 107, 25, 97)(12, 84, 16, 88, 34, 106, 28, 100)(14, 86, 31, 103, 32, 104, 29, 101)(17, 89, 36, 108, 22, 94, 38, 110)(20, 92, 42, 114, 27, 99, 40, 112)(24, 96, 45, 117, 60, 132, 46, 118)(26, 98, 43, 115, 65, 137, 49, 121)(30, 102, 51, 123, 61, 133, 39, 111)(37, 109, 57, 129, 52, 124, 58, 130)(41, 113, 62, 134, 68, 140, 55, 127)(44, 116, 64, 136, 48, 120, 59, 131)(47, 119, 54, 126, 53, 125, 63, 135)(50, 122, 56, 128, 69, 141, 66, 138)(67, 139, 71, 143, 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, 170)(12, 171)(13, 173)(14, 149)(15, 176)(16, 150)(17, 181)(18, 183)(19, 184)(20, 152)(21, 180)(22, 153)(23, 155)(24, 158)(25, 191)(26, 192)(27, 188)(28, 194)(29, 177)(30, 157)(31, 190)(32, 198)(33, 199)(34, 167)(35, 160)(36, 162)(37, 164)(38, 203)(39, 204)(40, 172)(41, 163)(42, 202)(43, 165)(44, 166)(45, 169)(46, 205)(47, 210)(48, 200)(49, 211)(50, 207)(51, 201)(52, 174)(53, 175)(54, 179)(55, 196)(56, 178)(57, 182)(58, 212)(59, 193)(60, 187)(61, 214)(62, 197)(63, 185)(64, 186)(65, 189)(66, 215)(67, 195)(68, 216)(69, 208)(70, 206)(71, 209)(72, 213)(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, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.266
Graph:: simple bipartite
	v = 90 e = 144 f = 48
	degree seq :: [ 2^72, 8^18 ]

E4.268 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 3, 12})
Quotient :: regular
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T2)^2, (F * T1)^2, (T1^-1 * T2)^3, T1^-2 * T2 * T1^4 * T2 * T1^-2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, T1^12 ]
Map:: polytopal non-degenerate
	R = (1, 2, 5, 11, 21, 37, 58, 57, 36, 20, 10, 4)(3, 7, 15, 27, 38, 60, 72, 68, 53, 31, 17, 8)(6, 13, 25, 43, 59, 47, 69, 56, 35, 46, 26, 14)(9, 18, 32, 40, 22, 39, 61, 52, 70, 50, 29, 16)(12, 23, 41, 62, 71, 65, 55, 33, 19, 34, 42, 24)(28, 48, 63, 45, 67, 54, 66, 44, 30, 51, 64, 49)
	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, 47)(29, 48)(31, 52)(32, 54)(34, 56)(36, 53)(37, 59)(40, 60)(41, 63)(42, 64)(43, 65)(46, 68)(49, 69)(50, 62)(51, 61)(55, 66)(57, 70)(58, 71)(67, 72)
	local type(s) :: { ( 3^12 ) }
Outer automorphisms :: reflexible
Dual of E4.269
Transitivity :: ET+ VT+ AT+ REG+
Graph::
	v = 6 e = 36 f = 24
	degree seq :: [ 12^6 ]

E4.269 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 3, 12})
Quotient :: regular
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1 * T2 * T1^-1)^3, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ]
Map:: polytopal 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, 64, 69)(55, 58, 66)(56, 70, 71)(57, 65, 67)(59, 68, 72)
	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, 69)(61, 70)(62, 71)(63, 72)
	local type(s) :: { ( 12^3 ) }
Outer automorphisms :: reflexible
Dual of E4.268
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 24 e = 36 f = 6
	degree seq :: [ 3^24 ]

E4.270 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1 * T2^-1 * T1)^3, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
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, 74)(75, 79)(76, 80)(77, 81)(78, 82)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(89, 97)(90, 98)(99, 115)(100, 116)(101, 109)(102, 117)(103, 118)(104, 112)(105, 119)(106, 120)(107, 121)(108, 122)(110, 123)(111, 124)(113, 125)(114, 126)(127, 136)(128, 141)(129, 138)(130, 142)(131, 143)(132, 137)(133, 139)(134, 140)(135, 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) :: { ( 24, 24 ), ( 24^3 ) }
Outer automorphisms :: reflexible
Dual of E4.274
Transitivity :: ET+
Graph:: simple bipartite
	v = 60 e = 72 f = 6
	degree seq :: [ 2^36, 3^24 ]

E4.271 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^3, T1^-1 * T2^3 * T1^-1 * T2^-5, T1^-1 * T2 * T1 * T2^-2 * T1 * T2^5 ]
Map:: polytopal non-degenerate
	R = (1, 3, 9, 19, 37, 63, 72, 56, 48, 26, 13, 5)(2, 6, 14, 27, 50, 38, 65, 59, 57, 32, 16, 7)(4, 11, 22, 41, 64, 51, 69, 47, 60, 34, 17, 8)(10, 21, 40, 66, 67, 42, 46, 25, 45, 61, 35, 18)(12, 23, 43, 62, 36, 20, 39, 31, 55, 68, 44, 24)(15, 29, 53, 70, 49, 28, 52, 33, 58, 71, 54, 30)(73, 74, 76)(75, 80, 82)(77, 84, 78)(79, 87, 83)(81, 90, 92)(85, 97, 95)(86, 96, 100)(88, 103, 101)(89, 105, 93)(91, 108, 110)(94, 102, 114)(98, 119, 117)(99, 121, 123)(104, 128, 127)(106, 131, 130)(107, 125, 111)(109, 122, 136)(112, 124, 116)(113, 139, 135)(115, 118, 126)(120, 129, 132)(133, 141, 142)(134, 143, 137)(138, 140, 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) :: { ( 4^3 ), ( 4^12 ) }
Outer automorphisms :: reflexible
Dual of E4.275
Transitivity :: ET+
Graph:: simple bipartite
	v = 30 e = 72 f = 36
	degree seq :: [ 3^24, 12^6 ]

E4.272 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 3, 12})
Quotient :: edge
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^4 * T2 * T1^-2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, T1^12 ]
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, 47)(29, 48)(31, 52)(32, 54)(34, 56)(36, 53)(37, 59)(40, 60)(41, 63)(42, 64)(43, 65)(46, 68)(49, 69)(50, 62)(51, 61)(55, 66)(57, 70)(58, 71)(67, 72)(73, 74, 77, 83, 93, 109, 130, 129, 108, 92, 82, 76)(75, 79, 87, 99, 110, 132, 144, 140, 125, 103, 89, 80)(78, 85, 97, 115, 131, 119, 141, 128, 107, 118, 98, 86)(81, 90, 104, 112, 94, 111, 133, 124, 142, 122, 101, 88)(84, 95, 113, 134, 143, 137, 127, 105, 91, 106, 114, 96)(100, 120, 135, 117, 139, 126, 138, 116, 102, 123, 136, 121)
	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) :: { ( 6, 6 ), ( 6^12 ) }
Outer automorphisms :: reflexible
Dual of E4.273
Transitivity :: ET+
Graph:: simple bipartite
	v = 42 e = 72 f = 24
	degree seq :: [ 2^36, 12^6 ]

E4.273 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1 * T2^-1 * T1)^3, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ]
Map::
	R = (1, 73, 3, 75, 4, 76)(2, 74, 5, 77, 6, 78)(7, 79, 11, 83, 12, 84)(8, 80, 13, 85, 14, 86)(9, 81, 15, 87, 16, 88)(10, 82, 17, 89, 18, 90)(19, 91, 27, 99, 28, 100)(20, 92, 29, 101, 30, 102)(21, 93, 31, 103, 32, 104)(22, 94, 33, 105, 34, 106)(23, 95, 35, 107, 36, 108)(24, 96, 37, 109, 38, 110)(25, 97, 39, 111, 40, 112)(26, 98, 41, 113, 42, 114)(43, 115, 55, 127, 56, 128)(44, 116, 47, 119, 57, 129)(45, 117, 58, 130, 59, 131)(46, 118, 60, 132, 61, 133)(48, 120, 62, 134, 63, 135)(49, 121, 64, 136, 65, 137)(50, 122, 53, 125, 66, 138)(51, 123, 67, 139, 68, 140)(52, 124, 69, 141, 70, 142)(54, 126, 71, 143, 72, 144)
	L = (1, 74)(2, 73)(3, 79)(4, 80)(5, 81)(6, 82)(7, 75)(8, 76)(9, 77)(10, 78)(11, 91)(12, 92)(13, 93)(14, 94)(15, 95)(16, 96)(17, 97)(18, 98)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 115)(28, 116)(29, 109)(30, 117)(31, 118)(32, 112)(33, 119)(34, 120)(35, 121)(36, 122)(37, 101)(38, 123)(39, 124)(40, 104)(41, 125)(42, 126)(43, 99)(44, 100)(45, 102)(46, 103)(47, 105)(48, 106)(49, 107)(50, 108)(51, 110)(52, 111)(53, 113)(54, 114)(55, 136)(56, 141)(57, 138)(58, 142)(59, 143)(60, 137)(61, 139)(62, 140)(63, 144)(64, 127)(65, 132)(66, 129)(67, 133)(68, 134)(69, 128)(70, 130)(71, 131)(72, 135)
	local type(s) :: { ( 2, 12, 2, 12, 2, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.272
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 72 f = 42
	degree seq :: [ 6^24 ]

E4.274 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^3, T1^-1 * T2^3 * T1^-1 * T2^-5, T1^-1 * T2 * T1 * T2^-2 * T1 * T2^5 ]
Map::
	R = (1, 73, 3, 75, 9, 81, 19, 91, 37, 109, 63, 135, 72, 144, 56, 128, 48, 120, 26, 98, 13, 85, 5, 77)(2, 74, 6, 78, 14, 86, 27, 99, 50, 122, 38, 110, 65, 137, 59, 131, 57, 129, 32, 104, 16, 88, 7, 79)(4, 76, 11, 83, 22, 94, 41, 113, 64, 136, 51, 123, 69, 141, 47, 119, 60, 132, 34, 106, 17, 89, 8, 80)(10, 82, 21, 93, 40, 112, 66, 138, 67, 139, 42, 114, 46, 118, 25, 97, 45, 117, 61, 133, 35, 107, 18, 90)(12, 84, 23, 95, 43, 115, 62, 134, 36, 108, 20, 92, 39, 111, 31, 103, 55, 127, 68, 140, 44, 116, 24, 96)(15, 87, 29, 101, 53, 125, 70, 142, 49, 121, 28, 100, 52, 124, 33, 105, 58, 130, 71, 143, 54, 126, 30, 102)
	L = (1, 74)(2, 76)(3, 80)(4, 73)(5, 84)(6, 77)(7, 87)(8, 82)(9, 90)(10, 75)(11, 79)(12, 78)(13, 97)(14, 96)(15, 83)(16, 103)(17, 105)(18, 92)(19, 108)(20, 81)(21, 89)(22, 102)(23, 85)(24, 100)(25, 95)(26, 119)(27, 121)(28, 86)(29, 88)(30, 114)(31, 101)(32, 128)(33, 93)(34, 131)(35, 125)(36, 110)(37, 122)(38, 91)(39, 107)(40, 124)(41, 139)(42, 94)(43, 118)(44, 112)(45, 98)(46, 126)(47, 117)(48, 129)(49, 123)(50, 136)(51, 99)(52, 116)(53, 111)(54, 115)(55, 104)(56, 127)(57, 132)(58, 106)(59, 130)(60, 120)(61, 141)(62, 143)(63, 113)(64, 109)(65, 134)(66, 140)(67, 135)(68, 144)(69, 142)(70, 133)(71, 137)(72, 138)
	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 ) }
Outer automorphisms :: reflexible
Dual of E4.270
Transitivity :: ET+ VT+ AT
Graph::
	v = 6 e = 72 f = 60
	degree seq :: [ 24^6 ]

E4.275 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 3, 12})
Quotient :: loop
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^4 * T2 * T1^-2, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, T1^12 ]
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, 13, 85)(10, 82, 19, 91)(11, 83, 22, 94)(14, 86, 23, 95)(15, 87, 28, 100)(17, 89, 30, 102)(18, 90, 33, 105)(20, 92, 35, 107)(21, 93, 38, 110)(24, 96, 39, 111)(25, 97, 44, 116)(26, 98, 45, 117)(27, 99, 47, 119)(29, 101, 48, 120)(31, 103, 52, 124)(32, 104, 54, 126)(34, 106, 56, 128)(36, 108, 53, 125)(37, 109, 59, 131)(40, 112, 60, 132)(41, 113, 63, 135)(42, 114, 64, 136)(43, 115, 65, 137)(46, 118, 68, 140)(49, 121, 69, 141)(50, 122, 62, 134)(51, 123, 61, 133)(55, 127, 66, 138)(57, 129, 70, 142)(58, 130, 71, 143)(67, 139, 72, 144)
	L = (1, 74)(2, 77)(3, 79)(4, 73)(5, 83)(6, 85)(7, 87)(8, 75)(9, 90)(10, 76)(11, 93)(12, 95)(13, 97)(14, 78)(15, 99)(16, 81)(17, 80)(18, 104)(19, 106)(20, 82)(21, 109)(22, 111)(23, 113)(24, 84)(25, 115)(26, 86)(27, 110)(28, 120)(29, 88)(30, 123)(31, 89)(32, 112)(33, 91)(34, 114)(35, 118)(36, 92)(37, 130)(38, 132)(39, 133)(40, 94)(41, 134)(42, 96)(43, 131)(44, 102)(45, 139)(46, 98)(47, 141)(48, 135)(49, 100)(50, 101)(51, 136)(52, 142)(53, 103)(54, 138)(55, 105)(56, 107)(57, 108)(58, 129)(59, 119)(60, 144)(61, 124)(62, 143)(63, 117)(64, 121)(65, 127)(66, 116)(67, 126)(68, 125)(69, 128)(70, 122)(71, 137)(72, 140)
	local type(s) :: { ( 3, 12, 3, 12 ) }
Outer automorphisms :: reflexible
Dual of E4.271
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 36 e = 72 f = 30
	degree seq :: [ 4^36 ]

E4.276 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|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, (Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^12 ]
Map::
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 8, 80)(5, 77, 9, 81)(6, 78, 10, 82)(11, 83, 19, 91)(12, 84, 20, 92)(13, 85, 21, 93)(14, 86, 22, 94)(15, 87, 23, 95)(16, 88, 24, 96)(17, 89, 25, 97)(18, 90, 26, 98)(27, 99, 43, 115)(28, 100, 44, 116)(29, 101, 37, 109)(30, 102, 45, 117)(31, 103, 46, 118)(32, 104, 40, 112)(33, 105, 47, 119)(34, 106, 48, 120)(35, 107, 49, 121)(36, 108, 50, 122)(38, 110, 51, 123)(39, 111, 52, 124)(41, 113, 53, 125)(42, 114, 54, 126)(55, 127, 64, 136)(56, 128, 69, 141)(57, 129, 66, 138)(58, 130, 70, 142)(59, 131, 71, 143)(60, 132, 65, 137)(61, 133, 67, 139)(62, 134, 68, 140)(63, 135, 72, 144)(145, 217, 147, 219, 148, 220)(146, 218, 149, 221, 150, 222)(151, 223, 155, 227, 156, 228)(152, 224, 157, 229, 158, 230)(153, 225, 159, 231, 160, 232)(154, 226, 161, 233, 162, 234)(163, 235, 171, 243, 172, 244)(164, 236, 173, 245, 174, 246)(165, 237, 175, 247, 176, 248)(166, 238, 177, 249, 178, 250)(167, 239, 179, 251, 180, 252)(168, 240, 181, 253, 182, 254)(169, 241, 183, 255, 184, 256)(170, 242, 185, 257, 186, 258)(187, 259, 199, 271, 200, 272)(188, 260, 191, 263, 201, 273)(189, 261, 202, 274, 203, 275)(190, 262, 204, 276, 205, 277)(192, 264, 206, 278, 207, 279)(193, 265, 208, 280, 209, 281)(194, 266, 197, 269, 210, 282)(195, 267, 211, 283, 212, 284)(196, 268, 213, 285, 214, 286)(198, 270, 215, 287, 216, 288)
	L = (1, 146)(2, 145)(3, 151)(4, 152)(5, 153)(6, 154)(7, 147)(8, 148)(9, 149)(10, 150)(11, 163)(12, 164)(13, 165)(14, 166)(15, 167)(16, 168)(17, 169)(18, 170)(19, 155)(20, 156)(21, 157)(22, 158)(23, 159)(24, 160)(25, 161)(26, 162)(27, 187)(28, 188)(29, 181)(30, 189)(31, 190)(32, 184)(33, 191)(34, 192)(35, 193)(36, 194)(37, 173)(38, 195)(39, 196)(40, 176)(41, 197)(42, 198)(43, 171)(44, 172)(45, 174)(46, 175)(47, 177)(48, 178)(49, 179)(50, 180)(51, 182)(52, 183)(53, 185)(54, 186)(55, 208)(56, 213)(57, 210)(58, 214)(59, 215)(60, 209)(61, 211)(62, 212)(63, 216)(64, 199)(65, 204)(66, 201)(67, 205)(68, 206)(69, 200)(70, 202)(71, 203)(72, 207)(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, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.279
Graph:: bipartite
	v = 60 e = 144 f = 78
	degree seq :: [ 4^36, 6^24 ]

E4.277 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y2^-2)^3, Y2^-2 * Y1^-1 * Y2^3 * Y1^-1 * Y2^-3, Y1^-1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^5 ]
Map::
	R = (1, 73, 2, 74, 4, 76)(3, 75, 8, 80, 10, 82)(5, 77, 12, 84, 6, 78)(7, 79, 15, 87, 11, 83)(9, 81, 18, 90, 20, 92)(13, 85, 25, 97, 23, 95)(14, 86, 24, 96, 28, 100)(16, 88, 31, 103, 29, 101)(17, 89, 33, 105, 21, 93)(19, 91, 36, 108, 38, 110)(22, 94, 30, 102, 42, 114)(26, 98, 47, 119, 45, 117)(27, 99, 49, 121, 51, 123)(32, 104, 56, 128, 55, 127)(34, 106, 59, 131, 58, 130)(35, 107, 53, 125, 39, 111)(37, 109, 50, 122, 64, 136)(40, 112, 52, 124, 44, 116)(41, 113, 67, 139, 63, 135)(43, 115, 46, 118, 54, 126)(48, 120, 57, 129, 60, 132)(61, 133, 69, 141, 70, 142)(62, 134, 71, 143, 65, 137)(66, 138, 68, 140, 72, 144)(145, 217, 147, 219, 153, 225, 163, 235, 181, 253, 207, 279, 216, 288, 200, 272, 192, 264, 170, 242, 157, 229, 149, 221)(146, 218, 150, 222, 158, 230, 171, 243, 194, 266, 182, 254, 209, 281, 203, 275, 201, 273, 176, 248, 160, 232, 151, 223)(148, 220, 155, 227, 166, 238, 185, 257, 208, 280, 195, 267, 213, 285, 191, 263, 204, 276, 178, 250, 161, 233, 152, 224)(154, 226, 165, 237, 184, 256, 210, 282, 211, 283, 186, 258, 190, 262, 169, 241, 189, 261, 205, 277, 179, 251, 162, 234)(156, 228, 167, 239, 187, 259, 206, 278, 180, 252, 164, 236, 183, 255, 175, 247, 199, 271, 212, 284, 188, 260, 168, 240)(159, 231, 173, 245, 197, 269, 214, 286, 193, 265, 172, 244, 196, 268, 177, 249, 202, 274, 215, 287, 198, 270, 174, 246)
	L = (1, 147)(2, 150)(3, 153)(4, 155)(5, 145)(6, 158)(7, 146)(8, 148)(9, 163)(10, 165)(11, 166)(12, 167)(13, 149)(14, 171)(15, 173)(16, 151)(17, 152)(18, 154)(19, 181)(20, 183)(21, 184)(22, 185)(23, 187)(24, 156)(25, 189)(26, 157)(27, 194)(28, 196)(29, 197)(30, 159)(31, 199)(32, 160)(33, 202)(34, 161)(35, 162)(36, 164)(37, 207)(38, 209)(39, 175)(40, 210)(41, 208)(42, 190)(43, 206)(44, 168)(45, 205)(46, 169)(47, 204)(48, 170)(49, 172)(50, 182)(51, 213)(52, 177)(53, 214)(54, 174)(55, 212)(56, 192)(57, 176)(58, 215)(59, 201)(60, 178)(61, 179)(62, 180)(63, 216)(64, 195)(65, 203)(66, 211)(67, 186)(68, 188)(69, 191)(70, 193)(71, 198)(72, 200)(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, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.278
Graph:: bipartite
	v = 30 e = 144 f = 108
	degree seq :: [ 6^24, 24^6 ]

E4.278 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^-1 * Y2 * Y3^4 * Y2 * Y3^-3, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^12 ]
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, 160, 232)(154, 226, 163, 235)(156, 228, 166, 238)(158, 230, 169, 241)(159, 231, 171, 243)(161, 233, 174, 246)(162, 234, 176, 248)(164, 236, 179, 251)(165, 237, 181, 253)(167, 239, 184, 256)(168, 240, 186, 258)(170, 242, 189, 261)(172, 244, 192, 264)(173, 245, 194, 266)(175, 247, 185, 257)(177, 249, 199, 271)(178, 250, 200, 272)(180, 252, 190, 262)(182, 254, 203, 275)(183, 255, 205, 277)(187, 259, 210, 282)(188, 260, 211, 283)(191, 263, 202, 274)(193, 265, 212, 284)(195, 267, 206, 278)(196, 268, 208, 280)(197, 269, 207, 279)(198, 270, 209, 281)(201, 273, 204, 276)(213, 285, 216, 288)(214, 286, 215, 287)
	L = (1, 147)(2, 149)(3, 152)(4, 145)(5, 156)(6, 146)(7, 157)(8, 161)(9, 162)(10, 148)(11, 153)(12, 167)(13, 168)(14, 150)(15, 151)(16, 171)(17, 175)(18, 177)(19, 178)(20, 154)(21, 155)(22, 181)(23, 185)(24, 187)(25, 188)(26, 158)(27, 191)(28, 159)(29, 160)(30, 194)(31, 197)(32, 163)(33, 196)(34, 195)(35, 193)(36, 164)(37, 202)(38, 165)(39, 166)(40, 205)(41, 208)(42, 169)(43, 207)(44, 206)(45, 204)(46, 170)(47, 203)(48, 213)(49, 172)(50, 211)(51, 173)(52, 174)(53, 214)(54, 176)(55, 209)(56, 179)(57, 180)(58, 192)(59, 215)(60, 182)(61, 200)(62, 183)(63, 184)(64, 216)(65, 186)(66, 198)(67, 189)(68, 190)(69, 199)(70, 201)(71, 210)(72, 212)(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) :: { ( 6, 24 ), ( 6, 24, 6, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.277
Graph:: simple bipartite
	v = 108 e = 144 f = 30
	degree seq :: [ 2^72, 4^36 ]

E4.279 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y3 * Y1^4 * Y3^-1 * Y1^-4, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-2, Y3 * Y1^2 * Y3 * Y1^-2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-2, Y1^12 ]
Map:: polytopal
	R = (1, 73, 2, 74, 5, 77, 11, 83, 21, 93, 37, 109, 58, 130, 57, 129, 36, 108, 20, 92, 10, 82, 4, 76)(3, 75, 7, 79, 15, 87, 27, 99, 38, 110, 60, 132, 72, 144, 68, 140, 53, 125, 31, 103, 17, 89, 8, 80)(6, 78, 13, 85, 25, 97, 43, 115, 59, 131, 47, 119, 69, 141, 56, 128, 35, 107, 46, 118, 26, 98, 14, 86)(9, 81, 18, 90, 32, 104, 40, 112, 22, 94, 39, 111, 61, 133, 52, 124, 70, 142, 50, 122, 29, 101, 16, 88)(12, 84, 23, 95, 41, 113, 62, 134, 71, 143, 65, 137, 55, 127, 33, 105, 19, 91, 34, 106, 42, 114, 24, 96)(28, 100, 48, 120, 63, 135, 45, 117, 67, 139, 54, 126, 66, 138, 44, 116, 30, 102, 51, 123, 64, 136, 49, 121)(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, 157)(9, 148)(10, 163)(11, 166)(12, 149)(13, 152)(14, 167)(15, 172)(16, 151)(17, 174)(18, 177)(19, 154)(20, 179)(21, 182)(22, 155)(23, 158)(24, 183)(25, 188)(26, 189)(27, 191)(28, 159)(29, 192)(30, 161)(31, 196)(32, 198)(33, 162)(34, 200)(35, 164)(36, 197)(37, 203)(38, 165)(39, 168)(40, 204)(41, 207)(42, 208)(43, 209)(44, 169)(45, 170)(46, 212)(47, 171)(48, 173)(49, 213)(50, 206)(51, 205)(52, 175)(53, 180)(54, 176)(55, 210)(56, 178)(57, 214)(58, 215)(59, 181)(60, 184)(61, 195)(62, 194)(63, 185)(64, 186)(65, 187)(66, 199)(67, 216)(68, 190)(69, 193)(70, 201)(71, 202)(72, 211)(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, 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 E4.276
Graph:: simple bipartite
	v = 78 e = 144 f = 60
	degree seq :: [ 2^72, 24^6 ]

E4.280 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, (Y2^-2 * R * Y2^-2)^2, Y2^-1 * Y1 * Y2^4 * Y1 * Y2^-3, (Y2 * Y1 * Y2^-1 * Y1)^3, Y2^12 ]
Map::
	R = (1, 73, 2, 74)(3, 75, 7, 79)(4, 76, 9, 81)(5, 77, 11, 83)(6, 78, 13, 85)(8, 80, 16, 88)(10, 82, 19, 91)(12, 84, 22, 94)(14, 86, 25, 97)(15, 87, 27, 99)(17, 89, 30, 102)(18, 90, 32, 104)(20, 92, 35, 107)(21, 93, 37, 109)(23, 95, 40, 112)(24, 96, 42, 114)(26, 98, 45, 117)(28, 100, 48, 120)(29, 101, 50, 122)(31, 103, 41, 113)(33, 105, 55, 127)(34, 106, 56, 128)(36, 108, 46, 118)(38, 110, 59, 131)(39, 111, 61, 133)(43, 115, 66, 138)(44, 116, 67, 139)(47, 119, 58, 130)(49, 121, 68, 140)(51, 123, 62, 134)(52, 124, 64, 136)(53, 125, 63, 135)(54, 126, 65, 137)(57, 129, 60, 132)(69, 141, 72, 144)(70, 142, 71, 143)(145, 217, 147, 219, 152, 224, 161, 233, 175, 247, 197, 269, 214, 286, 201, 273, 180, 252, 164, 236, 154, 226, 148, 220)(146, 218, 149, 221, 156, 228, 167, 239, 185, 257, 208, 280, 216, 288, 212, 284, 190, 262, 170, 242, 158, 230, 150, 222)(151, 223, 157, 229, 168, 240, 187, 259, 207, 279, 184, 256, 205, 277, 200, 272, 179, 251, 193, 265, 172, 244, 159, 231)(153, 225, 162, 234, 177, 249, 196, 268, 174, 246, 194, 266, 211, 283, 189, 261, 204, 276, 182, 254, 165, 237, 155, 227)(160, 232, 171, 243, 191, 263, 203, 275, 215, 287, 210, 282, 198, 270, 176, 248, 163, 235, 178, 250, 195, 267, 173, 245)(166, 238, 181, 253, 202, 274, 192, 264, 213, 285, 199, 271, 209, 281, 186, 258, 169, 241, 188, 260, 206, 278, 183, 255)
	L = (1, 146)(2, 145)(3, 151)(4, 153)(5, 155)(6, 157)(7, 147)(8, 160)(9, 148)(10, 163)(11, 149)(12, 166)(13, 150)(14, 169)(15, 171)(16, 152)(17, 174)(18, 176)(19, 154)(20, 179)(21, 181)(22, 156)(23, 184)(24, 186)(25, 158)(26, 189)(27, 159)(28, 192)(29, 194)(30, 161)(31, 185)(32, 162)(33, 199)(34, 200)(35, 164)(36, 190)(37, 165)(38, 203)(39, 205)(40, 167)(41, 175)(42, 168)(43, 210)(44, 211)(45, 170)(46, 180)(47, 202)(48, 172)(49, 212)(50, 173)(51, 206)(52, 208)(53, 207)(54, 209)(55, 177)(56, 178)(57, 204)(58, 191)(59, 182)(60, 201)(61, 183)(62, 195)(63, 197)(64, 196)(65, 198)(66, 187)(67, 188)(68, 193)(69, 216)(70, 215)(71, 214)(72, 213)(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, 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 E4.281
Graph:: bipartite
	v = 42 e = 144 f = 96
	degree seq :: [ 4^36, 24^6 ]

E4.281 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 3, 12})
Quotient :: dipole
Aut^+ = C3 x S4 (small group id <72, 42>)
Aut   = S3 x S4 (small group id <144, 183>)
|r| :: 2
Presentation :: [ Y2, R^2, Y1^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-2)^3, Y3^3 * Y1^-1 * Y3^-5 * Y1^-1, (Y3 * Y2^-1)^12 ]
Map:: polytopal
	R = (1, 73, 2, 74, 4, 76)(3, 75, 8, 80, 10, 82)(5, 77, 12, 84, 6, 78)(7, 79, 15, 87, 11, 83)(9, 81, 18, 90, 20, 92)(13, 85, 25, 97, 23, 95)(14, 86, 24, 96, 28, 100)(16, 88, 31, 103, 29, 101)(17, 89, 33, 105, 21, 93)(19, 91, 36, 108, 38, 110)(22, 94, 30, 102, 42, 114)(26, 98, 47, 119, 45, 117)(27, 99, 49, 121, 51, 123)(32, 104, 56, 128, 55, 127)(34, 106, 59, 131, 58, 130)(35, 107, 53, 125, 39, 111)(37, 109, 50, 122, 64, 136)(40, 112, 52, 124, 44, 116)(41, 113, 67, 139, 63, 135)(43, 115, 46, 118, 54, 126)(48, 120, 57, 129, 60, 132)(61, 133, 69, 141, 70, 142)(62, 134, 71, 143, 65, 137)(66, 138, 68, 140, 72, 144)(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, 153)(4, 155)(5, 145)(6, 158)(7, 146)(8, 148)(9, 163)(10, 165)(11, 166)(12, 167)(13, 149)(14, 171)(15, 173)(16, 151)(17, 152)(18, 154)(19, 181)(20, 183)(21, 184)(22, 185)(23, 187)(24, 156)(25, 189)(26, 157)(27, 194)(28, 196)(29, 197)(30, 159)(31, 199)(32, 160)(33, 202)(34, 161)(35, 162)(36, 164)(37, 207)(38, 209)(39, 175)(40, 210)(41, 208)(42, 190)(43, 206)(44, 168)(45, 205)(46, 169)(47, 204)(48, 170)(49, 172)(50, 182)(51, 213)(52, 177)(53, 214)(54, 174)(55, 212)(56, 192)(57, 176)(58, 215)(59, 201)(60, 178)(61, 179)(62, 180)(63, 216)(64, 195)(65, 203)(66, 211)(67, 186)(68, 188)(69, 191)(70, 193)(71, 198)(72, 200)(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, 24 ), ( 4, 24, 4, 24, 4, 24 ) }
Outer automorphisms :: reflexible
Dual of E4.280
Graph:: simple bipartite
	v = 96 e = 144 f = 42
	degree seq :: [ 2^72, 6^24 ]

E4.282 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 5})
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 * T2)^2, (F * T1)^2, T1^5, (T1^-1 * T2)^4, (T2 * T1^2 * T2 * T1^-2)^2, (T2 * T1 * T2 * T1^-1)^3 ]
Map:: polyhedral non-degenerate
	R = (1, 2, 5, 10, 4)(3, 7, 14, 17, 8)(6, 12, 23, 26, 13)(9, 18, 32, 34, 19)(11, 21, 37, 40, 22)(15, 28, 47, 49, 29)(16, 30, 50, 42, 24)(20, 35, 58, 60, 36)(25, 43, 68, 62, 38)(27, 45, 72, 64, 46)(31, 52, 80, 82, 53)(33, 55, 84, 85, 56)(39, 63, 92, 88, 59)(41, 65, 94, 89, 66)(44, 70, 54, 83, 71)(48, 69, 98, 101, 73)(51, 78, 107, 108, 79)(57, 86, 61, 90, 87)(67, 93, 100, 113, 95)(74, 102, 99, 96, 81)(75, 103, 115, 109, 104)(76, 105, 77, 106, 97)(91, 110, 112, 117, 111)(114, 116, 119, 120, 118)
	L = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 31)(18, 33)(19, 28)(21, 38)(22, 39)(23, 41)(26, 44)(29, 48)(30, 51)(32, 54)(34, 57)(35, 59)(36, 55)(37, 61)(40, 64)(42, 67)(43, 69)(45, 73)(46, 74)(47, 75)(49, 76)(50, 77)(52, 81)(53, 78)(56, 79)(58, 80)(60, 89)(62, 91)(63, 93)(65, 95)(66, 96)(68, 97)(70, 99)(71, 98)(72, 100)(82, 109)(83, 108)(84, 110)(85, 106)(86, 102)(87, 103)(88, 104)(90, 111)(92, 105)(94, 112)(101, 114)(107, 116)(113, 118)(115, 119)(117, 120)
	local type(s) :: { ( 4^5 ) }
Outer automorphisms :: reflexible
Dual of E4.283
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple bipartite
	v = 24 e = 60 f = 30
	degree seq :: [ 5^24 ]

E4.283 :: Family: { 1 } :: Oriented family(ies): { E1b }
Signature :: (0; {2, 4, 5})
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, (T2 * T1^-1)^5, (T2 * T1^-1 * T2 * T1)^3, (T2 * T1^-2 * T2 * T1 * T2 * T1^-2)^2, (T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1)^2 ]
Map:: polyhedral 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, 41, 25)(15, 26, 44, 27)(21, 35, 57, 36)(22, 37, 59, 38)(23, 39, 61, 40)(29, 47, 72, 48)(30, 49, 65, 42)(32, 51, 76, 52)(33, 53, 78, 54)(34, 55, 80, 56)(43, 60, 86, 66)(45, 68, 97, 69)(46, 70, 98, 71)(50, 74, 103, 75)(58, 79, 109, 84)(62, 88, 108, 89)(63, 90, 106, 91)(64, 92, 105, 93)(67, 95, 104, 96)(73, 102, 107, 77)(81, 111, 94, 112)(82, 113, 101, 114)(83, 115, 100, 116)(85, 117, 99, 118)(87, 119, 120, 110)
	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, 42)(25, 43)(26, 45)(27, 35)(28, 46)(31, 50)(36, 58)(37, 60)(38, 51)(39, 62)(40, 63)(41, 64)(44, 67)(47, 54)(48, 69)(49, 73)(52, 77)(53, 79)(55, 81)(56, 82)(57, 83)(59, 85)(61, 87)(65, 94)(66, 88)(68, 91)(70, 99)(71, 100)(72, 101)(74, 104)(75, 105)(76, 106)(78, 108)(80, 110)(84, 111)(86, 114)(89, 116)(90, 112)(92, 109)(93, 117)(95, 113)(96, 107)(97, 118)(98, 119)(102, 115)(103, 120)
	local type(s) :: { ( 5^4 ) }
Outer automorphisms :: reflexible
Dual of E4.282
Transitivity :: ET+ VT+ AT+ REG+
Graph:: simple
	v = 30 e = 60 f = 24
	degree seq :: [ 4^30 ]

E4.284 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 5})
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^-1 * T1)^5, (T1 * T2^-1 * T1 * T2)^3, (T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1)^2, T2^-2 * T1 * T2^2 * T1 * T2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2 * T1 ]
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, 44, 27)(20, 34, 55, 35)(23, 38, 60, 39)(25, 41, 64, 42)(28, 46, 70, 47)(30, 49, 50, 31)(33, 52, 77, 53)(36, 57, 83, 58)(40, 62, 90, 63)(43, 65, 93, 66)(45, 68, 97, 69)(48, 71, 100, 72)(51, 75, 106, 76)(54, 78, 109, 79)(56, 81, 113, 82)(59, 84, 116, 85)(61, 87, 105, 88)(67, 95, 119, 96)(73, 102, 117, 94)(74, 103, 89, 104)(80, 111, 120, 112)(86, 118, 101, 110)(91, 115, 98, 108)(92, 107, 99, 114)(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, 156)(142, 158)(144, 160)(146, 163)(147, 165)(149, 168)(152, 171)(154, 174)(155, 176)(157, 179)(159, 181)(161, 172)(162, 185)(164, 187)(166, 189)(167, 178)(169, 193)(170, 194)(173, 198)(175, 200)(177, 202)(180, 206)(182, 209)(183, 211)(184, 212)(186, 214)(188, 207)(190, 218)(191, 219)(192, 221)(195, 225)(196, 227)(197, 228)(199, 230)(201, 223)(203, 234)(204, 235)(205, 237)(208, 224)(210, 232)(213, 233)(215, 236)(216, 226)(217, 229)(220, 231)(222, 238)(239, 240)
	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) :: { ( 10, 10 ), ( 10^4 ) }
Outer automorphisms :: reflexible
Dual of E4.288
Transitivity :: ET+
Graph:: simple bipartite
	v = 90 e = 120 f = 24
	degree seq :: [ 2^60, 4^30 ]

E4.285 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 5})
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, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^5, (T2^2 * T1^-1 * T2 * T1^-1)^2, T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-2 * T2^-2 * T1^-1 ]
Map:: polyhedral non-degenerate
	R = (1, 3, 10, 14, 5)(2, 7, 17, 20, 8)(4, 12, 26, 22, 9)(6, 15, 31, 34, 16)(11, 25, 47, 45, 23)(13, 28, 52, 55, 29)(18, 37, 66, 64, 35)(19, 38, 68, 71, 39)(21, 41, 73, 76, 42)(24, 46, 81, 56, 30)(27, 51, 87, 85, 49)(32, 59, 96, 94, 57)(33, 60, 98, 101, 61)(36, 65, 80, 72, 40)(43, 50, 86, 90, 77)(44, 78, 99, 114, 79)(48, 83, 54, 92, 82)(53, 91, 117, 93, 89)(58, 95, 105, 102, 62)(63, 103, 74, 111, 104)(67, 107, 70, 110, 106)(69, 109, 115, 84, 108)(75, 112, 116, 88, 113)(97, 119, 100, 120, 118)(121, 122, 126, 124)(123, 129, 141, 131)(125, 133, 138, 127)(128, 139, 152, 135)(130, 143, 164, 144)(132, 136, 153, 147)(134, 150, 173, 148)(137, 155, 183, 156)(140, 160, 189, 158)(142, 163, 194, 161)(145, 162, 195, 168)(146, 169, 204, 170)(149, 174, 187, 157)(151, 177, 213, 178)(154, 182, 219, 180)(159, 190, 217, 179)(165, 200, 218, 198)(166, 199, 230, 191)(167, 202, 229, 192)(171, 181, 220, 208)(172, 209, 214, 210)(175, 206, 235, 212)(176, 207, 236, 211)(184, 225, 193, 223)(185, 224, 240, 221)(186, 226, 234, 222)(188, 228, 205, 201)(196, 215, 237, 232)(197, 216, 238, 231)(203, 233, 239, 227)
	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 ), ( 4^5 ) }
Outer automorphisms :: reflexible
Dual of E4.289
Transitivity :: ET+
Graph:: simple bipartite
	v = 54 e = 120 f = 60
	degree seq :: [ 4^30, 5^24 ]

E4.286 :: Family: { 2 } :: Oriented family(ies): { E3b }
Signature :: (0; {2, 4, 5})
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, T1^5, (T2 * T1^-1)^4, (T2 * T1^2 * T2 * T1^-2)^2, (T2 * T1 * T2 * T1^-1)^3 ]
Map:: polytopal
	R = (1, 3)(2, 6)(4, 9)(5, 11)(7, 15)(8, 16)(10, 20)(12, 24)(13, 25)(14, 27)(17, 31)(18, 33)(19, 28)(21, 38)(22, 39)(23, 41)(26, 44)(29, 48)(30, 51)(32, 54)(34, 57)(35, 59)(36, 55)(37, 61)(40, 64)(42, 67)(43, 69)(45, 73)(46, 74)(47, 75)(49, 76)(50, 77)(52, 81)(53, 78)(56, 79)(58, 80)(60, 89)(62, 91)(63, 93)(65, 95)(66, 96)(68, 97)(70, 99)(71, 98)(72, 100)(82, 109)(83, 108)(84, 110)(85, 106)(86, 102)(87, 103)(88, 104)(90, 111)(92, 105)(94, 112)(101, 114)(107, 116)(113, 118)(115, 119)(117, 120)(121, 122, 125, 130, 124)(123, 127, 134, 137, 128)(126, 132, 143, 146, 133)(129, 138, 152, 154, 139)(131, 141, 157, 160, 142)(135, 148, 167, 169, 149)(136, 150, 170, 162, 144)(140, 155, 178, 180, 156)(145, 163, 188, 182, 158)(147, 165, 192, 184, 166)(151, 172, 200, 202, 173)(153, 175, 204, 205, 176)(159, 183, 212, 208, 179)(161, 185, 214, 209, 186)(164, 190, 174, 203, 191)(168, 189, 218, 221, 193)(171, 198, 227, 228, 199)(177, 206, 181, 210, 207)(187, 213, 220, 233, 215)(194, 222, 219, 216, 201)(195, 223, 235, 229, 224)(196, 225, 197, 226, 217)(211, 230, 232, 237, 231)(234, 236, 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) :: { ( 8, 8 ), ( 8^5 ) }
Outer automorphisms :: reflexible
Dual of E4.287
Transitivity :: ET+
Graph:: simple bipartite
	v = 84 e = 120 f = 30
	degree seq :: [ 2^60, 5^24 ]

E4.287 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 5})
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^-1 * T1)^5, (T1 * T2^-1 * T1 * T2)^3, (T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1)^2, T2^-2 * T1 * T2^2 * T1 * T2 * T1 * T2^2 * T1 * T2^-2 * T1 * T2 * T1 ]
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, 37, 157, 22, 142)(15, 135, 26, 146, 44, 164, 27, 147)(20, 140, 34, 154, 55, 175, 35, 155)(23, 143, 38, 158, 60, 180, 39, 159)(25, 145, 41, 161, 64, 184, 42, 162)(28, 148, 46, 166, 70, 190, 47, 167)(30, 150, 49, 169, 50, 170, 31, 151)(33, 153, 52, 172, 77, 197, 53, 173)(36, 156, 57, 177, 83, 203, 58, 178)(40, 160, 62, 182, 90, 210, 63, 183)(43, 163, 65, 185, 93, 213, 66, 186)(45, 165, 68, 188, 97, 217, 69, 189)(48, 168, 71, 191, 100, 220, 72, 192)(51, 171, 75, 195, 106, 226, 76, 196)(54, 174, 78, 198, 109, 229, 79, 199)(56, 176, 81, 201, 113, 233, 82, 202)(59, 179, 84, 204, 116, 236, 85, 205)(61, 181, 87, 207, 105, 225, 88, 208)(67, 187, 95, 215, 119, 239, 96, 216)(73, 193, 102, 222, 117, 237, 94, 214)(74, 194, 103, 223, 89, 209, 104, 224)(80, 200, 111, 231, 120, 240, 112, 232)(86, 206, 118, 238, 101, 221, 110, 230)(91, 211, 115, 235, 98, 218, 108, 228)(92, 212, 107, 227, 99, 219, 114, 234)
	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, 156)(22, 158)(23, 133)(24, 160)(25, 134)(26, 163)(27, 165)(28, 136)(29, 168)(30, 137)(31, 138)(32, 171)(33, 139)(34, 174)(35, 176)(36, 141)(37, 179)(38, 142)(39, 181)(40, 144)(41, 172)(42, 185)(43, 146)(44, 187)(45, 147)(46, 189)(47, 178)(48, 149)(49, 193)(50, 194)(51, 152)(52, 161)(53, 198)(54, 154)(55, 200)(56, 155)(57, 202)(58, 167)(59, 157)(60, 206)(61, 159)(62, 209)(63, 211)(64, 212)(65, 162)(66, 214)(67, 164)(68, 207)(69, 166)(70, 218)(71, 219)(72, 221)(73, 169)(74, 170)(75, 225)(76, 227)(77, 228)(78, 173)(79, 230)(80, 175)(81, 223)(82, 177)(83, 234)(84, 235)(85, 237)(86, 180)(87, 188)(88, 224)(89, 182)(90, 232)(91, 183)(92, 184)(93, 233)(94, 186)(95, 236)(96, 226)(97, 229)(98, 190)(99, 191)(100, 231)(101, 192)(102, 238)(103, 201)(104, 208)(105, 195)(106, 216)(107, 196)(108, 197)(109, 217)(110, 199)(111, 220)(112, 210)(113, 213)(114, 203)(115, 204)(116, 215)(117, 205)(118, 222)(119, 240)(120, 239)
	local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.286
Transitivity :: ET+ VT+ AT
Graph::
	v = 30 e = 120 f = 84
	degree seq :: [ 8^30 ]

E4.288 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 5})
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, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, T2^5, (T2^2 * T1^-1 * T2 * T1^-1)^2, T1^-1 * T2^-1 * T1 * T2^2 * T1 * T2^-1 * T1^-2 * T2^-2 * T1^-1 ]
Map::
	R = (1, 121, 3, 123, 10, 130, 14, 134, 5, 125)(2, 122, 7, 127, 17, 137, 20, 140, 8, 128)(4, 124, 12, 132, 26, 146, 22, 142, 9, 129)(6, 126, 15, 135, 31, 151, 34, 154, 16, 136)(11, 131, 25, 145, 47, 167, 45, 165, 23, 143)(13, 133, 28, 148, 52, 172, 55, 175, 29, 149)(18, 138, 37, 157, 66, 186, 64, 184, 35, 155)(19, 139, 38, 158, 68, 188, 71, 191, 39, 159)(21, 141, 41, 161, 73, 193, 76, 196, 42, 162)(24, 144, 46, 166, 81, 201, 56, 176, 30, 150)(27, 147, 51, 171, 87, 207, 85, 205, 49, 169)(32, 152, 59, 179, 96, 216, 94, 214, 57, 177)(33, 153, 60, 180, 98, 218, 101, 221, 61, 181)(36, 156, 65, 185, 80, 200, 72, 192, 40, 160)(43, 163, 50, 170, 86, 206, 90, 210, 77, 197)(44, 164, 78, 198, 99, 219, 114, 234, 79, 199)(48, 168, 83, 203, 54, 174, 92, 212, 82, 202)(53, 173, 91, 211, 117, 237, 93, 213, 89, 209)(58, 178, 95, 215, 105, 225, 102, 222, 62, 182)(63, 183, 103, 223, 74, 194, 111, 231, 104, 224)(67, 187, 107, 227, 70, 190, 110, 230, 106, 226)(69, 189, 109, 229, 115, 235, 84, 204, 108, 228)(75, 195, 112, 232, 116, 236, 88, 208, 113, 233)(97, 217, 119, 239, 100, 220, 120, 240, 118, 238)
	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, 150)(15, 128)(16, 153)(17, 155)(18, 127)(19, 152)(20, 160)(21, 131)(22, 163)(23, 164)(24, 130)(25, 162)(26, 169)(27, 132)(28, 134)(29, 174)(30, 173)(31, 177)(32, 135)(33, 147)(34, 182)(35, 183)(36, 137)(37, 149)(38, 140)(39, 190)(40, 189)(41, 142)(42, 195)(43, 194)(44, 144)(45, 200)(46, 199)(47, 202)(48, 145)(49, 204)(50, 146)(51, 181)(52, 209)(53, 148)(54, 187)(55, 206)(56, 207)(57, 213)(58, 151)(59, 159)(60, 154)(61, 220)(62, 219)(63, 156)(64, 225)(65, 224)(66, 226)(67, 157)(68, 228)(69, 158)(70, 217)(71, 166)(72, 167)(73, 223)(74, 161)(75, 168)(76, 215)(77, 216)(78, 165)(79, 230)(80, 218)(81, 188)(82, 229)(83, 233)(84, 170)(85, 201)(86, 235)(87, 236)(88, 171)(89, 214)(90, 172)(91, 176)(92, 175)(93, 178)(94, 210)(95, 237)(96, 238)(97, 179)(98, 198)(99, 180)(100, 208)(101, 185)(102, 186)(103, 184)(104, 240)(105, 193)(106, 234)(107, 203)(108, 205)(109, 192)(110, 191)(111, 197)(112, 196)(113, 239)(114, 222)(115, 212)(116, 211)(117, 232)(118, 231)(119, 227)(120, 221)
	local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.284
Transitivity :: ET+ VT+ AT
Graph:: bipartite
	v = 24 e = 120 f = 90
	degree seq :: [ 10^24 ]

E4.289 :: Family: { 2* } :: Oriented family(ies): { E3*b }
Signature :: (0; {2, 4, 5})
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, T1^5, (T2 * T1^-1)^4, (T2 * T1^2 * T2 * T1^-2)^2, (T2 * T1 * T2 * T1^-1)^3 ]
Map:: polyhedral non-degenerate
	R = (1, 121, 3, 123)(2, 122, 6, 126)(4, 124, 9, 129)(5, 125, 11, 131)(7, 127, 15, 135)(8, 128, 16, 136)(10, 130, 20, 140)(12, 132, 24, 144)(13, 133, 25, 145)(14, 134, 27, 147)(17, 137, 31, 151)(18, 138, 33, 153)(19, 139, 28, 148)(21, 141, 38, 158)(22, 142, 39, 159)(23, 143, 41, 161)(26, 146, 44, 164)(29, 149, 48, 168)(30, 150, 51, 171)(32, 152, 54, 174)(34, 154, 57, 177)(35, 155, 59, 179)(36, 156, 55, 175)(37, 157, 61, 181)(40, 160, 64, 184)(42, 162, 67, 187)(43, 163, 69, 189)(45, 165, 73, 193)(46, 166, 74, 194)(47, 167, 75, 195)(49, 169, 76, 196)(50, 170, 77, 197)(52, 172, 81, 201)(53, 173, 78, 198)(56, 176, 79, 199)(58, 178, 80, 200)(60, 180, 89, 209)(62, 182, 91, 211)(63, 183, 93, 213)(65, 185, 95, 215)(66, 186, 96, 216)(68, 188, 97, 217)(70, 190, 99, 219)(71, 191, 98, 218)(72, 192, 100, 220)(82, 202, 109, 229)(83, 203, 108, 228)(84, 204, 110, 230)(85, 205, 106, 226)(86, 206, 102, 222)(87, 207, 103, 223)(88, 208, 104, 224)(90, 210, 111, 231)(92, 212, 105, 225)(94, 214, 112, 232)(101, 221, 114, 234)(107, 227, 116, 236)(113, 233, 118, 238)(115, 235, 119, 239)(117, 237, 120, 240)
	L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 130)(6, 132)(7, 134)(8, 123)(9, 138)(10, 124)(11, 141)(12, 143)(13, 126)(14, 137)(15, 148)(16, 150)(17, 128)(18, 152)(19, 129)(20, 155)(21, 157)(22, 131)(23, 146)(24, 136)(25, 163)(26, 133)(27, 165)(28, 167)(29, 135)(30, 170)(31, 172)(32, 154)(33, 175)(34, 139)(35, 178)(36, 140)(37, 160)(38, 145)(39, 183)(40, 142)(41, 185)(42, 144)(43, 188)(44, 190)(45, 192)(46, 147)(47, 169)(48, 189)(49, 149)(50, 162)(51, 198)(52, 200)(53, 151)(54, 203)(55, 204)(56, 153)(57, 206)(58, 180)(59, 159)(60, 156)(61, 210)(62, 158)(63, 212)(64, 166)(65, 214)(66, 161)(67, 213)(68, 182)(69, 218)(70, 174)(71, 164)(72, 184)(73, 168)(74, 222)(75, 223)(76, 225)(77, 226)(78, 227)(79, 171)(80, 202)(81, 194)(82, 173)(83, 191)(84, 205)(85, 176)(86, 181)(87, 177)(88, 179)(89, 186)(90, 207)(91, 230)(92, 208)(93, 220)(94, 209)(95, 187)(96, 201)(97, 196)(98, 221)(99, 216)(100, 233)(101, 193)(102, 219)(103, 235)(104, 195)(105, 197)(106, 217)(107, 228)(108, 199)(109, 224)(110, 232)(111, 211)(112, 237)(113, 215)(114, 236)(115, 229)(116, 239)(117, 231)(118, 234)(119, 240)(120, 238)
	local type(s) :: { ( 4, 5, 4, 5 ) }
Outer automorphisms :: reflexible
Dual of E4.285
Transitivity :: ET+ VT+ AT
Graph:: simple
	v = 60 e = 120 f = 54
	degree seq :: [ 4^60 ]

E4.290 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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, (Y3 * Y2^-1)^5, (Y1 * Y2^-1 * Y1 * Y2)^3, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y1 ]
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, 36, 156)(22, 142, 38, 158)(24, 144, 40, 160)(26, 146, 43, 163)(27, 147, 45, 165)(29, 149, 48, 168)(32, 152, 51, 171)(34, 154, 54, 174)(35, 155, 56, 176)(37, 157, 59, 179)(39, 159, 61, 181)(41, 161, 52, 172)(42, 162, 65, 185)(44, 164, 67, 187)(46, 166, 69, 189)(47, 167, 58, 178)(49, 169, 73, 193)(50, 170, 74, 194)(53, 173, 78, 198)(55, 175, 80, 200)(57, 177, 82, 202)(60, 180, 86, 206)(62, 182, 89, 209)(63, 183, 91, 211)(64, 184, 92, 212)(66, 186, 94, 214)(68, 188, 87, 207)(70, 190, 98, 218)(71, 191, 99, 219)(72, 192, 101, 221)(75, 195, 105, 225)(76, 196, 107, 227)(77, 197, 108, 228)(79, 199, 110, 230)(81, 201, 103, 223)(83, 203, 114, 234)(84, 204, 115, 235)(85, 205, 117, 237)(88, 208, 104, 224)(90, 210, 112, 232)(93, 213, 113, 233)(95, 215, 116, 236)(96, 216, 106, 226)(97, 217, 109, 229)(100, 220, 111, 231)(102, 222, 118, 238)(119, 239, 120, 240)(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, 277, 397, 262, 382)(255, 375, 266, 386, 284, 404, 267, 387)(260, 380, 274, 394, 295, 415, 275, 395)(263, 383, 278, 398, 300, 420, 279, 399)(265, 385, 281, 401, 304, 424, 282, 402)(268, 388, 286, 406, 310, 430, 287, 407)(270, 390, 289, 409, 290, 410, 271, 391)(273, 393, 292, 412, 317, 437, 293, 413)(276, 396, 297, 417, 323, 443, 298, 418)(280, 400, 302, 422, 330, 450, 303, 423)(283, 403, 305, 425, 333, 453, 306, 426)(285, 405, 308, 428, 337, 457, 309, 429)(288, 408, 311, 431, 340, 460, 312, 432)(291, 411, 315, 435, 346, 466, 316, 436)(294, 414, 318, 438, 349, 469, 319, 439)(296, 416, 321, 441, 353, 473, 322, 442)(299, 419, 324, 444, 356, 476, 325, 445)(301, 421, 327, 447, 345, 465, 328, 448)(307, 427, 335, 455, 359, 479, 336, 456)(313, 433, 342, 462, 357, 477, 334, 454)(314, 434, 343, 463, 329, 449, 344, 464)(320, 440, 351, 471, 360, 480, 352, 472)(326, 446, 358, 478, 341, 461, 350, 470)(331, 451, 355, 475, 338, 458, 348, 468)(332, 452, 347, 467, 339, 459, 354, 474)
	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, 276)(22, 278)(23, 253)(24, 280)(25, 254)(26, 283)(27, 285)(28, 256)(29, 288)(30, 257)(31, 258)(32, 291)(33, 259)(34, 294)(35, 296)(36, 261)(37, 299)(38, 262)(39, 301)(40, 264)(41, 292)(42, 305)(43, 266)(44, 307)(45, 267)(46, 309)(47, 298)(48, 269)(49, 313)(50, 314)(51, 272)(52, 281)(53, 318)(54, 274)(55, 320)(56, 275)(57, 322)(58, 287)(59, 277)(60, 326)(61, 279)(62, 329)(63, 331)(64, 332)(65, 282)(66, 334)(67, 284)(68, 327)(69, 286)(70, 338)(71, 339)(72, 341)(73, 289)(74, 290)(75, 345)(76, 347)(77, 348)(78, 293)(79, 350)(80, 295)(81, 343)(82, 297)(83, 354)(84, 355)(85, 357)(86, 300)(87, 308)(88, 344)(89, 302)(90, 352)(91, 303)(92, 304)(93, 353)(94, 306)(95, 356)(96, 346)(97, 349)(98, 310)(99, 311)(100, 351)(101, 312)(102, 358)(103, 321)(104, 328)(105, 315)(106, 336)(107, 316)(108, 317)(109, 337)(110, 319)(111, 340)(112, 330)(113, 333)(114, 323)(115, 324)(116, 335)(117, 325)(118, 342)(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, 10, 2, 10 ), ( 2, 10, 2, 10, 2, 10, 2, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.293
Graph:: bipartite
	v = 90 e = 240 f = 144
	degree seq :: [ 4^60, 8^30 ]

E4.291 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y3^-1 * Y1^-1)^2, Y2^5, (Y2^2 * Y1^-1 * Y2 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-2 * Y2^-2 * Y1^-1 ]
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, 32, 152, 15, 135)(10, 130, 23, 143, 44, 164, 24, 144)(12, 132, 16, 136, 33, 153, 27, 147)(14, 134, 30, 150, 53, 173, 28, 148)(17, 137, 35, 155, 63, 183, 36, 156)(20, 140, 40, 160, 69, 189, 38, 158)(22, 142, 43, 163, 74, 194, 41, 161)(25, 145, 42, 162, 75, 195, 48, 168)(26, 146, 49, 169, 84, 204, 50, 170)(29, 149, 54, 174, 67, 187, 37, 157)(31, 151, 57, 177, 93, 213, 58, 178)(34, 154, 62, 182, 99, 219, 60, 180)(39, 159, 70, 190, 97, 217, 59, 179)(45, 165, 80, 200, 98, 218, 78, 198)(46, 166, 79, 199, 110, 230, 71, 191)(47, 167, 82, 202, 109, 229, 72, 192)(51, 171, 61, 181, 100, 220, 88, 208)(52, 172, 89, 209, 94, 214, 90, 210)(55, 175, 86, 206, 115, 235, 92, 212)(56, 176, 87, 207, 116, 236, 91, 211)(64, 184, 105, 225, 73, 193, 103, 223)(65, 185, 104, 224, 120, 240, 101, 221)(66, 186, 106, 226, 114, 234, 102, 222)(68, 188, 108, 228, 85, 205, 81, 201)(76, 196, 95, 215, 117, 237, 112, 232)(77, 197, 96, 216, 118, 238, 111, 231)(83, 203, 113, 233, 119, 239, 107, 227)(241, 361, 243, 363, 250, 370, 254, 374, 245, 365)(242, 362, 247, 367, 257, 377, 260, 380, 248, 368)(244, 364, 252, 372, 266, 386, 262, 382, 249, 369)(246, 366, 255, 375, 271, 391, 274, 394, 256, 376)(251, 371, 265, 385, 287, 407, 285, 405, 263, 383)(253, 373, 268, 388, 292, 412, 295, 415, 269, 389)(258, 378, 277, 397, 306, 426, 304, 424, 275, 395)(259, 379, 278, 398, 308, 428, 311, 431, 279, 399)(261, 381, 281, 401, 313, 433, 316, 436, 282, 402)(264, 384, 286, 406, 321, 441, 296, 416, 270, 390)(267, 387, 291, 411, 327, 447, 325, 445, 289, 409)(272, 392, 299, 419, 336, 456, 334, 454, 297, 417)(273, 393, 300, 420, 338, 458, 341, 461, 301, 421)(276, 396, 305, 425, 320, 440, 312, 432, 280, 400)(283, 403, 290, 410, 326, 446, 330, 450, 317, 437)(284, 404, 318, 438, 339, 459, 354, 474, 319, 439)(288, 408, 323, 443, 294, 414, 332, 452, 322, 442)(293, 413, 331, 451, 357, 477, 333, 453, 329, 449)(298, 418, 335, 455, 345, 465, 342, 462, 302, 422)(303, 423, 343, 463, 314, 434, 351, 471, 344, 464)(307, 427, 347, 467, 310, 430, 350, 470, 346, 466)(309, 429, 349, 469, 355, 475, 324, 444, 348, 468)(315, 435, 352, 472, 356, 476, 328, 448, 353, 473)(337, 457, 359, 479, 340, 460, 360, 480, 358, 478)
	L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 254)(11, 265)(12, 266)(13, 268)(14, 245)(15, 271)(16, 246)(17, 260)(18, 277)(19, 278)(20, 248)(21, 281)(22, 249)(23, 251)(24, 286)(25, 287)(26, 262)(27, 291)(28, 292)(29, 253)(30, 264)(31, 274)(32, 299)(33, 300)(34, 256)(35, 258)(36, 305)(37, 306)(38, 308)(39, 259)(40, 276)(41, 313)(42, 261)(43, 290)(44, 318)(45, 263)(46, 321)(47, 285)(48, 323)(49, 267)(50, 326)(51, 327)(52, 295)(53, 331)(54, 332)(55, 269)(56, 270)(57, 272)(58, 335)(59, 336)(60, 338)(61, 273)(62, 298)(63, 343)(64, 275)(65, 320)(66, 304)(67, 347)(68, 311)(69, 349)(70, 350)(71, 279)(72, 280)(73, 316)(74, 351)(75, 352)(76, 282)(77, 283)(78, 339)(79, 284)(80, 312)(81, 296)(82, 288)(83, 294)(84, 348)(85, 289)(86, 330)(87, 325)(88, 353)(89, 293)(90, 317)(91, 357)(92, 322)(93, 329)(94, 297)(95, 345)(96, 334)(97, 359)(98, 341)(99, 354)(100, 360)(101, 301)(102, 302)(103, 314)(104, 303)(105, 342)(106, 307)(107, 310)(108, 309)(109, 355)(110, 346)(111, 344)(112, 356)(113, 315)(114, 319)(115, 324)(116, 328)(117, 333)(118, 337)(119, 340)(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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) }
Outer automorphisms :: reflexible
Dual of E4.292
Graph:: bipartite
	v = 54 e = 240 f = 180
	degree seq :: [ 8^30, 10^24 ]

E4.292 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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 * Y2)^4, (Y3^-1 * Y1^-1)^5, (Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1)^2, (Y3 * Y2 * Y3^-1 * Y2)^3 ]
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, 260, 380)(252, 372, 263, 383)(254, 374, 266, 386)(255, 375, 265, 385)(256, 376, 268, 388)(258, 378, 272, 392)(259, 379, 261, 381)(262, 382, 278, 398)(264, 384, 282, 402)(267, 387, 287, 407)(269, 389, 290, 410)(270, 390, 289, 409)(271, 391, 292, 412)(273, 393, 296, 416)(274, 394, 297, 417)(275, 395, 298, 418)(276, 396, 294, 414)(277, 397, 301, 421)(279, 399, 304, 424)(280, 400, 303, 423)(281, 401, 306, 426)(283, 403, 310, 430)(284, 404, 311, 431)(285, 405, 312, 432)(286, 406, 308, 428)(288, 408, 302, 422)(291, 411, 321, 441)(293, 413, 307, 427)(295, 415, 309, 429)(299, 419, 313, 433)(300, 420, 329, 449)(305, 425, 336, 456)(314, 434, 344, 464)(315, 435, 342, 462)(316, 436, 343, 463)(317, 437, 335, 455)(318, 438, 346, 466)(319, 439, 347, 467)(320, 440, 332, 452)(322, 442, 341, 461)(323, 443, 350, 470)(324, 444, 340, 460)(325, 445, 339, 459)(326, 446, 337, 457)(327, 447, 330, 450)(328, 448, 331, 451)(333, 453, 352, 472)(334, 454, 349, 469)(338, 458, 354, 474)(345, 465, 355, 475)(348, 468, 356, 476)(351, 471, 357, 477)(353, 473, 358, 478)(359, 479, 360, 480)
	L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 250)(9, 258)(10, 244)(11, 261)(12, 254)(13, 264)(14, 246)(15, 267)(16, 247)(17, 270)(18, 273)(19, 249)(20, 275)(21, 277)(22, 251)(23, 280)(24, 283)(25, 253)(26, 285)(27, 269)(28, 288)(29, 256)(30, 291)(31, 257)(32, 294)(33, 274)(34, 259)(35, 299)(36, 260)(37, 279)(38, 302)(39, 262)(40, 305)(41, 263)(42, 308)(43, 284)(44, 265)(45, 313)(46, 266)(47, 315)(48, 317)(49, 268)(50, 319)(51, 293)(52, 322)(53, 271)(54, 323)(55, 272)(56, 325)(57, 326)(58, 292)(59, 300)(60, 276)(61, 330)(62, 332)(63, 278)(64, 334)(65, 307)(66, 337)(67, 281)(68, 338)(69, 282)(70, 340)(71, 341)(72, 306)(73, 314)(74, 286)(75, 345)(76, 287)(77, 318)(78, 289)(79, 296)(80, 290)(81, 348)(82, 349)(83, 324)(84, 295)(85, 320)(86, 321)(87, 297)(88, 298)(89, 316)(90, 351)(91, 301)(92, 333)(93, 303)(94, 310)(95, 304)(96, 353)(97, 347)(98, 339)(99, 309)(100, 335)(101, 336)(102, 311)(103, 312)(104, 331)(105, 329)(106, 350)(107, 343)(108, 327)(109, 328)(110, 355)(111, 344)(112, 354)(113, 342)(114, 357)(115, 359)(116, 346)(117, 360)(118, 352)(119, 356)(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, 10 ), ( 8, 10, 8, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.291
Graph:: simple bipartite
	v = 180 e = 240 f = 54
	degree seq :: [ 2^120, 4^60 ]

E4.293 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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 * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y3 * Y1^2 * Y3 * Y1^-2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 ]
Map:: polytopal
	R = (1, 121, 2, 122, 5, 125, 10, 130, 4, 124)(3, 123, 7, 127, 14, 134, 17, 137, 8, 128)(6, 126, 12, 132, 23, 143, 26, 146, 13, 133)(9, 129, 18, 138, 32, 152, 34, 154, 19, 139)(11, 131, 21, 141, 37, 157, 40, 160, 22, 142)(15, 135, 28, 148, 47, 167, 49, 169, 29, 149)(16, 136, 30, 150, 50, 170, 42, 162, 24, 144)(20, 140, 35, 155, 58, 178, 60, 180, 36, 156)(25, 145, 43, 163, 68, 188, 62, 182, 38, 158)(27, 147, 45, 165, 72, 192, 64, 184, 46, 166)(31, 151, 52, 172, 80, 200, 82, 202, 53, 173)(33, 153, 55, 175, 84, 204, 85, 205, 56, 176)(39, 159, 63, 183, 92, 212, 88, 208, 59, 179)(41, 161, 65, 185, 94, 214, 89, 209, 66, 186)(44, 164, 70, 190, 54, 174, 83, 203, 71, 191)(48, 168, 69, 189, 98, 218, 101, 221, 73, 193)(51, 171, 78, 198, 107, 227, 108, 228, 79, 199)(57, 177, 86, 206, 61, 181, 90, 210, 87, 207)(67, 187, 93, 213, 100, 220, 113, 233, 95, 215)(74, 194, 102, 222, 99, 219, 96, 216, 81, 201)(75, 195, 103, 223, 115, 235, 109, 229, 104, 224)(76, 196, 105, 225, 77, 197, 106, 226, 97, 217)(91, 211, 110, 230, 112, 232, 117, 237, 111, 231)(114, 234, 116, 236, 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, 246)(3, 241)(4, 249)(5, 251)(6, 242)(7, 255)(8, 256)(9, 244)(10, 260)(11, 245)(12, 264)(13, 265)(14, 267)(15, 247)(16, 248)(17, 271)(18, 273)(19, 268)(20, 250)(21, 278)(22, 279)(23, 281)(24, 252)(25, 253)(26, 284)(27, 254)(28, 259)(29, 288)(30, 291)(31, 257)(32, 294)(33, 258)(34, 297)(35, 299)(36, 295)(37, 301)(38, 261)(39, 262)(40, 304)(41, 263)(42, 307)(43, 309)(44, 266)(45, 313)(46, 314)(47, 315)(48, 269)(49, 316)(50, 317)(51, 270)(52, 321)(53, 318)(54, 272)(55, 276)(56, 319)(57, 274)(58, 320)(59, 275)(60, 329)(61, 277)(62, 331)(63, 333)(64, 280)(65, 335)(66, 336)(67, 282)(68, 337)(69, 283)(70, 339)(71, 338)(72, 340)(73, 285)(74, 286)(75, 287)(76, 289)(77, 290)(78, 293)(79, 296)(80, 298)(81, 292)(82, 349)(83, 348)(84, 350)(85, 346)(86, 342)(87, 343)(88, 344)(89, 300)(90, 351)(91, 302)(92, 345)(93, 303)(94, 352)(95, 305)(96, 306)(97, 308)(98, 311)(99, 310)(100, 312)(101, 354)(102, 326)(103, 327)(104, 328)(105, 332)(106, 325)(107, 356)(108, 323)(109, 322)(110, 324)(111, 330)(112, 334)(113, 358)(114, 341)(115, 359)(116, 347)(117, 360)(118, 353)(119, 355)(120, 357)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.290
Graph:: simple bipartite
	v = 144 e = 240 f = 90
	degree seq :: [ 2^120, 10^24 ]

E4.294 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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, Y2^5, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y3 * Y2^-1)^4, (Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^3 ]
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, 20, 140)(12, 132, 23, 143)(14, 134, 26, 146)(15, 135, 25, 145)(16, 136, 28, 148)(18, 138, 32, 152)(19, 139, 21, 141)(22, 142, 38, 158)(24, 144, 42, 162)(27, 147, 47, 167)(29, 149, 50, 170)(30, 150, 49, 169)(31, 151, 52, 172)(33, 153, 56, 176)(34, 154, 57, 177)(35, 155, 58, 178)(36, 156, 54, 174)(37, 157, 61, 181)(39, 159, 64, 184)(40, 160, 63, 183)(41, 161, 66, 186)(43, 163, 70, 190)(44, 164, 71, 191)(45, 165, 72, 192)(46, 166, 68, 188)(48, 168, 62, 182)(51, 171, 81, 201)(53, 173, 67, 187)(55, 175, 69, 189)(59, 179, 73, 193)(60, 180, 89, 209)(65, 185, 96, 216)(74, 194, 104, 224)(75, 195, 102, 222)(76, 196, 103, 223)(77, 197, 95, 215)(78, 198, 106, 226)(79, 199, 107, 227)(80, 200, 92, 212)(82, 202, 101, 221)(83, 203, 110, 230)(84, 204, 100, 220)(85, 205, 99, 219)(86, 206, 97, 217)(87, 207, 90, 210)(88, 208, 91, 211)(93, 213, 112, 232)(94, 214, 109, 229)(98, 218, 114, 234)(105, 225, 115, 235)(108, 228, 116, 236)(111, 231, 117, 237)(113, 233, 118, 238)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 254, 374, 246, 366)(247, 367, 255, 375, 267, 387, 269, 389, 256, 376)(249, 369, 258, 378, 273, 393, 274, 394, 259, 379)(251, 371, 261, 381, 277, 397, 279, 399, 262, 382)(253, 373, 264, 384, 283, 403, 284, 404, 265, 385)(257, 377, 270, 390, 291, 411, 293, 413, 271, 391)(260, 380, 275, 395, 299, 419, 300, 420, 276, 396)(263, 383, 280, 400, 305, 425, 307, 427, 281, 401)(266, 386, 285, 405, 313, 433, 314, 434, 286, 406)(268, 388, 288, 408, 317, 437, 318, 438, 289, 409)(272, 392, 294, 414, 323, 443, 324, 444, 295, 415)(278, 398, 302, 422, 332, 452, 333, 453, 303, 423)(282, 402, 308, 428, 338, 458, 339, 459, 309, 429)(287, 407, 315, 435, 345, 465, 329, 449, 316, 436)(290, 410, 319, 439, 296, 416, 325, 445, 320, 440)(292, 412, 322, 442, 349, 469, 328, 448, 298, 418)(297, 417, 326, 446, 321, 441, 348, 468, 327, 447)(301, 421, 330, 450, 351, 471, 344, 464, 331, 451)(304, 424, 334, 454, 310, 430, 340, 460, 335, 455)(306, 426, 337, 457, 347, 467, 343, 463, 312, 432)(311, 431, 341, 461, 336, 456, 353, 473, 342, 462)(346, 466, 350, 470, 355, 475, 359, 479, 356, 476)(352, 472, 354, 474, 357, 477, 360, 480, 358, 478)
	L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 257)(9, 244)(10, 260)(11, 245)(12, 263)(13, 246)(14, 266)(15, 265)(16, 268)(17, 248)(18, 272)(19, 261)(20, 250)(21, 259)(22, 278)(23, 252)(24, 282)(25, 255)(26, 254)(27, 287)(28, 256)(29, 290)(30, 289)(31, 292)(32, 258)(33, 296)(34, 297)(35, 298)(36, 294)(37, 301)(38, 262)(39, 304)(40, 303)(41, 306)(42, 264)(43, 310)(44, 311)(45, 312)(46, 308)(47, 267)(48, 302)(49, 270)(50, 269)(51, 321)(52, 271)(53, 307)(54, 276)(55, 309)(56, 273)(57, 274)(58, 275)(59, 313)(60, 329)(61, 277)(62, 288)(63, 280)(64, 279)(65, 336)(66, 281)(67, 293)(68, 286)(69, 295)(70, 283)(71, 284)(72, 285)(73, 299)(74, 344)(75, 342)(76, 343)(77, 335)(78, 346)(79, 347)(80, 332)(81, 291)(82, 341)(83, 350)(84, 340)(85, 339)(86, 337)(87, 330)(88, 331)(89, 300)(90, 327)(91, 328)(92, 320)(93, 352)(94, 349)(95, 317)(96, 305)(97, 326)(98, 354)(99, 325)(100, 324)(101, 322)(102, 315)(103, 316)(104, 314)(105, 355)(106, 318)(107, 319)(108, 356)(109, 334)(110, 323)(111, 357)(112, 333)(113, 358)(114, 338)(115, 345)(116, 348)(117, 351)(118, 353)(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 ) }
Outer automorphisms :: reflexible
Dual of E4.295
Graph:: bipartite
	v = 84 e = 240 f = 150
	degree seq :: [ 4^60, 10^24 ]

E4.295 :: Family: { 3 } :: Oriented family(ies): { E5a }
Signature :: (0; {2, 4, 5})
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, (Y3^2 * Y1^-1 * Y3 * Y1^-1)^2, (Y3 * Y2^-1)^5, Y1^-1 * Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1^-2 * Y3^-2 * Y1^-1 ]
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, 32, 152, 15, 135)(10, 130, 23, 143, 44, 164, 24, 144)(12, 132, 16, 136, 33, 153, 27, 147)(14, 134, 30, 150, 53, 173, 28, 148)(17, 137, 35, 155, 63, 183, 36, 156)(20, 140, 40, 160, 69, 189, 38, 158)(22, 142, 43, 163, 74, 194, 41, 161)(25, 145, 42, 162, 75, 195, 48, 168)(26, 146, 49, 169, 84, 204, 50, 170)(29, 149, 54, 174, 67, 187, 37, 157)(31, 151, 57, 177, 93, 213, 58, 178)(34, 154, 62, 182, 99, 219, 60, 180)(39, 159, 70, 190, 97, 217, 59, 179)(45, 165, 80, 200, 98, 218, 78, 198)(46, 166, 79, 199, 110, 230, 71, 191)(47, 167, 82, 202, 109, 229, 72, 192)(51, 171, 61, 181, 100, 220, 88, 208)(52, 172, 89, 209, 94, 214, 90, 210)(55, 175, 86, 206, 115, 235, 92, 212)(56, 176, 87, 207, 116, 236, 91, 211)(64, 184, 105, 225, 73, 193, 103, 223)(65, 185, 104, 224, 120, 240, 101, 221)(66, 186, 106, 226, 114, 234, 102, 222)(68, 188, 108, 228, 85, 205, 81, 201)(76, 196, 95, 215, 117, 237, 112, 232)(77, 197, 96, 216, 118, 238, 111, 231)(83, 203, 113, 233, 119, 239, 107, 227)(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, 254)(11, 265)(12, 266)(13, 268)(14, 245)(15, 271)(16, 246)(17, 260)(18, 277)(19, 278)(20, 248)(21, 281)(22, 249)(23, 251)(24, 286)(25, 287)(26, 262)(27, 291)(28, 292)(29, 253)(30, 264)(31, 274)(32, 299)(33, 300)(34, 256)(35, 258)(36, 305)(37, 306)(38, 308)(39, 259)(40, 276)(41, 313)(42, 261)(43, 290)(44, 318)(45, 263)(46, 321)(47, 285)(48, 323)(49, 267)(50, 326)(51, 327)(52, 295)(53, 331)(54, 332)(55, 269)(56, 270)(57, 272)(58, 335)(59, 336)(60, 338)(61, 273)(62, 298)(63, 343)(64, 275)(65, 320)(66, 304)(67, 347)(68, 311)(69, 349)(70, 350)(71, 279)(72, 280)(73, 316)(74, 351)(75, 352)(76, 282)(77, 283)(78, 339)(79, 284)(80, 312)(81, 296)(82, 288)(83, 294)(84, 348)(85, 289)(86, 330)(87, 325)(88, 353)(89, 293)(90, 317)(91, 357)(92, 322)(93, 329)(94, 297)(95, 345)(96, 334)(97, 359)(98, 341)(99, 354)(100, 360)(101, 301)(102, 302)(103, 314)(104, 303)(105, 342)(106, 307)(107, 310)(108, 309)(109, 355)(110, 346)(111, 344)(112, 356)(113, 315)(114, 319)(115, 324)(116, 328)(117, 333)(118, 337)(119, 340)(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) :: { ( 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10 ) }
Outer automorphisms :: reflexible
Dual of E4.294
Graph:: simple bipartite
	v = 150 e = 240 f = 84
	degree seq :: [ 2^120, 8^30 ]

## Checksum: 295 records.
## Written on: Tue Oct 15 09:21:29 CEST 2019