## Begin on: Tue Oct 15 09:08:08 CEST 2019 ENUMERATION No. of records: 229 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 20 (16 non-degenerate) 2 [ E3b] : 43 (23 non-degenerate) 2* [E3*b] : 43 (23 non-degenerate) 2ex [E3*c] : 1 (1 non-degenerate) 2*ex [ E3c] : 1 (1 non-degenerate) 2P [ E2] : 2 (0 non-degenerate) 2Pex [ E1a] : 0 3 [ E5a] : 104 (14 non-degenerate) 4 [ E4] : 6 (3 non-degenerate) 4* [ E4*] : 6 (3 non-degenerate) 4P [ E6] : 1 (0 non-degenerate) 5 [ E3a] : 1 (1 non-degenerate) 5* [E3*a] : 1 (1 non-degenerate) 5P [ E5b] : 0 E3.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C3 (small group id <3, 1>) Aut = S3 (small group id <6, 1>) |r| :: 2 Presentation :: [ A, B, A, B, A, B, S^2, Z^3, S^-1 * Z * S * Z, S^-1 * A * S * B, S^-1 * B * S * A, (Z^-1 * A * B^-1 * A^-1 * B)^3 ] Map:: R = (1, 5, 8, 11, 2, 6, 9, 12, 3, 4, 7, 10) L = (1, 7)(2, 8)(3, 9)(4, 10)(5, 11)(6, 12) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 6 f = 1 degree seq :: [ 12 ] E3.2 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 6}) Quotient :: dipole Aut^+ = C6 (small group id <6, 2>) Aut = D12 (small group id <12, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, Y2^3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^6, (Y3 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 7, 2, 8)(3, 9, 5, 11)(4, 10, 6, 12)(13, 19, 15, 21, 16, 22)(14, 20, 17, 23, 18, 24) L = (1, 16)(2, 18)(3, 13)(4, 15)(5, 14)(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 ) } Outer automorphisms :: reflexible Dual of E3.3 Graph:: bipartite v = 5 e = 12 f = 3 degree seq :: [ 4^3, 6^2 ] E3.3 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 3, 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 * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate 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, 14)(2, 16)(3, 17)(4, 13)(5, 18)(6, 15)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24) local type(s) :: { ( 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.2 Graph:: bipartite v = 3 e = 12 f = 5 degree seq :: [ 6^2, 12 ] E3.4 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C6 (small group id <6, 2>) Aut = D12 (small group id <12, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y1^2, R^2, Y2^3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 7, 2, 8)(3, 9, 5, 11)(4, 10, 6, 12)(13, 19, 15, 21, 18, 24, 14, 20, 17, 23, 16, 22) 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) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 12 f = 4 degree seq :: [ 4^3, 12 ] E3.5 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 7, 7}) Quotient :: edge Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^3 ] Map:: non-degenerate R = (1, 3, 7, 4, 2, 6, 5)(8, 9, 10, 13, 14, 12, 11) L = (1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14) local type(s) :: { ( 14^7 ) } Outer automorphisms :: reflexible Dual of E3.8 Transitivity :: ET+ Graph:: bipartite v = 2 e = 7 f = 1 degree seq :: [ 7^2 ] E3.6 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 7, 7}) Quotient :: edge Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T1 * T2^-3 ] Map:: non-degenerate R = (1, 3, 6, 2, 4, 7, 5)(8, 9, 12, 13, 14, 10, 11) L = (1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14) local type(s) :: { ( 14^7 ) } Outer automorphisms :: reflexible Dual of E3.7 Transitivity :: ET+ Graph:: bipartite v = 2 e = 7 f = 1 degree seq :: [ 7^2 ] E3.7 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 7, 7}) Quotient :: loop Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T1^7, T2^7, (T2^-1 * T1^-1)^7 ] Map:: non-degenerate R = (1, 8, 2, 9, 4, 11, 6, 13, 7, 14, 5, 12, 3, 10) L = (1, 9)(2, 11)(3, 8)(4, 13)(5, 10)(6, 14)(7, 12) local type(s) :: { ( 7^14 ) } Outer automorphisms :: reflexible Dual of E3.6 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 7 f = 2 degree seq :: [ 14 ] E3.8 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 7, 7}) Quotient :: loop Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^3 ] Map:: non-degenerate R = (1, 8, 3, 10, 7, 14, 4, 11, 2, 9, 6, 13, 5, 12) L = (1, 9)(2, 10)(3, 13)(4, 8)(5, 11)(6, 14)(7, 12) local type(s) :: { ( 7^14 ) } Outer automorphisms :: reflexible Dual of E3.5 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 7 f = 2 degree seq :: [ 14 ] E3.9 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 7}) Quotient :: dipole Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7 ] Map:: R = (1, 8, 2, 9, 6, 13, 3, 10, 5, 12, 7, 14, 4, 11)(15, 22, 17, 24, 18, 25, 20, 27, 21, 28, 16, 23, 19, 26) L = (1, 18)(2, 15)(3, 20)(4, 21)(5, 17)(6, 16)(7, 19)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E3.11 Graph:: bipartite v = 2 e = 14 f = 8 degree seq :: [ 14^2 ] E3.10 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 7}) Quotient :: dipole Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^7 ] Map:: R = (1, 8, 2, 9, 6, 13, 5, 12, 3, 10, 7, 14, 4, 11)(15, 22, 17, 24, 16, 23, 21, 28, 20, 27, 18, 25, 19, 26) L = (1, 18)(2, 15)(3, 19)(4, 21)(5, 20)(6, 16)(7, 17)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E3.12 Graph:: bipartite v = 2 e = 14 f = 8 degree seq :: [ 14^2 ] E3.11 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 7}) Quotient :: dipole Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2^7, (Y3 * Y2^-1)^7, (Y3^-1 * Y1^-1)^7 ] Map:: R = (1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22, 16, 23, 18, 25, 20, 27, 21, 28, 19, 26, 17, 24) L = (1, 17)(2, 15)(3, 19)(4, 16)(5, 21)(6, 18)(7, 20)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 14, 14 ), ( 14^14 ) } Outer automorphisms :: reflexible Dual of E3.9 Graph:: bipartite v = 8 e = 14 f = 2 degree seq :: [ 2^7, 14 ] E3.12 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 7}) Quotient :: dipole Aut^+ = C7 (small group id <7, 1>) Aut = D14 (small group id <14, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3 * Y2, Y2 * Y3^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^7 ] Map:: R = (1, 8)(2, 9)(3, 10)(4, 11)(5, 12)(6, 13)(7, 14)(15, 22, 16, 23, 19, 26, 20, 27, 21, 28, 17, 24, 18, 25) L = (1, 17)(2, 18)(3, 20)(4, 21)(5, 15)(6, 16)(7, 19)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 14, 14 ), ( 14^14 ) } Outer automorphisms :: reflexible Dual of E3.10 Graph:: bipartite v = 8 e = 14 f = 2 degree seq :: [ 2^7, 14 ] E3.13 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3, Y1^4, (Y1^-1 * Y2)^2 ] Map:: R = (1, 10, 2, 13, 5, 12, 4, 9)(3, 15, 7, 16, 8, 14, 6, 11) L = (1, 3)(2, 6)(4, 7)(5, 8)(9, 11)(10, 14)(12, 15)(13, 16) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 8 f = 2 degree seq :: [ 8^2 ] E3.14 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2 ] Map:: R = (1, 9, 3, 11, 7, 15, 4, 12)(2, 10, 5, 13, 8, 16, 6, 14)(17, 18)(19, 22)(20, 21)(23, 24)(25, 26)(27, 30)(28, 29)(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) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E3.16 Graph:: simple bipartite v = 10 e = 16 f = 2 degree seq :: [ 2^8, 8^2 ] E3.15 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y1^4, Y2^4 ] Map:: non-degenerate R = (1, 9, 4, 12)(2, 10, 6, 14)(3, 11, 7, 15)(5, 13, 8, 16)(17, 18, 21, 19)(20, 23, 24, 22)(25, 27, 29, 26)(28, 30, 32, 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 ) } Outer automorphisms :: reflexible Dual of E3.17 Graph:: simple bipartite v = 8 e = 16 f = 4 degree seq :: [ 4^8 ] E3.16 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2 ] Map:: R = (1, 9, 17, 25, 3, 11, 19, 27, 7, 15, 23, 31, 4, 12, 20, 28)(2, 10, 18, 26, 5, 13, 21, 29, 8, 16, 24, 32, 6, 14, 22, 30) L = (1, 10)(2, 9)(3, 14)(4, 13)(5, 12)(6, 11)(7, 16)(8, 15)(17, 26)(18, 25)(19, 30)(20, 29)(21, 28)(22, 27)(23, 32)(24, 31) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.14 Transitivity :: VT+ Graph:: bipartite v = 2 e = 16 f = 10 degree seq :: [ 16^2 ] E3.17 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y1^4, Y2^4 ] Map:: non-degenerate R = (1, 9, 17, 25, 4, 12, 20, 28)(2, 10, 18, 26, 6, 14, 22, 30)(3, 11, 19, 27, 7, 15, 23, 31)(5, 13, 21, 29, 8, 16, 24, 32) L = (1, 10)(2, 13)(3, 9)(4, 15)(5, 11)(6, 12)(7, 16)(8, 14)(17, 27)(18, 25)(19, 29)(20, 30)(21, 26)(22, 32)(23, 28)(24, 31) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.15 Transitivity :: VT+ Graph:: bipartite v = 4 e = 16 f = 8 degree seq :: [ 8^4 ] E3.18 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x C2 (small group id <8, 2>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y2^4, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ] Map:: R = (1, 9, 2, 10)(3, 11, 5, 13)(4, 12, 6, 14)(7, 15, 8, 16)(17, 25, 19, 27, 23, 31, 20, 28)(18, 26, 21, 29, 24, 32, 22, 30) 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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.19 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y1^2, R^2, Y2^4, (Y2 * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, (Y3 * Y2^-1)^4 ] Map:: R = (1, 9, 2, 10)(3, 11, 6, 14)(4, 12, 5, 13)(7, 15, 8, 16)(17, 25, 19, 27, 23, 31, 20, 28)(18, 26, 21, 29, 24, 32, 22, 30) 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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.20 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x C2 (small group id <8, 2>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y1 * Y2^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 9, 2, 10)(3, 11, 5, 13)(4, 12, 6, 14)(7, 15, 8, 16)(17, 25, 19, 27, 18, 26, 21, 29)(20, 28, 23, 31, 22, 30, 24, 32) L = (1, 20)(2, 22)(3, 23)(4, 17)(5, 24)(6, 18)(7, 19)(8, 21)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.21 Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.21 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x C2 (small group id <8, 2>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y3, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y1, (R * Y2 * Y3)^2 ] Map:: non-degenerate R = (1, 9, 2, 10)(3, 11, 6, 14)(4, 12, 7, 15)(5, 13, 8, 16)(17, 25, 19, 27, 23, 31, 21, 29)(18, 26, 22, 30, 20, 28, 24, 32) L = (1, 20)(2, 23)(3, 24)(4, 17)(5, 22)(6, 21)(7, 18)(8, 19)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.20 Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.22 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x C2 (small group id <8, 2>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^2 * Y3, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 9, 2, 10)(3, 11, 6, 14)(4, 12, 7, 15)(5, 13, 8, 16)(17, 25, 19, 27, 20, 28, 21, 29)(18, 26, 22, 30, 23, 31, 24, 32) L = (1, 20)(2, 23)(3, 21)(4, 17)(5, 19)(6, 24)(7, 18)(8, 22)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.23 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = D8 (small group id <8, 3>) Aut = C2 x D8 (small group id <16, 11>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^2 * Y3, (R * Y1)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^2 ] Map:: non-degenerate R = (1, 9, 2, 10)(3, 11, 8, 16)(4, 12, 7, 15)(5, 13, 6, 14)(17, 25, 19, 27, 20, 28, 21, 29)(18, 26, 22, 30, 23, 31, 24, 32) L = (1, 20)(2, 23)(3, 21)(4, 17)(5, 19)(6, 24)(7, 18)(8, 22)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 6 e = 16 f = 6 degree seq :: [ 4^4, 8^2 ] E3.24 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 8}) Quotient :: edge Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^4 ] Map:: non-degenerate R = (1, 3, 4, 8, 6, 7, 2, 5)(9, 10, 14, 12)(11, 13, 15, 16) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E3.26 Transitivity :: ET+ Graph:: bipartite v = 3 e = 8 f = 1 degree seq :: [ 4^2, 8 ] E3.25 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 8, 8}) Quotient :: edge Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ F^2, T1 * T2^-2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 8, 4, 5)(9, 10, 14, 12)(11, 15, 16, 13) L = (1, 9)(2, 10)(3, 11)(4, 12)(5, 13)(6, 14)(7, 15)(8, 16) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E3.27 Transitivity :: ET+ Graph:: bipartite v = 3 e = 8 f = 1 degree seq :: [ 4^2, 8 ] E3.26 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 8}) Quotient :: loop Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^4 ] Map:: non-degenerate R = (1, 9, 3, 11, 4, 12, 8, 16, 6, 14, 7, 15, 2, 10, 5, 13) L = (1, 10)(2, 14)(3, 13)(4, 9)(5, 15)(6, 12)(7, 16)(8, 11) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.24 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 8 f = 3 degree seq :: [ 16 ] E3.27 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 8, 8}) Quotient :: loop Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ F^2, T1 * T2^-2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 9, 3, 11, 2, 10, 7, 15, 6, 14, 8, 16, 4, 12, 5, 13) L = (1, 10)(2, 14)(3, 15)(4, 9)(5, 11)(6, 12)(7, 16)(8, 13) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.25 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 8 f = 3 degree seq :: [ 16 ] E3.28 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8}) Quotient :: dipole Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y1^3 * Y3^-1, (R * Y2)^2, (Y2, Y3^-1), Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 ] Map:: R = (1, 9, 2, 10, 6, 14, 4, 12)(3, 11, 7, 15, 8, 16, 5, 13)(17, 25, 19, 27, 18, 26, 23, 31, 22, 30, 24, 32, 20, 28, 21, 29) L = (1, 20)(2, 17)(3, 21)(4, 22)(5, 24)(6, 18)(7, 19)(8, 23)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) 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 ) } Outer automorphisms :: reflexible Dual of E3.31 Graph:: bipartite v = 3 e = 16 f = 9 degree seq :: [ 8^2, 16 ] E3.29 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8}) Quotient :: dipole Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (Y3^-1, Y2^-1), Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 9, 2, 10, 6, 14, 4, 12)(3, 11, 5, 13, 7, 15, 8, 16)(17, 25, 19, 27, 20, 28, 24, 32, 22, 30, 23, 31, 18, 26, 21, 29) L = (1, 20)(2, 17)(3, 24)(4, 22)(5, 19)(6, 18)(7, 21)(8, 23)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) 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 ) } Outer automorphisms :: reflexible Dual of E3.30 Graph:: bipartite v = 3 e = 16 f = 9 degree seq :: [ 8^2, 16 ] E3.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8}) Quotient :: dipole Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ] Map:: R = (1, 9, 2, 10, 5, 13, 6, 14, 7, 15, 8, 16, 3, 11, 4, 12)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32) L = (1, 19)(2, 20)(3, 23)(4, 24)(5, 17)(6, 18)(7, 21)(8, 22)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E3.29 Graph:: bipartite v = 9 e = 16 f = 3 degree seq :: [ 2^8, 16 ] E3.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8}) Quotient :: dipole Aut^+ = C8 (small group id <8, 1>) Aut = D16 (small group id <16, 7>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3^-1, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 9, 2, 10, 3, 11, 6, 14, 7, 15, 8, 16, 5, 13, 4, 12)(17, 25)(18, 26)(19, 27)(20, 28)(21, 29)(22, 30)(23, 31)(24, 32) L = (1, 19)(2, 22)(3, 23)(4, 18)(5, 17)(6, 24)(7, 21)(8, 20)(9, 25)(10, 26)(11, 27)(12, 28)(13, 29)(14, 30)(15, 31)(16, 32) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E3.28 Graph:: bipartite v = 9 e = 16 f = 3 degree seq :: [ 2^8, 16 ] E3.32 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 9, 9}) Quotient :: edge Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 3, 7, 2, 6, 9, 4, 8, 5)(10, 11, 13)(12, 15, 17)(14, 16, 18) L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18) local type(s) :: { ( 18^3 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E3.36 Transitivity :: ET+ Graph:: bipartite v = 4 e = 9 f = 1 degree seq :: [ 3^3, 9 ] E3.33 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 9, 9}) Quotient :: edge Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1) ] Map:: non-degenerate R = (1, 3, 8, 4, 9, 7, 2, 6, 5)(10, 11, 13)(12, 15, 18)(14, 16, 17) L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18) local type(s) :: { ( 18^3 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E3.35 Transitivity :: ET+ Graph:: bipartite v = 4 e = 9 f = 1 degree seq :: [ 3^3, 9 ] E3.34 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 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 * T1)^2, (F * T2)^2, T1 * T2^4 ] Map:: non-degenerate R = (1, 3, 7, 8, 4, 2, 6, 9, 5)(10, 11, 12, 15, 16, 18, 17, 14, 13) L = (1, 10)(2, 11)(3, 12)(4, 13)(5, 14)(6, 15)(7, 16)(8, 17)(9, 18) local type(s) :: { ( 6^9 ) } Outer automorphisms :: reflexible Dual of E3.37 Transitivity :: ET+ Graph:: bipartite v = 2 e = 9 f = 3 degree seq :: [ 9^2 ] E3.35 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 9, 9}) Quotient :: loop Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 10, 3, 12, 7, 16, 2, 11, 6, 15, 9, 18, 4, 13, 8, 17, 5, 14) L = (1, 11)(2, 13)(3, 15)(4, 10)(5, 16)(6, 17)(7, 18)(8, 12)(9, 14) local type(s) :: { ( 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9 ) } Outer automorphisms :: reflexible Dual of E3.33 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 9 f = 4 degree seq :: [ 18 ] E3.36 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 9, 9}) Quotient :: loop Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1) ] Map:: non-degenerate R = (1, 10, 3, 12, 8, 17, 4, 13, 9, 18, 7, 16, 2, 11, 6, 15, 5, 14) L = (1, 11)(2, 13)(3, 15)(4, 10)(5, 16)(6, 18)(7, 17)(8, 14)(9, 12) local type(s) :: { ( 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9 ) } Outer automorphisms :: reflexible Dual of E3.32 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 9 f = 4 degree seq :: [ 18 ] E3.37 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 9, 9}) Quotient :: loop Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ F^2, T2^3, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 10, 3, 12, 5, 14)(2, 11, 7, 16, 8, 17)(4, 13, 6, 15, 9, 18) L = (1, 11)(2, 15)(3, 16)(4, 10)(5, 17)(6, 12)(7, 18)(8, 13)(9, 14) local type(s) :: { ( 9^6 ) } Outer automorphisms :: reflexible Dual of E3.34 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 9 f = 2 degree seq :: [ 6^3 ] E3.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^3, Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 9, 18)(5, 14, 7, 16, 8, 17)(19, 28, 21, 30, 26, 35, 22, 31, 27, 36, 25, 34, 20, 29, 24, 33, 23, 32) L = (1, 22)(2, 19)(3, 27)(4, 20)(5, 26)(6, 21)(7, 23)(8, 25)(9, 24)(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, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E3.42 Graph:: bipartite v = 4 e = 18 f = 10 degree seq :: [ 6^3, 18 ] E3.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, Y2^3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 10, 2, 11, 4, 13)(3, 12, 6, 15, 8, 17)(5, 14, 7, 16, 9, 18)(19, 28, 21, 30, 25, 34, 20, 29, 24, 33, 27, 36, 22, 31, 26, 35, 23, 32) L = (1, 22)(2, 19)(3, 26)(4, 20)(5, 27)(6, 21)(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, 2, 18, 2, 18, 2, 18 ) } Outer automorphisms :: reflexible Dual of E3.43 Graph:: bipartite v = 4 e = 18 f = 10 degree seq :: [ 6^3, 18 ] E3.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^4, (Y3^-1 * Y1^-1)^3 ] Map:: R = (1, 10, 2, 11, 6, 15, 9, 18, 5, 14, 3, 12, 7, 16, 8, 17, 4, 13)(19, 28, 21, 30, 20, 29, 25, 34, 24, 33, 26, 35, 27, 36, 22, 31, 23, 32) L = (1, 21)(2, 25)(3, 20)(4, 23)(5, 19)(6, 26)(7, 24)(8, 27)(9, 22)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) 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 E3.41 Graph:: bipartite v = 2 e = 18 f = 12 degree seq :: [ 18^2 ] E3.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, Y3^-2 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1^-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)(21, 30, 24, 33, 26, 35)(23, 32, 25, 34, 27, 36) L = (1, 21)(2, 24)(3, 25)(4, 26)(5, 19)(6, 27)(7, 20)(8, 23)(9, 22)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 18, 18 ), ( 18^6 ) } Outer automorphisms :: reflexible Dual of E3.40 Graph:: simple bipartite v = 12 e = 18 f = 2 degree seq :: [ 2^9, 6^3 ] E3.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, Y3 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 10, 2, 11, 6, 15, 3, 12, 7, 16, 9, 18, 5, 14, 8, 17, 4, 13)(19, 28)(20, 29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36) L = (1, 21)(2, 25)(3, 23)(4, 24)(5, 19)(6, 27)(7, 26)(8, 20)(9, 22)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E3.38 Graph:: bipartite v = 10 e = 18 f = 4 degree seq :: [ 2^9, 18 ] E3.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 9, 9}) Quotient :: dipole Aut^+ = C9 (small group id <9, 1>) Aut = D18 (small group id <18, 1>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, Y1^-2 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3 ] Map:: R = (1, 10, 2, 11, 6, 15, 5, 14, 8, 17, 9, 18, 3, 12, 7, 16, 4, 13)(19, 28)(20, 29)(21, 30)(22, 31)(23, 32)(24, 33)(25, 34)(26, 35)(27, 36) L = (1, 21)(2, 25)(3, 23)(4, 27)(5, 19)(6, 22)(7, 26)(8, 20)(9, 24)(10, 28)(11, 29)(12, 30)(13, 31)(14, 32)(15, 33)(16, 34)(17, 35)(18, 36) local type(s) :: { ( 6, 18 ), ( 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18, 6, 18 ) } Outer automorphisms :: reflexible Dual of E3.39 Graph:: bipartite v = 10 e = 18 f = 4 degree seq :: [ 2^9, 18 ] E3.44 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 3}) Quotient :: halfedge^2 Aut^+ = A4 (small group id <12, 3>) Aut = S4 (small group id <24, 12>) |r| :: 2 Presentation :: [ Y2^2, Y3^2, R^2, Y1^3, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1 * Y3 * Y1^-1, (Y3 * Y2)^2, Y1 * Y3 * Y2 * Y1^-1 * Y3 ] Map:: R = (1, 14, 2, 17, 5, 13)(3, 19, 7, 21, 9, 15)(4, 22, 10, 23, 11, 16)(6, 24, 12, 20, 8, 18) L = (1, 3)(2, 6)(4, 8)(5, 11)(7, 10)(9, 12)(13, 16)(14, 19)(15, 20)(17, 24)(18, 22)(21, 23) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 4 e = 12 f = 4 degree seq :: [ 6^4 ] E3.45 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = A4 (small group id <12, 3>) Aut = S4 (small group id <24, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, R * Y1 * R * Y2, (R * Y3)^2, (Y1 * Y2)^2, Y3 * Y1 * Y3^-1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3^-1 ] 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, 33)(29, 36)(31, 35)(32, 34)(37, 39)(38, 42)(40, 47)(41, 44)(43, 45)(46, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E3.47 Graph:: simple bipartite v = 16 e = 24 f = 4 degree seq :: [ 2^12, 6^4 ] E3.46 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 3}) Quotient :: edge^2 Aut^+ = A4 (small group id <12, 3>) Aut = C2 x A4 (small group id <24, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^2 * Y2^-1, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 4, 16)(2, 14, 5, 17)(3, 15, 6, 18)(7, 19, 12, 24)(8, 20, 9, 21)(10, 22, 11, 23)(25, 26, 27)(28, 31, 32)(29, 33, 34)(30, 35, 36)(37, 39, 38)(40, 44, 43)(41, 46, 45)(42, 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) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E3.48 Graph:: simple bipartite v = 14 e = 24 f = 6 degree seq :: [ 3^8, 4^6 ] E3.47 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = A4 (small group id <12, 3>) Aut = S4 (small group id <24, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, R * Y1 * R * Y2, (R * Y3)^2, (Y1 * Y2)^2, Y3 * Y1 * Y3^-1 * Y2, Y2 * Y1 * Y3 * Y2 * Y3^-1 ] 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, 21)(5, 24)(6, 15)(7, 23)(8, 22)(9, 16)(10, 20)(11, 19)(12, 17)(25, 39)(26, 42)(27, 37)(28, 47)(29, 44)(30, 38)(31, 45)(32, 41)(33, 43)(34, 48)(35, 40)(36, 46) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E3.45 Transitivity :: VT+ Graph:: v = 4 e = 24 f = 16 degree seq :: [ 12^4 ] E3.48 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 3}) Quotient :: loop^2 Aut^+ = A4 (small group id <12, 3>) Aut = C2 x A4 (small group id <24, 13>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^2 * Y2^-1, Y2^3, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 13, 25, 37, 4, 16, 28, 40)(2, 14, 26, 38, 5, 17, 29, 41)(3, 15, 27, 39, 6, 18, 30, 42)(7, 19, 31, 43, 12, 24, 36, 48)(8, 20, 32, 44, 9, 21, 33, 45)(10, 22, 34, 46, 11, 23, 35, 47) L = (1, 14)(2, 15)(3, 13)(4, 19)(5, 21)(6, 23)(7, 20)(8, 16)(9, 22)(10, 17)(11, 24)(12, 18)(25, 39)(26, 37)(27, 38)(28, 44)(29, 46)(30, 48)(31, 40)(32, 43)(33, 41)(34, 45)(35, 42)(36, 47) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E3.46 Transitivity :: VT+ Graph:: v = 6 e = 24 f = 14 degree seq :: [ 8^6 ] E3.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 3}) Quotient :: dipole Aut^+ = A4 (small group id <12, 3>) Aut = S4 (small group id <24, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y1^2, R^2, Y2^3, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-1)^3, (Y3 * Y2^-1)^3 ] Map:: 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, 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, 6 ), ( 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 24 f = 10 degree seq :: [ 4^6, 6^4 ] E3.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, 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 ] Map:: non-degenerate R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 8, 20)(6, 18, 10, 22)(7, 19, 11, 23)(9, 21, 12, 24)(25, 37, 27, 39)(26, 38, 29, 41)(28, 40, 31, 43)(30, 42, 33, 45)(32, 44, 35, 47)(34, 46, 36, 48) L = (1, 28)(2, 30)(3, 31)(4, 25)(5, 33)(6, 26)(7, 27)(8, 36)(9, 29)(10, 35)(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) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E3.51 Graph:: simple bipartite v = 12 e = 24 f = 8 degree seq :: [ 4^12 ] E3.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 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, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^2 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 13, 2, 14, 6, 18, 10, 22, 12, 24, 5, 17)(3, 15, 9, 21, 8, 20, 4, 16, 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, 35)(6, 33)(7, 36)(8, 26)(9, 30)(10, 27)(11, 29)(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) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E3.50 Graph:: bipartite v = 8 e = 24 f = 12 degree seq :: [ 4^6, 12^2 ] E3.52 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 6}) Quotient :: edge Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2 * T1 * T2 * T1^-1, T1^-2 * T2^3 ] Map:: non-degenerate R = (1, 3, 9, 6, 12, 5)(2, 7, 10, 4, 11, 8)(13, 14, 18, 16)(15, 20, 24, 22)(17, 19, 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) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E3.53 Transitivity :: ET+ Graph:: bipartite v = 5 e = 12 f = 3 degree seq :: [ 4^3, 6^2 ] E3.53 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 6}) Quotient :: loop Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ F^2, T2^4, T1^2 * T2^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 13, 3, 15, 6, 18, 5, 17)(2, 14, 7, 19, 4, 16, 8, 20)(9, 21, 11, 23, 10, 22, 12, 24) L = (1, 14)(2, 18)(3, 21)(4, 13)(5, 22)(6, 16)(7, 23)(8, 24)(9, 17)(10, 15)(11, 20)(12, 19) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.52 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 12 f = 5 degree seq :: [ 8^3 ] E3.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2^-1, Y2^6, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 8, 20, 12, 24, 10, 22)(5, 17, 7, 19, 9, 21, 11, 23)(25, 37, 27, 39, 33, 45, 30, 42, 36, 48, 29, 41)(26, 38, 31, 43, 34, 46, 28, 40, 35, 47, 32, 44) L = (1, 27)(2, 31)(3, 33)(4, 35)(5, 25)(6, 36)(7, 34)(8, 26)(9, 30)(10, 28)(11, 32)(12, 29)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E3.55 Graph:: bipartite v = 5 e = 24 f = 15 degree seq :: [ 8^3, 12^2 ] E3.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6}) Quotient :: dipole Aut^+ = C3 : C4 (small group id <12, 1>) Aut = (C6 x C2) : C2 (small group id <24, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, R * Y2 * Y3 * R * Y2^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3^2, (Y3^-1 * Y1^-1)^6 ] 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, 32, 44, 36, 48, 34, 46)(29, 41, 31, 43, 33, 45, 35, 47) L = (1, 27)(2, 31)(3, 33)(4, 35)(5, 25)(6, 36)(7, 34)(8, 26)(9, 30)(10, 28)(11, 32)(12, 29)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E3.54 Graph:: simple bipartite v = 15 e = 24 f = 5 degree seq :: [ 2^12, 8^3 ] E3.56 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 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 * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1) ] Map:: non-degenerate R = (1, 3, 8, 5)(2, 6, 11, 7)(4, 9, 12, 10)(13, 14, 16)(15, 18, 21)(17, 19, 22)(20, 23, 24) 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 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E3.60 Transitivity :: ET+ Graph:: simple bipartite v = 7 e = 12 f = 1 degree seq :: [ 3^4, 4^3 ] E3.57 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1, T1^-1), (T1^-1 * T2^-1)^3 ] Map:: non-degenerate R = (1, 3, 8, 2, 7, 12, 6, 11, 10, 4, 9, 5)(13, 14, 18, 16)(15, 19, 23, 21)(17, 20, 24, 22) 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) :: { ( 6^4 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E3.61 Transitivity :: ET+ Graph:: bipartite v = 4 e = 12 f = 4 degree seq :: [ 4^3, 12 ] E3.58 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 12}) Quotient :: edge Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4 ] Map:: non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 9, 11)(6, 10, 12)(13, 14, 18, 23, 17, 20, 24, 21, 15, 19, 22, 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) :: { ( 8^3 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E3.59 Transitivity :: ET+ Graph:: bipartite v = 5 e = 12 f = 3 degree seq :: [ 3^4, 12 ] E3.59 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 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 * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1) ] Map:: non-degenerate R = (1, 13, 3, 15, 8, 20, 5, 17)(2, 14, 6, 18, 11, 23, 7, 19)(4, 16, 9, 21, 12, 24, 10, 22) L = (1, 14)(2, 16)(3, 18)(4, 13)(5, 19)(6, 21)(7, 22)(8, 23)(9, 15)(10, 17)(11, 24)(12, 20) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E3.58 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 12 f = 5 degree seq :: [ 8^3 ] E3.60 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1, T1^-1), (T1^-1 * T2^-1)^3 ] Map:: non-degenerate R = (1, 13, 3, 15, 8, 20, 2, 14, 7, 19, 12, 24, 6, 18, 11, 23, 10, 22, 4, 16, 9, 21, 5, 17) L = (1, 14)(2, 18)(3, 19)(4, 13)(5, 20)(6, 16)(7, 23)(8, 24)(9, 15)(10, 17)(11, 21)(12, 22) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E3.56 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 12 f = 7 degree seq :: [ 24 ] E3.61 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 12}) Quotient :: loop Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^4 ] Map:: non-degenerate R = (1, 13, 3, 15, 5, 17)(2, 14, 7, 19, 8, 20)(4, 16, 9, 21, 11, 23)(6, 18, 10, 22, 12, 24) L = (1, 14)(2, 18)(3, 19)(4, 13)(5, 20)(6, 23)(7, 22)(8, 24)(9, 15)(10, 16)(11, 17)(12, 21) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E3.57 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 12 f = 4 degree seq :: [ 6^4 ] E3.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^12 ] Map:: R = (1, 13, 2, 14, 4, 16)(3, 15, 6, 18, 9, 21)(5, 17, 7, 19, 10, 22)(8, 20, 11, 23, 12, 24)(25, 37, 27, 39, 32, 44, 29, 41)(26, 38, 30, 42, 35, 47, 31, 43)(28, 40, 33, 45, 36, 48, 34, 46) L = (1, 28)(2, 25)(3, 33)(4, 26)(5, 34)(6, 27)(7, 29)(8, 36)(9, 30)(10, 31)(11, 32)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E3.65 Graph:: bipartite v = 7 e = 24 f = 13 degree seq :: [ 6^4, 8^3 ] E3.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^3 ] Map:: R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 11, 23, 9, 21)(5, 17, 8, 20, 12, 24, 10, 22)(25, 37, 27, 39, 32, 44, 26, 38, 31, 43, 36, 48, 30, 42, 35, 47, 34, 46, 28, 40, 33, 45, 29, 41) 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) :: { ( 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 E3.64 Graph:: bipartite v = 4 e = 24 f = 16 degree seq :: [ 8^3, 24 ] E3.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^4, (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, 28, 40)(27, 39, 30, 42, 33, 45)(29, 41, 31, 43, 34, 46)(32, 44, 36, 48, 35, 47) L = (1, 27)(2, 30)(3, 32)(4, 33)(5, 25)(6, 36)(7, 26)(8, 31)(9, 35)(10, 28)(11, 29)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E3.63 Graph:: simple bipartite v = 16 e = 24 f = 4 degree seq :: [ 2^12, 6^4 ] E3.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 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 * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3 ] Map:: R = (1, 13, 2, 14, 6, 18, 11, 23, 5, 17, 8, 20, 12, 24, 9, 21, 3, 15, 7, 19, 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, 34)(7, 32)(8, 26)(9, 35)(10, 36)(11, 28)(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) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E3.62 Graph:: bipartite v = 13 e = 24 f = 7 degree seq :: [ 2^12, 24 ] E3.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3^-1 * Y2^4 ] Map:: R = (1, 13, 2, 14, 4, 16)(3, 15, 6, 18, 9, 21)(5, 17, 7, 19, 10, 22)(8, 20, 11, 23, 12, 24)(25, 37, 27, 39, 32, 44, 34, 46, 28, 40, 33, 45, 36, 48, 31, 43, 26, 38, 30, 42, 35, 47, 29, 41) L = (1, 28)(2, 25)(3, 33)(4, 26)(5, 34)(6, 27)(7, 29)(8, 36)(9, 30)(10, 31)(11, 32)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E3.67 Graph:: bipartite v = 5 e = 24 f = 15 degree seq :: [ 6^4, 24 ] E3.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-2 * Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^12 ] Map:: R = (1, 13, 2, 14, 6, 18, 4, 16)(3, 15, 7, 19, 11, 23, 9, 21)(5, 17, 8, 20, 12, 24, 10, 22)(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, 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) :: { ( 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E3.66 Graph:: simple bipartite v = 15 e = 24 f = 5 degree seq :: [ 2^12, 8^3 ] E3.68 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 12, 12}) Quotient :: regular Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^6 ] Map:: R = (1, 2, 5, 9, 11, 7, 3, 6, 10, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 12) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 6 f = 1 degree seq :: [ 12 ] E3.69 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 12}) Quotient :: edge Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^6 * T1 ] Map:: R = (1, 3, 7, 11, 10, 6, 2, 5, 9, 12, 8, 4)(13, 14)(15, 17)(16, 18)(19, 21)(20, 22)(23, 24) L = (1, 13)(2, 14)(3, 15)(4, 16)(5, 17)(6, 18)(7, 19)(8, 20)(9, 21)(10, 22)(11, 23)(12, 24) local type(s) :: { ( 24, 24 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E3.70 Transitivity :: ET+ Graph:: bipartite v = 7 e = 12 f = 1 degree seq :: [ 2^6, 12 ] E3.70 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 12}) Quotient :: loop Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^6 * T1 ] Map:: R = (1, 13, 3, 15, 7, 19, 11, 23, 10, 22, 6, 18, 2, 14, 5, 17, 9, 21, 12, 24, 8, 20, 4, 16) L = (1, 14)(2, 13)(3, 17)(4, 18)(5, 15)(6, 16)(7, 21)(8, 22)(9, 19)(10, 20)(11, 24)(12, 23) 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 ) } Outer automorphisms :: reflexible Dual of E3.69 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 12 f = 7 degree seq :: [ 24 ] E3.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |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, Y2^6 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 13, 2, 14)(3, 15, 5, 17)(4, 16, 6, 18)(7, 19, 9, 21)(8, 20, 10, 22)(11, 23, 12, 24)(25, 37, 27, 39, 31, 43, 35, 47, 34, 46, 30, 42, 26, 38, 29, 41, 33, 45, 36, 48, 32, 44, 28, 40) L = (1, 26)(2, 25)(3, 29)(4, 30)(5, 27)(6, 28)(7, 33)(8, 34)(9, 31)(10, 32)(11, 36)(12, 35)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 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 E3.72 Graph:: bipartite v = 7 e = 24 f = 13 degree seq :: [ 4^6, 24 ] E3.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 12}) Quotient :: dipole Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^6 ] Map:: R = (1, 13, 2, 14, 5, 17, 9, 21, 11, 23, 7, 19, 3, 15, 6, 18, 10, 22, 12, 24, 8, 20, 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, 30)(3, 25)(4, 31)(5, 34)(6, 26)(7, 28)(8, 35)(9, 36)(10, 29)(11, 32)(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, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E3.71 Graph:: bipartite v = 13 e = 24 f = 7 degree seq :: [ 2^12, 24 ] E3.73 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 7, 14}) Quotient :: regular Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-7 ] Map:: R = (1, 2, 5, 9, 13, 11, 7, 3, 6, 10, 14, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 13) local type(s) :: { ( 7^14 ) } Outer automorphisms :: reflexible Dual of E3.74 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 7 f = 2 degree seq :: [ 14 ] E3.74 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 7, 14}) Quotient :: regular Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^7 ] Map:: R = (1, 2, 5, 9, 12, 8, 4)(3, 6, 10, 13, 14, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 13)(12, 14) local type(s) :: { ( 14^7 ) } Outer automorphisms :: reflexible Dual of E3.73 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 7 f = 1 degree seq :: [ 7^2 ] E3.75 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^7 ] Map:: R = (1, 3, 7, 11, 12, 8, 4)(2, 5, 9, 13, 14, 10, 6)(15, 16)(17, 19)(18, 20)(21, 23)(22, 24)(25, 27)(26, 28) L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 28, 28 ), ( 28^7 ) } Outer automorphisms :: reflexible Dual of E3.79 Transitivity :: ET+ Graph:: simple bipartite v = 9 e = 14 f = 1 degree seq :: [ 2^7, 7^2 ] E3.76 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^2, T2^-6 * T1 ] Map:: non-degenerate R = (1, 3, 9, 13, 11, 8, 2, 7, 4, 10, 14, 12, 6, 5)(15, 16, 20, 25, 28, 23, 18)(17, 21, 19, 22, 26, 27, 24) L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 4^7 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E3.80 Transitivity :: ET+ Graph:: bipartite v = 3 e = 14 f = 7 degree seq :: [ 7^2, 14 ] E3.77 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 7, 14}) Quotient :: edge Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-7 ] Map:: R = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 13)(15, 16, 19, 23, 27, 25, 21, 17, 20, 24, 28, 26, 22, 18) L = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28) local type(s) :: { ( 14, 14 ), ( 14^14 ) } Outer automorphisms :: reflexible Dual of E3.78 Transitivity :: ET+ Graph:: bipartite v = 8 e = 14 f = 2 degree seq :: [ 2^7, 14 ] E3.78 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^7 ] Map:: R = (1, 15, 3, 17, 7, 21, 11, 25, 12, 26, 8, 22, 4, 18)(2, 16, 5, 19, 9, 23, 13, 27, 14, 28, 10, 24, 6, 20) L = (1, 16)(2, 15)(3, 19)(4, 20)(5, 17)(6, 18)(7, 23)(8, 24)(9, 21)(10, 22)(11, 27)(12, 28)(13, 25)(14, 26) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E3.77 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 14 f = 8 degree seq :: [ 14^2 ] E3.79 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (T2^-1 * T1^-1)^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^2, T2^-6 * T1 ] Map:: R = (1, 15, 3, 17, 9, 23, 13, 27, 11, 25, 8, 22, 2, 16, 7, 21, 4, 18, 10, 24, 14, 28, 12, 26, 6, 20, 5, 19) L = (1, 16)(2, 20)(3, 21)(4, 15)(5, 22)(6, 25)(7, 19)(8, 26)(9, 18)(10, 17)(11, 28)(12, 27)(13, 24)(14, 23) local type(s) :: { ( 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E3.75 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 14 f = 9 degree seq :: [ 28 ] E3.80 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 7, 14}) Quotient :: loop Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-7 ] Map:: non-degenerate R = (1, 15, 3, 17)(2, 16, 6, 20)(4, 18, 7, 21)(5, 19, 10, 24)(8, 22, 11, 25)(9, 23, 14, 28)(12, 26, 13, 27) L = (1, 16)(2, 19)(3, 20)(4, 15)(5, 23)(6, 24)(7, 17)(8, 18)(9, 27)(10, 28)(11, 21)(12, 22)(13, 25)(14, 26) local type(s) :: { ( 7, 14, 7, 14 ) } Outer automorphisms :: reflexible Dual of E3.76 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 14 f = 3 degree seq :: [ 4^7 ] E3.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |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, Y2^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16)(3, 17, 5, 19)(4, 18, 6, 20)(7, 21, 9, 23)(8, 22, 10, 24)(11, 25, 13, 27)(12, 26, 14, 28)(29, 43, 31, 45, 35, 49, 39, 53, 40, 54, 36, 50, 32, 46)(30, 44, 33, 47, 37, 51, 41, 55, 42, 56, 38, 52, 34, 48) L = (1, 30)(2, 29)(3, 33)(4, 34)(5, 31)(6, 32)(7, 37)(8, 38)(9, 35)(10, 36)(11, 41)(12, 42)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E3.84 Graph:: bipartite v = 9 e = 28 f = 15 degree seq :: [ 4^7, 14^2 ] E3.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y1^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1^2, (Y3^-1 * Y1^-1)^2, Y2^-6 * Y1 ] Map:: R = (1, 15, 2, 16, 6, 20, 11, 25, 14, 28, 9, 23, 4, 18)(3, 17, 7, 21, 5, 19, 8, 22, 12, 26, 13, 27, 10, 24)(29, 43, 31, 45, 37, 51, 41, 55, 39, 53, 36, 50, 30, 44, 35, 49, 32, 46, 38, 52, 42, 56, 40, 54, 34, 48, 33, 47) L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 33)(7, 32)(8, 30)(9, 41)(10, 42)(11, 36)(12, 34)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 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 E3.83 Graph:: bipartite v = 3 e = 28 f = 21 degree seq :: [ 14^2, 28 ] E3.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^7 * Y2, (Y3^-1 * Y1^-1)^14 ] Map:: R = (1, 15)(2, 16)(3, 17)(4, 18)(5, 19)(6, 20)(7, 21)(8, 22)(9, 23)(10, 24)(11, 25)(12, 26)(13, 27)(14, 28)(29, 43, 30, 44)(31, 45, 33, 47)(32, 46, 34, 48)(35, 49, 37, 51)(36, 50, 38, 52)(39, 53, 41, 55)(40, 54, 42, 56) L = (1, 31)(2, 33)(3, 35)(4, 29)(5, 37)(6, 30)(7, 39)(8, 32)(9, 41)(10, 34)(11, 42)(12, 36)(13, 40)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14, 28 ), ( 14, 28, 14, 28 ) } Outer automorphisms :: reflexible Dual of E3.82 Graph:: simple bipartite v = 21 e = 28 f = 3 degree seq :: [ 2^14, 4^7 ] E3.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-7 ] Map:: R = (1, 15, 2, 16, 5, 19, 9, 23, 13, 27, 11, 25, 7, 21, 3, 17, 6, 20, 10, 24, 14, 28, 12, 26, 8, 22, 4, 18)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56) L = (1, 31)(2, 34)(3, 29)(4, 35)(5, 38)(6, 30)(7, 32)(8, 39)(9, 42)(10, 33)(11, 36)(12, 41)(13, 40)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E3.81 Graph:: bipartite v = 15 e = 28 f = 9 degree seq :: [ 2^14, 28 ] E3.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |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, Y2^7 * Y1, (Y3 * Y2^-1)^7 ] Map:: R = (1, 15, 2, 16)(3, 17, 5, 19)(4, 18, 6, 20)(7, 21, 9, 23)(8, 22, 10, 24)(11, 25, 13, 27)(12, 26, 14, 28)(29, 43, 31, 45, 35, 49, 39, 53, 42, 56, 38, 52, 34, 48, 30, 44, 33, 47, 37, 51, 41, 55, 40, 54, 36, 50, 32, 46) L = (1, 30)(2, 29)(3, 33)(4, 34)(5, 31)(6, 32)(7, 37)(8, 38)(9, 35)(10, 36)(11, 41)(12, 42)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E3.86 Graph:: bipartite v = 8 e = 28 f = 16 degree seq :: [ 4^7, 28 ] E3.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 7, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y1 * Y3^2 * Y1, Y3^-2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^6, Y1^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 11, 25, 14, 28, 9, 23, 4, 18)(3, 17, 7, 21, 5, 19, 8, 22, 12, 26, 13, 27, 10, 24)(29, 43)(30, 44)(31, 45)(32, 46)(33, 47)(34, 48)(35, 49)(36, 50)(37, 51)(38, 52)(39, 53)(40, 54)(41, 55)(42, 56) L = (1, 31)(2, 35)(3, 37)(4, 38)(5, 29)(6, 33)(7, 32)(8, 30)(9, 41)(10, 42)(11, 36)(12, 34)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E3.85 Graph:: simple bipartite v = 16 e = 28 f = 8 degree seq :: [ 2^14, 14^2 ] E3.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x D8 (small group id <16, 11>) Aut = C2 x C2 x D8 (small group id <32, 46>) |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)^4 ] Map:: polytopal 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, 14, 30)(15, 31, 16, 32)(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, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.88 Graph:: simple bipartite v = 16 e = 32 f = 12 degree seq :: [ 4^16 ] E3.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = C2 x D8 (small group id <16, 11>) Aut = C2 x C2 x D8 (small group id <32, 46>) |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)^2 ] Map:: polytopal non-degenerate R = (1, 17, 2, 18, 6, 22, 5, 21)(3, 19, 9, 25, 12, 28, 7, 23)(4, 20, 11, 27, 13, 29, 8, 24)(10, 26, 14, 30, 16, 32, 15, 31)(33, 49, 35, 51)(34, 50, 39, 55)(36, 52, 42, 58)(37, 53, 41, 57)(38, 54, 44, 60)(40, 56, 46, 62)(43, 59, 47, 63)(45, 61, 48, 64) L = (1, 36)(2, 40)(3, 42)(4, 33)(5, 43)(6, 45)(7, 46)(8, 34)(9, 47)(10, 35)(11, 37)(12, 48)(13, 38)(14, 39)(15, 41)(16, 44)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.87 Graph:: simple bipartite v = 12 e = 32 f = 16 degree seq :: [ 4^8, 8^4 ] E3.89 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 4}) Quotient :: edge Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 14, 8)(4, 9, 15, 11)(6, 12, 16, 13)(17, 18, 22, 20)(19, 25, 28, 23)(21, 27, 29, 24)(26, 30, 32, 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 ) } Outer automorphisms :: reflexible Dual of E3.90 Transitivity :: ET+ Graph:: simple bipartite v = 8 e = 16 f = 4 degree seq :: [ 4^8 ] E3.90 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 4}) Quotient :: loop Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 17, 3, 19, 10, 26, 5, 21)(2, 18, 7, 23, 14, 30, 8, 24)(4, 20, 9, 25, 15, 31, 11, 27)(6, 22, 12, 28, 16, 32, 13, 29) L = (1, 18)(2, 22)(3, 25)(4, 17)(5, 27)(6, 20)(7, 19)(8, 21)(9, 28)(10, 30)(11, 29)(12, 23)(13, 24)(14, 32)(15, 26)(16, 31) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.89 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 16 f = 8 degree seq :: [ 8^4 ] E3.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y3^4, Y1^4, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 8, 24, 12, 28, 10, 26)(5, 21, 7, 23, 13, 29, 11, 27)(9, 25, 14, 30, 16, 32, 15, 31)(33, 49, 35, 51, 41, 57, 37, 53)(34, 50, 39, 55, 46, 62, 40, 56)(36, 52, 43, 59, 47, 63, 42, 58)(38, 54, 44, 60, 48, 64, 45, 61) L = (1, 36)(2, 33)(3, 42)(4, 38)(5, 43)(6, 34)(7, 37)(8, 35)(9, 47)(10, 44)(11, 45)(12, 40)(13, 39)(14, 41)(15, 48)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.92 Graph:: bipartite v = 8 e = 32 f = 20 degree seq :: [ 8^8 ] E3.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 4}) Quotient :: dipole Aut^+ = C4 : C4 (small group id <16, 4>) Aut = (C4 x C2 x C2) : C2 (small group id <32, 28>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4 ] 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, 44, 60, 42, 58)(37, 53, 39, 55, 45, 61, 43, 59)(41, 57, 46, 62, 48, 64, 47, 63) L = (1, 35)(2, 39)(3, 41)(4, 43)(5, 33)(6, 44)(7, 46)(8, 34)(9, 37)(10, 36)(11, 47)(12, 48)(13, 38)(14, 40)(15, 42)(16, 45)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E3.91 Graph:: simple bipartite v = 20 e = 32 f = 8 degree seq :: [ 2^16, 8^4 ] E3.93 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 8}) Quotient :: regular Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^8 ] Map:: R = (1, 2, 5, 9, 13, 12, 8, 4)(3, 6, 10, 14, 16, 15, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 16) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 8 f = 2 degree seq :: [ 8^2 ] E3.94 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 8}) Quotient :: edge Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^8 ] Map:: R = (1, 3, 7, 11, 15, 12, 8, 4)(2, 5, 9, 13, 16, 14, 10, 6)(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) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E3.95 Transitivity :: ET+ Graph:: simple bipartite v = 10 e = 16 f = 2 degree seq :: [ 2^8, 8^2 ] E3.95 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 8}) Quotient :: loop Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1, T2^8 ] Map:: R = (1, 17, 3, 19, 7, 23, 11, 27, 15, 31, 12, 28, 8, 24, 4, 20)(2, 18, 5, 21, 9, 25, 13, 29, 16, 32, 14, 30, 10, 26, 6, 22) 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, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.94 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 16 f = 10 degree seq :: [ 16^2 ] E3.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |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, (Y3 * Y2^-1)^8 ] 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, 44, 60, 40, 56, 36, 52)(34, 50, 37, 53, 41, 57, 45, 61, 48, 64, 46, 62, 42, 58, 38, 54) 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, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E3.97 Graph:: bipartite v = 10 e = 32 f = 18 degree seq :: [ 4^8, 16^2 ] E3.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8}) Quotient :: dipole Aut^+ = C8 x C2 (small group id <16, 5>) Aut = C2 x D16 (small group id <32, 39>) |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^-8, Y1^8 ] Map:: R = (1, 17, 2, 18, 5, 21, 9, 25, 13, 29, 12, 28, 8, 24, 4, 20)(3, 19, 6, 22, 10, 26, 14, 30, 16, 32, 15, 31, 11, 27, 7, 23)(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, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E3.96 Graph:: simple bipartite v = 18 e = 32 f = 10 degree seq :: [ 2^16, 16^2 ] E3.98 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 8}) Quotient :: regular Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^2 * T2 * T1^-2 ] Map:: non-degenerate R = (1, 2, 5, 11, 16, 15, 10, 4)(3, 7, 12, 9, 14, 6, 13, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 11)(10, 13)(14, 16) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 8 f = 2 degree seq :: [ 8^2 ] E3.99 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 8}) Quotient :: edge Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-3 * T1, (T1 * T2^-1 * T1 * T2)^2 ] Map:: R = (1, 3, 8, 13, 16, 11, 10, 4)(2, 5, 12, 9, 15, 7, 14, 6)(17, 18)(19, 23)(20, 25)(21, 27)(22, 29)(24, 28)(26, 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) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E3.100 Transitivity :: ET+ Graph:: simple bipartite v = 10 e = 16 f = 2 degree seq :: [ 2^8, 8^2 ] E3.100 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 8}) Quotient :: loop Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-3 * T1, (T1 * T2^-1 * T1 * T2)^2 ] Map:: R = (1, 17, 3, 19, 8, 24, 13, 29, 16, 32, 11, 27, 10, 26, 4, 20)(2, 18, 5, 21, 12, 28, 9, 25, 15, 31, 7, 23, 14, 30, 6, 22) L = (1, 18)(2, 17)(3, 23)(4, 25)(5, 27)(6, 29)(7, 19)(8, 28)(9, 20)(10, 30)(11, 21)(12, 24)(13, 22)(14, 26)(15, 32)(16, 31) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.99 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 16 f = 10 degree seq :: [ 16^2 ] E3.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2^2)^2, (R * Y2 * Y3^-1)^2, R * Y2^-1 * R * Y1 * Y2^-1 * Y1, Y2^-2 * R * Y2 * R * Y2^-1, Y2^2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 17, 2, 18)(3, 19, 7, 23)(4, 20, 9, 25)(5, 21, 11, 27)(6, 22, 13, 29)(8, 24, 12, 28)(10, 26, 14, 30)(15, 31, 16, 32)(33, 49, 35, 51, 40, 56, 45, 61, 48, 64, 43, 59, 42, 58, 36, 52)(34, 50, 37, 53, 44, 60, 41, 57, 47, 63, 39, 55, 46, 62, 38, 54) L = (1, 34)(2, 33)(3, 39)(4, 41)(5, 43)(6, 45)(7, 35)(8, 44)(9, 36)(10, 46)(11, 37)(12, 40)(13, 38)(14, 42)(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, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E3.102 Graph:: bipartite v = 10 e = 32 f = 18 degree seq :: [ 4^8, 16^2 ] E3.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 8}) Quotient :: dipole Aut^+ = C8 : C2 (small group id <16, 6>) Aut = (C2 x D8) : C2 (small group id <32, 43>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-2 * Y3 * Y1^2, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2 ] Map:: R = (1, 17, 2, 18, 5, 21, 11, 27, 16, 32, 15, 31, 10, 26, 4, 20)(3, 19, 7, 23, 12, 28, 9, 25, 14, 30, 6, 22, 13, 29, 8, 24)(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, 41)(5, 44)(6, 34)(7, 47)(8, 43)(9, 36)(10, 45)(11, 40)(12, 37)(13, 42)(14, 48)(15, 39)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E3.101 Graph:: simple bipartite v = 18 e = 32 f = 10 degree seq :: [ 2^16, 16^2 ] E3.103 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 7}) Quotient :: edge Aut^+ = C7 : C3 (small group id <21, 1>) Aut = C7 : C3 (small group id <21, 1>) |r| :: 1 Presentation :: [ X1^3, X2^2 * X1^-1 * X2^-1 * X1, X2^2 * X1^-1 * X2^-1 * X1, (X2^-1 * X1^-1)^3, (X2 * X1^-1)^3, X2^7 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 17)(7, 18, 19)(9, 21, 11)(12, 15, 20)(22, 24, 30, 40, 38, 36, 26)(23, 27, 29, 41, 42, 34, 28)(25, 32, 37, 35, 31, 39, 33) L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42) local type(s) :: { ( 6^3 ), ( 6^7 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 10 e = 21 f = 7 degree seq :: [ 3^7, 7^3 ] E3.104 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 7}) Quotient :: loop Aut^+ = C7 : C3 (small group id <21, 1>) Aut = C7 : C3 (small group id <21, 1>) |r| :: 1 Presentation :: [ X1^3, X2^3, X2 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1, (X2 * X1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 22, 2, 23, 4, 25)(3, 24, 8, 29, 9, 30)(5, 26, 12, 33, 13, 34)(6, 27, 14, 35, 15, 36)(7, 28, 16, 37, 17, 38)(10, 31, 18, 39, 20, 41)(11, 32, 21, 42, 19, 40) L = (1, 24)(2, 27)(3, 26)(4, 31)(5, 22)(6, 28)(7, 23)(8, 39)(9, 37)(10, 32)(11, 25)(12, 38)(13, 36)(14, 29)(15, 42)(16, 40)(17, 41)(18, 35)(19, 30)(20, 33)(21, 34) local type(s) :: { ( 3, 7, 3, 7, 3, 7 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 7 e = 21 f = 10 degree seq :: [ 6^7 ] E3.105 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {3, 3, 7}) Quotient :: loop Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, F * T1 * F * T2, T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 6, 7)(4, 10, 11)(8, 18, 14)(9, 16, 19)(12, 17, 20)(13, 15, 21)(22, 23, 25)(24, 29, 30)(26, 33, 34)(27, 35, 36)(28, 37, 38)(31, 39, 41)(32, 42, 40) L = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42) local type(s) :: { ( 14^3 ) } Outer automorphisms :: reflexible Dual of E3.106 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 14 e = 21 f = 3 degree seq :: [ 3^14 ] E3.106 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {3, 3, 7}) Quotient :: edge Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, T2^2 * T1^-1 * T2^-1 * T1, F * T1 * T2 * F * T1^-1, T2^2 * T1^-1 * T2^-1 * T1, (T2^-1 * T1^-1)^3, (T2 * T1^-1)^3, T2^7 ] Map:: polytopal non-degenerate R = (1, 22, 3, 24, 9, 30, 19, 40, 17, 38, 15, 36, 5, 26)(2, 23, 6, 27, 8, 29, 20, 41, 21, 42, 13, 34, 7, 28)(4, 25, 11, 32, 16, 37, 14, 35, 10, 31, 18, 39, 12, 33) L = (1, 23)(2, 25)(3, 29)(4, 22)(5, 34)(6, 37)(7, 39)(8, 31)(9, 42)(10, 24)(11, 30)(12, 36)(13, 35)(14, 26)(15, 41)(16, 38)(17, 27)(18, 40)(19, 28)(20, 33)(21, 32) local type(s) :: { ( 3^14 ) } Outer automorphisms :: reflexible Dual of E3.105 Transitivity :: ET+ VT+ Graph:: v = 3 e = 21 f = 14 degree seq :: [ 14^3 ] E3.107 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3^-2 * Y1^-1, Y1^-1 * Y2^-1 * Y3^5 ] Map:: polytopal non-degenerate R = (1, 22, 4, 25, 15, 36, 20, 41, 21, 42, 11, 32, 7, 28)(2, 23, 8, 29, 6, 27, 12, 33, 17, 38, 19, 40, 10, 31)(3, 24, 5, 26, 18, 39, 9, 30, 14, 35, 16, 37, 13, 34)(43, 44, 47)(45, 53, 54)(46, 48, 58)(49, 61, 56)(50, 51, 63)(52, 55, 62)(57, 59, 60)(64, 66, 69)(65, 70, 72)(67, 77, 80)(68, 73, 78)(71, 83, 79)(74, 76, 82)(75, 84, 81) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 4^3 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E3.110 Graph:: simple bipartite v = 17 e = 42 f = 21 degree seq :: [ 3^14, 14^3 ] E3.108 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ Y3, R^2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1, (Y2 * Y1^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal R = (1, 22)(2, 23)(3, 24)(4, 25)(5, 26)(6, 27)(7, 28)(8, 29)(9, 30)(10, 31)(11, 32)(12, 33)(13, 34)(14, 35)(15, 36)(16, 37)(17, 38)(18, 39)(19, 40)(20, 41)(21, 42)(43, 44, 46)(45, 50, 51)(47, 54, 55)(48, 56, 57)(49, 58, 59)(52, 60, 62)(53, 63, 61)(64, 66, 68)(65, 69, 70)(67, 73, 74)(71, 81, 77)(72, 79, 82)(75, 80, 83)(76, 78, 84) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28, 28 ), ( 28^3 ) } Outer automorphisms :: reflexible Dual of E3.109 Graph:: simple bipartite v = 35 e = 42 f = 3 degree seq :: [ 2^21, 3^14 ] E3.109 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^-1 * Y3^-2 * Y1^-1, Y1^-1 * Y2^-1 * Y3^5 ] Map:: R = (1, 22, 43, 64, 4, 25, 46, 67, 15, 36, 57, 78, 20, 41, 62, 83, 21, 42, 63, 84, 11, 32, 53, 74, 7, 28, 49, 70)(2, 23, 44, 65, 8, 29, 50, 71, 6, 27, 48, 69, 12, 33, 54, 75, 17, 38, 59, 80, 19, 40, 61, 82, 10, 31, 52, 73)(3, 24, 45, 66, 5, 26, 47, 68, 18, 39, 60, 81, 9, 30, 51, 72, 14, 35, 56, 77, 16, 37, 58, 79, 13, 34, 55, 76) L = (1, 23)(2, 26)(3, 32)(4, 27)(5, 22)(6, 37)(7, 40)(8, 30)(9, 42)(10, 34)(11, 33)(12, 24)(13, 41)(14, 28)(15, 38)(16, 25)(17, 39)(18, 36)(19, 35)(20, 31)(21, 29)(43, 66)(44, 70)(45, 69)(46, 77)(47, 73)(48, 64)(49, 72)(50, 83)(51, 65)(52, 78)(53, 76)(54, 84)(55, 82)(56, 80)(57, 68)(58, 71)(59, 67)(60, 75)(61, 74)(62, 79)(63, 81) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E3.108 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 35 degree seq :: [ 28^3 ] E3.110 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ Y3, R^2, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1, (Y2 * Y1^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal non-degenerate R = (1, 22, 43, 64)(2, 23, 44, 65)(3, 24, 45, 66)(4, 25, 46, 67)(5, 26, 47, 68)(6, 27, 48, 69)(7, 28, 49, 70)(8, 29, 50, 71)(9, 30, 51, 72)(10, 31, 52, 73)(11, 32, 53, 74)(12, 33, 54, 75)(13, 34, 55, 76)(14, 35, 56, 77)(15, 36, 57, 78)(16, 37, 58, 79)(17, 38, 59, 80)(18, 39, 60, 81)(19, 40, 61, 82)(20, 41, 62, 83)(21, 42, 63, 84) L = (1, 23)(2, 25)(3, 29)(4, 22)(5, 33)(6, 35)(7, 37)(8, 30)(9, 24)(10, 39)(11, 42)(12, 34)(13, 26)(14, 36)(15, 27)(16, 38)(17, 28)(18, 41)(19, 32)(20, 31)(21, 40)(43, 66)(44, 69)(45, 68)(46, 73)(47, 64)(48, 70)(49, 65)(50, 81)(51, 79)(52, 74)(53, 67)(54, 80)(55, 78)(56, 71)(57, 84)(58, 82)(59, 83)(60, 77)(61, 72)(62, 75)(63, 76) local type(s) :: { ( 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E3.107 Transitivity :: VT+ Graph:: simple v = 21 e = 42 f = 17 degree seq :: [ 4^21 ] E3.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 3}) 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, (Y3 * Y1)^3, (Y1 * Y2)^4, Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 ] 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, 15, 39)(11, 35, 19, 43)(13, 37, 17, 41)(14, 38, 22, 46)(16, 40, 24, 48)(18, 42, 23, 47)(20, 44, 21, 45)(49, 73, 51, 75)(50, 74, 53, 77)(52, 76, 56, 80)(54, 78, 59, 83)(55, 79, 61, 85)(57, 81, 64, 88)(58, 82, 65, 89)(60, 84, 68, 92)(62, 86, 69, 93)(63, 87, 71, 95)(66, 90, 72, 96)(67, 91, 70, 94) L = (1, 52)(2, 54)(3, 56)(4, 49)(5, 59)(6, 50)(7, 62)(8, 51)(9, 60)(10, 66)(11, 53)(12, 57)(13, 69)(14, 55)(15, 70)(16, 68)(17, 72)(18, 58)(19, 71)(20, 64)(21, 61)(22, 63)(23, 67)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.114 Graph:: simple bipartite v = 24 e = 48 f = 20 degree seq :: [ 4^24 ] E3.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 3}) 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, (Y1 * Y2)^3, (Y3 * Y1)^3 ] 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, 17, 41)(13, 37, 19, 43)(15, 39, 20, 44)(16, 40, 21, 45)(18, 42, 22, 46)(23, 47, 24, 48)(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, 66, 90)(61, 85, 64, 88)(62, 86, 68, 92)(65, 89, 70, 94)(67, 91, 71, 95)(69, 93, 72, 96) L = (1, 52)(2, 54)(3, 56)(4, 49)(5, 59)(6, 50)(7, 61)(8, 51)(9, 60)(10, 64)(11, 53)(12, 57)(13, 55)(14, 67)(15, 66)(16, 58)(17, 69)(18, 63)(19, 62)(20, 71)(21, 65)(22, 72)(23, 68)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.113 Graph:: simple bipartite v = 24 e = 48 f = 20 degree seq :: [ 4^24 ] E3.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 3}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 10, 34)(4, 28, 11, 35, 7, 31)(6, 30, 13, 37, 15, 39)(9, 33, 18, 42, 17, 41)(12, 36, 20, 44, 16, 40)(14, 38, 22, 46, 21, 45)(19, 43, 23, 47, 24, 48)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 57, 81)(53, 77, 60, 84)(55, 79, 62, 86)(56, 80, 64, 88)(58, 82, 61, 85)(59, 83, 67, 91)(63, 87, 68, 92)(65, 89, 71, 95)(66, 90, 69, 93)(70, 94, 72, 96) L = (1, 52)(2, 55)(3, 57)(4, 49)(5, 59)(6, 62)(7, 50)(8, 65)(9, 51)(10, 66)(11, 53)(12, 67)(13, 69)(14, 54)(15, 70)(16, 71)(17, 56)(18, 58)(19, 60)(20, 72)(21, 61)(22, 63)(23, 64)(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) :: { ( 4^4 ), ( 4^6 ) } Outer automorphisms :: reflexible Dual of E3.112 Graph:: simple bipartite v = 20 e = 48 f = 24 degree seq :: [ 4^12, 6^8 ] E3.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 3}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2, (Y2 * Y1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 10, 34)(4, 28, 11, 35, 7, 31)(6, 30, 13, 37, 15, 39)(9, 33, 18, 42, 17, 41)(12, 36, 21, 45, 22, 46)(14, 38, 16, 40, 24, 48)(19, 43, 20, 44, 23, 47)(49, 73, 51, 75)(50, 74, 54, 78)(52, 76, 57, 81)(53, 77, 60, 84)(55, 79, 62, 86)(56, 80, 64, 88)(58, 82, 67, 91)(59, 83, 68, 92)(61, 85, 71, 95)(63, 87, 65, 89)(66, 90, 69, 93)(70, 94, 72, 96) L = (1, 52)(2, 55)(3, 57)(4, 49)(5, 59)(6, 62)(7, 50)(8, 65)(9, 51)(10, 66)(11, 53)(12, 68)(13, 72)(14, 54)(15, 64)(16, 63)(17, 56)(18, 58)(19, 69)(20, 60)(21, 67)(22, 71)(23, 70)(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) :: { ( 4^4 ), ( 4^6 ) } Outer automorphisms :: reflexible Dual of E3.111 Graph:: simple bipartite v = 20 e = 48 f = 24 degree seq :: [ 4^12, 6^8 ] E3.115 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 4, 4}) Quotient :: edge Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T2^4, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 3, 9, 5)(2, 6, 14, 7)(4, 10, 18, 11)(8, 15, 22, 16)(12, 17, 23, 19)(13, 20, 24, 21)(25, 26, 28)(27, 32, 31)(29, 34, 36)(30, 37, 35)(33, 41, 40)(38, 39, 45)(42, 44, 43)(46, 47, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 8^3 ), ( 8^4 ) } Outer automorphisms :: reflexible Dual of E3.116 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 24 f = 6 degree seq :: [ 3^8, 4^6 ] E3.116 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 4, 4}) Quotient :: loop Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T2^4, (T2^-1 * T1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 25, 3, 27, 9, 33, 5, 29)(2, 26, 6, 30, 14, 38, 7, 31)(4, 28, 10, 34, 18, 42, 11, 35)(8, 32, 15, 39, 22, 46, 16, 40)(12, 36, 17, 41, 23, 47, 19, 43)(13, 37, 20, 44, 24, 48, 21, 45) L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 34)(6, 37)(7, 27)(8, 31)(9, 41)(10, 36)(11, 30)(12, 29)(13, 35)(14, 39)(15, 45)(16, 33)(17, 40)(18, 44)(19, 42)(20, 43)(21, 38)(22, 47)(23, 48)(24, 46) local type(s) :: { ( 3, 4, 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E3.115 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 24 f = 14 degree seq :: [ 8^6 ] E3.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4 ] Map:: R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 7, 31)(5, 29, 10, 34, 12, 36)(6, 30, 13, 37, 11, 35)(9, 33, 17, 41, 16, 40)(14, 38, 15, 39, 21, 45)(18, 42, 20, 44, 19, 43)(22, 46, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 53, 77)(50, 74, 54, 78, 62, 86, 55, 79)(52, 76, 58, 82, 66, 90, 59, 83)(56, 80, 63, 87, 70, 94, 64, 88)(60, 84, 65, 89, 71, 95, 67, 91)(61, 85, 68, 92, 72, 96, 69, 93) L = (1, 52)(2, 49)(3, 55)(4, 50)(5, 60)(6, 59)(7, 56)(8, 51)(9, 64)(10, 53)(11, 61)(12, 58)(13, 54)(14, 69)(15, 62)(16, 65)(17, 57)(18, 67)(19, 68)(20, 66)(21, 63)(22, 72)(23, 70)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.118 Graph:: bipartite v = 14 e = 48 f = 30 degree seq :: [ 6^8, 8^6 ] E3.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4}) Quotient :: dipole Aut^+ = S4 (small group id <24, 12>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (Y1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 16, 40, 8, 32)(5, 29, 10, 34, 18, 42, 12, 36)(7, 31, 15, 39, 21, 45, 14, 38)(11, 35, 13, 37, 20, 44, 19, 43)(17, 41, 23, 47, 24, 48, 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, 53)(4, 58)(5, 49)(6, 61)(7, 56)(8, 50)(9, 65)(10, 59)(11, 52)(12, 57)(13, 62)(14, 54)(15, 70)(16, 63)(17, 60)(18, 71)(19, 66)(20, 72)(21, 68)(22, 64)(23, 67)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E3.117 Graph:: simple bipartite v = 30 e = 48 f = 14 degree seq :: [ 2^24, 8^6 ] E3.119 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 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^-1 * T1 * T2^2 * T1, T2^6, (T2^-1 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 9, 21, 15, 5)(2, 6, 10, 23, 19, 7)(4, 11, 17, 24, 13, 12)(8, 20, 22, 18, 16, 14)(25, 26, 28)(27, 32, 34)(29, 37, 38)(30, 40, 41)(31, 39, 42)(33, 35, 46)(36, 43, 44)(45, 47, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 6^3 ), ( 6^6 ) } Outer automorphisms :: reflexible Dual of E3.120 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 24 f = 8 degree seq :: [ 3^8, 6^4 ] E3.120 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 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, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 ] Map:: polytopal non-degenerate R = (1, 25, 3, 27, 5, 29)(2, 26, 6, 30, 7, 31)(4, 28, 10, 34, 11, 35)(8, 32, 14, 38, 18, 42)(9, 33, 19, 43, 20, 44)(12, 36, 15, 39, 23, 47)(13, 37, 17, 41, 22, 46)(16, 40, 21, 45, 24, 48) L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 36)(6, 38)(7, 40)(8, 33)(9, 27)(10, 42)(11, 44)(12, 37)(13, 29)(14, 39)(15, 30)(16, 41)(17, 31)(18, 45)(19, 47)(20, 46)(21, 34)(22, 35)(23, 48)(24, 43) local type(s) :: { ( 3, 6, 3, 6, 3, 6 ) } Outer automorphisms :: reflexible Dual of E3.119 Transitivity :: ET+ VT+ AT Graph:: simple v = 8 e = 24 f = 12 degree seq :: [ 6^8 ] E3.121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^2 * Y1, Y2^6, (Y3^-1 * Y1^-1)^3 ] Map:: R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 10, 34)(5, 29, 13, 37, 14, 38)(6, 30, 16, 40, 17, 41)(7, 31, 15, 39, 18, 42)(9, 33, 11, 35, 22, 46)(12, 36, 19, 43, 20, 44)(21, 45, 23, 47, 24, 48)(49, 73, 51, 75, 57, 81, 69, 93, 63, 87, 53, 77)(50, 74, 54, 78, 58, 82, 71, 95, 67, 91, 55, 79)(52, 76, 59, 83, 65, 89, 72, 96, 61, 85, 60, 84)(56, 80, 68, 92, 70, 94, 66, 90, 64, 88, 62, 86) 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) :: { ( 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E3.122 Graph:: bipartite v = 12 e = 48 f = 32 degree seq :: [ 6^8, 12^4 ] E3.122 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 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, Y3^-1 * Y2 * R * Y2^-1 * R, Y2 * Y3^-2 * Y2 * Y3, (Y3 * Y2^-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, 57, 81, 65, 89)(55, 79, 66, 90, 67, 91)(59, 83, 64, 88, 70, 94)(60, 84, 71, 95, 63, 87)(68, 92, 69, 93, 72, 96) L = (1, 51)(2, 54)(3, 57)(4, 59)(5, 49)(6, 64)(7, 50)(8, 68)(9, 69)(10, 66)(11, 56)(12, 52)(13, 58)(14, 55)(15, 53)(16, 72)(17, 71)(18, 65)(19, 60)(20, 67)(21, 63)(22, 61)(23, 70)(24, 62)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12 ), ( 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E3.121 Graph:: simple bipartite v = 32 e = 48 f = 12 degree seq :: [ 2^24, 6^8 ] E3.123 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 6}) Quotient :: regular Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1^-2 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 22, 18, 8)(6, 13, 24, 21, 17, 14)(9, 19, 16, 12, 23, 20) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 15)(14, 19)(18, 20)(23, 24) local type(s) :: { ( 6^6 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 4 e = 12 f = 4 degree seq :: [ 6^4 ] E3.124 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 6}) Quotient :: edge Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^6, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^2 * T1 * T2^-1 * T1 * T2^-1 ] Map:: R = (1, 3, 8, 18, 10, 4)(2, 5, 12, 22, 14, 6)(7, 15, 23, 21, 13, 16)(9, 19, 11, 17, 24, 20)(25, 26)(27, 31)(28, 33)(29, 35)(30, 37)(32, 41)(34, 45)(36, 39)(38, 44)(40, 43)(42, 46)(47, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 12, 12 ), ( 12^6 ) } Outer automorphisms :: reflexible Dual of E3.125 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 24 f = 4 degree seq :: [ 2^12, 6^4 ] E3.125 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 6}) Quotient :: loop Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^6, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^2 * T1 * T2^-1 * T1 * T2^-1 ] Map:: R = (1, 25, 3, 27, 8, 32, 18, 42, 10, 34, 4, 28)(2, 26, 5, 29, 12, 36, 22, 46, 14, 38, 6, 30)(7, 31, 15, 39, 23, 47, 21, 45, 13, 37, 16, 40)(9, 33, 19, 43, 11, 35, 17, 41, 24, 48, 20, 44) L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 35)(6, 37)(7, 27)(8, 41)(9, 28)(10, 45)(11, 29)(12, 39)(13, 30)(14, 44)(15, 36)(16, 43)(17, 32)(18, 46)(19, 40)(20, 38)(21, 34)(22, 42)(23, 48)(24, 47) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E3.124 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 24 f = 16 degree seq :: [ 12^4 ] E3.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-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, 17, 41)(10, 34, 21, 45)(12, 36, 15, 39)(14, 38, 20, 44)(16, 40, 19, 43)(18, 42, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 56, 80, 66, 90, 58, 82, 52, 76)(50, 74, 53, 77, 60, 84, 70, 94, 62, 86, 54, 78)(55, 79, 63, 87, 71, 95, 69, 93, 61, 85, 64, 88)(57, 81, 67, 91, 59, 83, 65, 89, 72, 96, 68, 92) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 63)(13, 54)(14, 68)(15, 60)(16, 67)(17, 56)(18, 70)(19, 64)(20, 62)(21, 58)(22, 66)(23, 72)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E3.127 Graph:: bipartite v = 16 e = 48 f = 28 degree seq :: [ 4^12, 12^4 ] E3.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 6}) Quotient :: dipole Aut^+ = C2 x A4 (small group id <24, 13>) Aut = C2 x S4 (small group id <48, 48>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^6, Y1 * Y3 * Y1^-2 * Y3 * Y1 * Y3 ] Map:: R = (1, 25, 2, 26, 5, 29, 11, 35, 10, 34, 4, 28)(3, 27, 7, 31, 15, 39, 22, 46, 18, 42, 8, 32)(6, 30, 13, 37, 24, 48, 21, 45, 17, 41, 14, 38)(9, 33, 19, 43, 16, 40, 12, 36, 23, 47, 20, 44)(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, 64)(8, 65)(9, 52)(10, 69)(11, 70)(12, 53)(13, 63)(14, 67)(15, 61)(16, 55)(17, 56)(18, 68)(19, 62)(20, 66)(21, 58)(22, 59)(23, 72)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E3.126 Graph:: simple bipartite v = 28 e = 48 f = 16 degree seq :: [ 2^24, 12^4 ] E3.128 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 12}) Quotient :: regular Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^2 * T2)^2, (T1 * T2)^4, T1^-2 * T2 * T1 * T2 * T1^-3 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 16, 23, 17, 24, 19, 10, 4)(3, 7, 15, 21, 14, 6, 13, 9, 18, 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, 20)(19, 22) local type(s) :: { ( 4^12 ) } Outer automorphisms :: reflexible Dual of E3.129 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 12 f = 6 degree seq :: [ 12^2 ] E3.129 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 12}) Quotient :: regular Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |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)^3 ] 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, 23, 22, 24) 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) local type(s) :: { ( 12^4 ) } Outer automorphisms :: reflexible Dual of E3.128 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 12 f = 2 degree seq :: [ 4^6 ] E3.130 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 12}) Quotient :: edge Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1)^2, (T1 * T2^-1 * T1 * T2)^3 ] 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, 26)(27, 31)(28, 33)(29, 34)(30, 36)(32, 35)(37, 41)(38, 42)(39, 43)(40, 44)(45, 47)(46, 48) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 24, 24 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E3.134 Transitivity :: ET+ Graph:: simple bipartite v = 18 e = 24 f = 2 degree seq :: [ 2^12, 4^6 ] E3.131 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 12}) Quotient :: edge Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-6 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 22, 14, 6, 13, 21, 20, 12, 5)(2, 7, 15, 23, 17, 9, 4, 11, 19, 24, 16, 8)(25, 26, 30, 28)(27, 33, 37, 32)(29, 35, 38, 31)(34, 40, 45, 41)(36, 39, 46, 43)(42, 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) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E3.135 Transitivity :: ET+ Graph:: bipartite v = 8 e = 24 f = 12 degree seq :: [ 4^6, 12^2 ] E3.132 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 12}) Quotient :: edge Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1 * T2 * T1^-3 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 20)(19, 22)(25, 26, 29, 35, 44, 40, 47, 41, 48, 43, 34, 28)(27, 31, 39, 45, 38, 30, 37, 33, 42, 46, 36, 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) :: { ( 8, 8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E3.133 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 24 f = 6 degree seq :: [ 2^12, 12^2 ] E3.133 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 12}) Quotient :: loop Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1)^2, (T1 * T2^-1 * T1 * T2)^3 ] Map:: R = (1, 25, 3, 27, 8, 32, 4, 28)(2, 26, 5, 29, 11, 35, 6, 30)(7, 31, 13, 37, 9, 33, 14, 38)(10, 34, 15, 39, 12, 36, 16, 40)(17, 41, 21, 45, 18, 42, 22, 46)(19, 43, 23, 47, 20, 44, 24, 48) L = (1, 26)(2, 25)(3, 31)(4, 33)(5, 34)(6, 36)(7, 27)(8, 35)(9, 28)(10, 29)(11, 32)(12, 30)(13, 41)(14, 42)(15, 43)(16, 44)(17, 37)(18, 38)(19, 39)(20, 40)(21, 47)(22, 48)(23, 45)(24, 46) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E3.132 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 24 f = 14 degree seq :: [ 8^6 ] E3.134 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 12}) Quotient :: loop Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-6 * T1^-1 ] Map:: R = (1, 25, 3, 27, 10, 34, 18, 42, 22, 46, 14, 38, 6, 30, 13, 37, 21, 45, 20, 44, 12, 36, 5, 29)(2, 26, 7, 31, 15, 39, 23, 47, 17, 41, 9, 33, 4, 28, 11, 35, 19, 43, 24, 48, 16, 40, 8, 32) L = (1, 26)(2, 30)(3, 33)(4, 25)(5, 35)(6, 28)(7, 29)(8, 27)(9, 37)(10, 40)(11, 38)(12, 39)(13, 32)(14, 31)(15, 46)(16, 45)(17, 34)(18, 47)(19, 36)(20, 48)(21, 41)(22, 43)(23, 44)(24, 42) 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 ) } Outer automorphisms :: reflexible Dual of E3.130 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 24 f = 18 degree seq :: [ 24^2 ] E3.135 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 12}) Quotient :: loop Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^2 * T2)^2, (T2 * T1)^4, T1^-2 * T2 * T1 * T2 * T1^-3 ] Map:: polytopal non-degenerate R = (1, 25, 3, 27)(2, 26, 6, 30)(4, 28, 9, 33)(5, 29, 12, 36)(7, 31, 16, 40)(8, 32, 17, 41)(10, 34, 15, 39)(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, 39)(8, 27)(9, 42)(10, 28)(11, 44)(12, 32)(13, 33)(14, 30)(15, 45)(16, 47)(17, 48)(18, 46)(19, 34)(20, 40)(21, 38)(22, 36)(23, 41)(24, 43) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E3.131 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 12 e = 24 f = 8 degree seq :: [ 4^12 ] E3.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) 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, 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^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 10, 34)(6, 30, 12, 36)(8, 32, 11, 35)(13, 37, 17, 41)(14, 38, 18, 42)(15, 39, 19, 43)(16, 40, 20, 44)(21, 45, 23, 47)(22, 46, 24, 48)(49, 73, 51, 75, 56, 80, 52, 76)(50, 74, 53, 77, 59, 83, 54, 78)(55, 79, 61, 85, 57, 81, 62, 86)(58, 82, 63, 87, 60, 84, 64, 88)(65, 89, 69, 93, 66, 90, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 58)(6, 60)(7, 51)(8, 59)(9, 52)(10, 53)(11, 56)(12, 54)(13, 65)(14, 66)(15, 67)(16, 68)(17, 61)(18, 62)(19, 63)(20, 64)(21, 71)(22, 72)(23, 69)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E3.139 Graph:: bipartite v = 18 e = 48 f = 26 degree seq :: [ 4^12, 8^6 ] E3.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, Y2^5 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 8, 32)(5, 29, 11, 35, 14, 38, 7, 31)(10, 34, 16, 40, 21, 45, 17, 41)(12, 36, 15, 39, 22, 46, 19, 43)(18, 42, 23, 47, 20, 44, 24, 48)(49, 73, 51, 75, 58, 82, 66, 90, 70, 94, 62, 86, 54, 78, 61, 85, 69, 93, 68, 92, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 71, 95, 65, 89, 57, 81, 52, 76, 59, 83, 67, 91, 72, 96, 64, 88, 56, 80) L = (1, 51)(2, 55)(3, 58)(4, 59)(5, 49)(6, 61)(7, 63)(8, 50)(9, 52)(10, 66)(11, 67)(12, 53)(13, 69)(14, 54)(15, 71)(16, 56)(17, 57)(18, 70)(19, 72)(20, 60)(21, 68)(22, 62)(23, 65)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 2, 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 E3.138 Graph:: bipartite v = 8 e = 48 f = 36 degree seq :: [ 8^6, 24^2 ] E3.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) 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, (Y3^2 * Y2)^2, (Y3^-1 * Y2)^4, Y3^3 * Y2 * Y3^-3 * Y2, (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, 62, 86)(58, 82, 60, 84)(63, 87, 68, 92)(64, 88, 71, 95)(65, 89, 70, 94)(66, 90, 69, 93)(67, 91, 72, 96) L = (1, 51)(2, 53)(3, 56)(4, 49)(5, 60)(6, 50)(7, 63)(8, 65)(9, 66)(10, 52)(11, 68)(12, 70)(13, 71)(14, 54)(15, 57)(16, 55)(17, 69)(18, 72)(19, 58)(20, 61)(21, 59)(22, 64)(23, 67)(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) :: { ( 8, 24 ), ( 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E3.137 Graph:: simple bipartite v = 36 e = 48 f = 8 degree seq :: [ 2^24, 4^12 ] E3.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y1^2 * Y3)^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1 * Y3 * Y1^-3 ] Map:: R = (1, 25, 2, 26, 5, 29, 11, 35, 20, 44, 16, 40, 23, 47, 17, 41, 24, 48, 19, 43, 10, 34, 4, 28)(3, 27, 7, 31, 15, 39, 21, 45, 14, 38, 6, 30, 13, 37, 9, 33, 18, 42, 22, 46, 12, 36, 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, 64)(8, 65)(9, 52)(10, 63)(11, 69)(12, 53)(13, 71)(14, 72)(15, 58)(16, 55)(17, 56)(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, 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 E3.136 Graph:: simple bipartite v = 26 e = 48 f = 18 degree seq :: [ 2^24, 24^2 ] E3.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) 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^-2 * Y1)^2, Y2^3 * Y1 * Y2^-3 * Y1, (Y3 * Y2^-1)^4 ] Map:: R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 11, 35)(6, 30, 13, 37)(8, 32, 14, 38)(10, 34, 12, 36)(15, 39, 20, 44)(16, 40, 23, 47)(17, 41, 22, 46)(18, 42, 21, 45)(19, 43, 24, 48)(49, 73, 51, 75, 56, 80, 65, 89, 69, 93, 59, 83, 68, 92, 61, 85, 71, 95, 67, 91, 58, 82, 52, 76)(50, 74, 53, 77, 60, 84, 70, 94, 64, 88, 55, 79, 63, 87, 57, 81, 66, 90, 72, 96, 62, 86, 54, 78) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 62)(9, 52)(10, 60)(11, 53)(12, 58)(13, 54)(14, 56)(15, 68)(16, 71)(17, 70)(18, 69)(19, 72)(20, 63)(21, 66)(22, 65)(23, 64)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E3.141 Graph:: bipartite v = 14 e = 48 f = 30 degree seq :: [ 4^12, 24^2 ] E3.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 12}) Quotient :: dipole Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |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^-6 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 8, 32)(5, 29, 11, 35, 14, 38, 7, 31)(10, 34, 16, 40, 21, 45, 17, 41)(12, 36, 15, 39, 22, 46, 19, 43)(18, 42, 23, 47, 20, 44, 24, 48)(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, 59)(5, 49)(6, 61)(7, 63)(8, 50)(9, 52)(10, 66)(11, 67)(12, 53)(13, 69)(14, 54)(15, 71)(16, 56)(17, 57)(18, 70)(19, 72)(20, 60)(21, 68)(22, 62)(23, 65)(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, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E3.140 Graph:: simple bipartite v = 30 e = 48 f = 14 degree seq :: [ 2^24, 8^6 ] E3.142 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 8}) Quotient :: regular Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, T1^8 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 15, 25, 28, 22, 12, 8)(6, 13, 9, 18, 27, 29, 21, 14)(16, 23, 17, 24, 30, 32, 31, 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, 28)(22, 30)(25, 31)(29, 32) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.143 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 16 f = 8 degree seq :: [ 8^4 ] E3.143 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 8}) Quotient :: regular Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^8 ] 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, 31, 30, 32) 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) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E3.142 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 16 f = 4 degree seq :: [ 4^8 ] E3.144 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^8 ] 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, 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, 63)(62, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E3.148 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 32 f = 4 degree seq :: [ 2^16, 4^8 ] E3.145 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 20, 12, 5)(2, 7, 15, 23, 30, 24, 16, 8)(4, 11, 19, 27, 31, 25, 17, 9)(6, 13, 21, 28, 32, 29, 22, 14)(33, 34, 38, 36)(35, 41, 45, 40)(37, 43, 46, 39)(42, 48, 53, 49)(44, 47, 54, 51)(50, 57, 60, 56)(52, 59, 61, 55)(58, 62, 64, 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 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.149 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 16 degree seq :: [ 4^8, 8^4 ] E3.146 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^8 ] 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, 28)(22, 30)(25, 31)(29, 32)(33, 34, 37, 43, 52, 51, 42, 36)(35, 39, 47, 57, 60, 54, 44, 40)(38, 45, 41, 50, 59, 61, 53, 46)(48, 55, 49, 56, 62, 64, 63, 58) 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 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E3.147 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 32 f = 8 degree seq :: [ 2^16, 8^4 ] E3.147 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^8 ] 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, 63)(30, 64)(31, 61)(32, 62) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.146 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 20 degree seq :: [ 8^8 ] E3.148 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^8 ] Map:: R = (1, 33, 3, 35, 10, 42, 18, 50, 26, 58, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 30, 62, 24, 56, 16, 48, 8, 40)(4, 36, 11, 43, 19, 51, 27, 59, 31, 63, 25, 57, 17, 49, 9, 41)(6, 38, 13, 45, 21, 53, 28, 60, 32, 64, 29, 61, 22, 54, 14, 46) 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, 60)(26, 62)(27, 61)(28, 56)(29, 55)(30, 64)(31, 58)(32, 63) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E3.144 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 24 degree seq :: [ 16^4 ] E3.149 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, T1^8 ] 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, 28, 60)(22, 54, 30, 62)(25, 57, 31, 63)(29, 61, 32, 64) 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, 51)(21, 46)(22, 44)(23, 49)(24, 62)(25, 60)(26, 48)(27, 61)(28, 54)(29, 53)(30, 64)(31, 58)(32, 63) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.145 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 16 e = 32 f = 12 degree seq :: [ 4^16 ] E3.150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |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)^8 ] 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, 31, 63)(30, 62, 32, 64)(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, 95)(30, 96)(31, 93)(32, 94)(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, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E3.153 Graph:: bipartite v = 24 e = 64 f = 36 degree seq :: [ 4^16, 8^8 ] E3.151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, Y2^8 ] 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, 28, 60, 24, 56)(20, 52, 27, 59, 29, 61, 23, 55)(26, 58, 30, 62, 32, 64, 31, 63)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 84, 116, 76, 108, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 94, 126, 88, 120, 80, 112, 72, 104)(68, 100, 75, 107, 83, 115, 91, 123, 95, 127, 89, 121, 81, 113, 73, 105)(70, 102, 77, 109, 85, 117, 92, 124, 96, 128, 93, 125, 86, 118, 78, 110) 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, 92)(22, 78)(23, 94)(24, 80)(25, 81)(26, 84)(27, 95)(28, 96)(29, 86)(30, 88)(31, 89)(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, 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 E3.152 Graph:: bipartite v = 12 e = 64 f = 48 degree seq :: [ 8^8, 16^4 ] E3.152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y2)^2, Y3^8, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^8 ] 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, 92, 124)(88, 120, 94, 126)(90, 122, 93, 125)(95, 127, 96, 128) 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, 93)(23, 94)(24, 78)(25, 80)(26, 83)(27, 95)(28, 85)(29, 88)(30, 96)(31, 89)(32, 92)(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, 16 ), ( 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E3.151 Graph:: simple bipartite v = 48 e = 64 f = 12 degree seq :: [ 2^32, 4^16 ] E3.153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |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, Y1^8 ] Map:: polytopal R = (1, 33, 2, 34, 5, 37, 11, 43, 20, 52, 19, 51, 10, 42, 4, 36)(3, 35, 7, 39, 15, 47, 25, 57, 28, 60, 22, 54, 12, 44, 8, 40)(6, 38, 13, 45, 9, 41, 18, 50, 27, 59, 29, 61, 21, 53, 14, 46)(16, 48, 23, 55, 17, 49, 24, 56, 30, 62, 32, 64, 31, 63, 26, 58)(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, 92)(21, 75)(22, 94)(23, 77)(24, 78)(25, 95)(26, 82)(27, 83)(28, 84)(29, 96)(30, 86)(31, 89)(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) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.150 Graph:: simple bipartite v = 36 e = 64 f = 24 degree seq :: [ 2^32, 16^4 ] E3.154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, Y2^8, (Y3 * Y2^-1)^4 ] 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, 28, 60)(24, 56, 30, 62)(26, 58, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 72, 104, 81, 113, 90, 122, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 93, 125, 88, 120, 78, 110, 70, 102)(71, 103, 79, 111, 73, 105, 82, 114, 91, 123, 95, 127, 89, 121, 80, 112)(75, 107, 84, 116, 77, 109, 87, 119, 94, 126, 96, 128, 92, 124, 85, 117) 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, 92)(23, 80)(24, 94)(25, 81)(26, 93)(27, 83)(28, 86)(29, 90)(30, 88)(31, 96)(32, 95)(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 ) } Outer automorphisms :: reflexible Dual of E3.155 Graph:: bipartite v = 20 e = 64 f = 40 degree seq :: [ 4^16, 16^4 ] E3.155 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C8 x C2) : C2 (small group id <32, 9>) Aut = (C2 x C2 x D8) : C2 (small group id <64, 128>) |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)^8 ] Map:: polytopal 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, 28, 60, 24, 56)(20, 52, 27, 59, 29, 61, 23, 55)(26, 58, 30, 62, 32, 64, 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, 92)(22, 78)(23, 94)(24, 80)(25, 81)(26, 84)(27, 95)(28, 96)(29, 86)(30, 88)(31, 89)(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) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E3.154 Graph:: simple bipartite v = 40 e = 64 f = 20 degree seq :: [ 2^32, 8^8 ] E3.156 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 8}) Quotient :: regular Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, (T1^-1 * T2)^4 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 29, 27, 17, 8)(6, 13, 21, 30, 28, 18, 9, 14)(15, 25, 31, 24, 32, 23, 16, 26) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 28)(20, 29)(22, 31)(26, 30)(27, 32) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.157 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 16 f = 8 degree seq :: [ 8^4 ] E3.157 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 8}) Quotient :: regular Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 26, 17)(10, 18, 27, 19)(14, 21, 28, 24)(15, 22, 29, 25)(23, 30, 32, 31) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 24)(17, 25)(18, 28)(19, 29)(20, 30)(26, 31)(27, 32) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E3.156 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 8 e = 16 f = 4 degree seq :: [ 4^8 ] E3.158 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 23, 14)(9, 16, 26, 17)(10, 18, 27, 19)(12, 21, 30, 22)(15, 24, 31, 25)(20, 28, 32, 29)(33, 34)(35, 39)(36, 41)(37, 42)(38, 44)(40, 47)(43, 52)(45, 50)(46, 53)(48, 51)(49, 54)(55, 60)(56, 59)(57, 62)(58, 61)(63, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E3.162 Transitivity :: ET+ Graph:: simple bipartite v = 24 e = 32 f = 4 degree seq :: [ 2^16, 4^8 ] E3.159 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, T2 * T1^-1 * T2^-3 * T1^-1, T1^-1 * T2 * T1^-1 * T2^5 ] Map:: polytopal non-degenerate R = (1, 3, 10, 23, 32, 19, 14, 5)(2, 7, 17, 11, 25, 29, 20, 8)(4, 12, 24, 28, 26, 13, 22, 9)(6, 15, 27, 18, 31, 21, 30, 16)(33, 34, 38, 36)(35, 41, 53, 43)(37, 45, 50, 39)(40, 51, 60, 47)(42, 49, 59, 56)(44, 48, 61, 55)(46, 52, 62, 54)(57, 63, 58, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.163 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 32 f = 16 degree seq :: [ 4^8, 8^4 ] E3.160 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 8}) Quotient :: edge Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T2 * T1^-1)^4, T1^8 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 28)(20, 29)(22, 31)(26, 30)(27, 32)(33, 34, 37, 43, 52, 51, 42, 36)(35, 39, 44, 54, 61, 59, 49, 40)(38, 45, 53, 62, 60, 50, 41, 46)(47, 57, 63, 56, 64, 55, 48, 58) 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 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E3.161 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 32 f = 8 degree seq :: [ 2^16, 8^4 ] E3.161 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 33, 3, 35, 8, 40, 4, 36)(2, 34, 5, 37, 11, 43, 6, 38)(7, 39, 13, 45, 23, 55, 14, 46)(9, 41, 16, 48, 26, 58, 17, 49)(10, 42, 18, 50, 27, 59, 19, 51)(12, 44, 21, 53, 30, 62, 22, 54)(15, 47, 24, 56, 31, 63, 25, 57)(20, 52, 28, 60, 32, 64, 29, 61) L = (1, 34)(2, 33)(3, 39)(4, 41)(5, 42)(6, 44)(7, 35)(8, 47)(9, 36)(10, 37)(11, 52)(12, 38)(13, 50)(14, 53)(15, 40)(16, 51)(17, 54)(18, 45)(19, 48)(20, 43)(21, 46)(22, 49)(23, 60)(24, 59)(25, 62)(26, 61)(27, 56)(28, 55)(29, 58)(30, 57)(31, 64)(32, 63) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.160 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 20 degree seq :: [ 8^8 ] E3.162 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, T2 * T1^-1 * T2^-3 * T1^-1, T1^-1 * T2 * T1^-1 * T2^5 ] Map:: R = (1, 33, 3, 35, 10, 42, 23, 55, 32, 64, 19, 51, 14, 46, 5, 37)(2, 34, 7, 39, 17, 49, 11, 43, 25, 57, 29, 61, 20, 52, 8, 40)(4, 36, 12, 44, 24, 56, 28, 60, 26, 58, 13, 45, 22, 54, 9, 41)(6, 38, 15, 47, 27, 59, 18, 50, 31, 63, 21, 53, 30, 62, 16, 48) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 45)(6, 36)(7, 37)(8, 51)(9, 53)(10, 49)(11, 35)(12, 48)(13, 50)(14, 52)(15, 40)(16, 61)(17, 59)(18, 39)(19, 60)(20, 62)(21, 43)(22, 46)(23, 44)(24, 42)(25, 63)(26, 64)(27, 56)(28, 47)(29, 55)(30, 54)(31, 58)(32, 57) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E3.158 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 32 f = 24 degree seq :: [ 16^4 ] E3.163 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 8}) Quotient :: loop Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, (T2 * T1^-1)^4, T1^8 ] Map:: polytopal non-degenerate R = (1, 33, 3, 35)(2, 34, 6, 38)(4, 36, 9, 41)(5, 37, 12, 44)(7, 39, 15, 47)(8, 40, 16, 48)(10, 42, 17, 49)(11, 43, 21, 53)(13, 45, 23, 55)(14, 46, 24, 56)(18, 50, 25, 57)(19, 51, 28, 60)(20, 52, 29, 61)(22, 54, 31, 63)(26, 58, 30, 62)(27, 59, 32, 64) L = (1, 34)(2, 37)(3, 39)(4, 33)(5, 43)(6, 45)(7, 44)(8, 35)(9, 46)(10, 36)(11, 52)(12, 54)(13, 53)(14, 38)(15, 57)(16, 58)(17, 40)(18, 41)(19, 42)(20, 51)(21, 62)(22, 61)(23, 48)(24, 64)(25, 63)(26, 47)(27, 49)(28, 50)(29, 59)(30, 60)(31, 56)(32, 55) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.159 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 16 e = 32 f = 12 degree seq :: [ 4^16 ] E3.164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |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 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 10, 42)(6, 38, 12, 44)(8, 40, 15, 47)(11, 43, 20, 52)(13, 45, 18, 50)(14, 46, 21, 53)(16, 48, 19, 51)(17, 49, 22, 54)(23, 55, 28, 60)(24, 56, 27, 59)(25, 57, 30, 62)(26, 58, 29, 61)(31, 63, 32, 64)(65, 97, 67, 99, 72, 104, 68, 100)(66, 98, 69, 101, 75, 107, 70, 102)(71, 103, 77, 109, 87, 119, 78, 110)(73, 105, 80, 112, 90, 122, 81, 113)(74, 106, 82, 114, 91, 123, 83, 115)(76, 108, 85, 117, 94, 126, 86, 118)(79, 111, 88, 120, 95, 127, 89, 121)(84, 116, 92, 124, 96, 128, 93, 125) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 74)(6, 76)(7, 67)(8, 79)(9, 68)(10, 69)(11, 84)(12, 70)(13, 82)(14, 85)(15, 72)(16, 83)(17, 86)(18, 77)(19, 80)(20, 75)(21, 78)(22, 81)(23, 92)(24, 91)(25, 94)(26, 93)(27, 88)(28, 87)(29, 90)(30, 89)(31, 96)(32, 95)(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, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E3.167 Graph:: bipartite v = 24 e = 64 f = 36 degree seq :: [ 4^16, 8^8 ] E3.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y1^-1 * Y2^2 * Y1 * Y2^-2, Y2^8 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 21, 53, 11, 43)(5, 37, 13, 45, 18, 50, 7, 39)(8, 40, 19, 51, 28, 60, 15, 47)(10, 42, 17, 49, 27, 59, 24, 56)(12, 44, 16, 48, 29, 61, 23, 55)(14, 46, 20, 52, 30, 62, 22, 54)(25, 57, 31, 63, 26, 58, 32, 64)(65, 97, 67, 99, 74, 106, 87, 119, 96, 128, 83, 115, 78, 110, 69, 101)(66, 98, 71, 103, 81, 113, 75, 107, 89, 121, 93, 125, 84, 116, 72, 104)(68, 100, 76, 108, 88, 120, 92, 124, 90, 122, 77, 109, 86, 118, 73, 105)(70, 102, 79, 111, 91, 123, 82, 114, 95, 127, 85, 117, 94, 126, 80, 112) L = (1, 67)(2, 71)(3, 74)(4, 76)(5, 65)(6, 79)(7, 81)(8, 66)(9, 68)(10, 87)(11, 89)(12, 88)(13, 86)(14, 69)(15, 91)(16, 70)(17, 75)(18, 95)(19, 78)(20, 72)(21, 94)(22, 73)(23, 96)(24, 92)(25, 93)(26, 77)(27, 82)(28, 90)(29, 84)(30, 80)(31, 85)(32, 83)(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 ) } Outer automorphisms :: reflexible Dual of E3.166 Graph:: bipartite v = 12 e = 64 f = 48 degree seq :: [ 8^8, 16^4 ] E3.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3 * Y2)^4, (Y3^-1 * Y1^-1)^8 ] 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, 76, 108)(74, 106, 78, 110)(79, 111, 87, 119)(80, 112, 90, 122)(81, 113, 89, 121)(82, 114, 84, 116)(83, 115, 92, 124)(85, 117, 94, 126)(86, 118, 93, 125)(88, 120, 96, 128)(91, 123, 95, 127) L = (1, 67)(2, 69)(3, 72)(4, 65)(5, 76)(6, 66)(7, 79)(8, 81)(9, 80)(10, 68)(11, 84)(12, 86)(13, 85)(14, 70)(15, 89)(16, 71)(17, 91)(18, 73)(19, 74)(20, 93)(21, 75)(22, 95)(23, 77)(24, 78)(25, 94)(26, 96)(27, 83)(28, 82)(29, 90)(30, 92)(31, 88)(32, 87)(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, 16 ), ( 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E3.165 Graph:: simple bipartite v = 48 e = 64 f = 12 degree seq :: [ 2^32, 4^16 ] E3.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1^-1)^4, Y1^8 ] Map:: polytopal R = (1, 33, 2, 34, 5, 37, 11, 43, 20, 52, 19, 51, 10, 42, 4, 36)(3, 35, 7, 39, 12, 44, 22, 54, 29, 61, 27, 59, 17, 49, 8, 40)(6, 38, 13, 45, 21, 53, 30, 62, 28, 60, 18, 50, 9, 41, 14, 46)(15, 47, 25, 57, 31, 63, 24, 56, 32, 64, 23, 55, 16, 48, 26, 58)(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, 79)(8, 80)(9, 68)(10, 81)(11, 85)(12, 69)(13, 87)(14, 88)(15, 71)(16, 72)(17, 74)(18, 89)(19, 92)(20, 93)(21, 75)(22, 95)(23, 77)(24, 78)(25, 82)(26, 94)(27, 96)(28, 83)(29, 84)(30, 90)(31, 86)(32, 91)(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 ) } Outer automorphisms :: reflexible Dual of E3.164 Graph:: simple bipartite v = 36 e = 64 f = 24 degree seq :: [ 2^32, 16^4 ] E3.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y3 * Y2^-1)^4, Y2^8 ] Map:: R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 9, 41)(5, 37, 11, 43)(6, 38, 13, 45)(8, 40, 12, 44)(10, 42, 14, 46)(15, 47, 23, 55)(16, 48, 26, 58)(17, 49, 25, 57)(18, 50, 20, 52)(19, 51, 28, 60)(21, 53, 30, 62)(22, 54, 29, 61)(24, 56, 32, 64)(27, 59, 31, 63)(65, 97, 67, 99, 72, 104, 81, 113, 91, 123, 83, 115, 74, 106, 68, 100)(66, 98, 69, 101, 76, 108, 86, 118, 95, 127, 88, 120, 78, 110, 70, 102)(71, 103, 79, 111, 89, 121, 94, 126, 92, 124, 82, 114, 73, 105, 80, 112)(75, 107, 84, 116, 93, 125, 90, 122, 96, 128, 87, 119, 77, 109, 85, 117) L = (1, 66)(2, 65)(3, 71)(4, 73)(5, 75)(6, 77)(7, 67)(8, 76)(9, 68)(10, 78)(11, 69)(12, 72)(13, 70)(14, 74)(15, 87)(16, 90)(17, 89)(18, 84)(19, 92)(20, 82)(21, 94)(22, 93)(23, 79)(24, 96)(25, 81)(26, 80)(27, 95)(28, 83)(29, 86)(30, 85)(31, 91)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.169 Graph:: bipartite v = 20 e = 64 f = 40 degree seq :: [ 4^16, 16^4 ] E3.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 8}) Quotient :: dipole Aut^+ = (C4 x C4) : C2 (small group id <32, 11>) Aut = ((C4 x C4) : C2) : C2 (small group id <64, 134>) |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 * Y3^-1, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 21, 53, 11, 43)(5, 37, 13, 45, 18, 50, 7, 39)(8, 40, 19, 51, 28, 60, 15, 47)(10, 42, 17, 49, 27, 59, 24, 56)(12, 44, 16, 48, 29, 61, 23, 55)(14, 46, 20, 52, 30, 62, 22, 54)(25, 57, 31, 63, 26, 58, 32, 64)(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, 76)(5, 65)(6, 79)(7, 81)(8, 66)(9, 68)(10, 87)(11, 89)(12, 88)(13, 86)(14, 69)(15, 91)(16, 70)(17, 75)(18, 95)(19, 78)(20, 72)(21, 94)(22, 73)(23, 96)(24, 92)(25, 93)(26, 77)(27, 82)(28, 90)(29, 84)(30, 80)(31, 85)(32, 83)(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, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E3.168 Graph:: simple bipartite v = 40 e = 64 f = 20 degree seq :: [ 2^32, 8^8 ] E3.170 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 3, 4}) Quotient :: edge Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, T2^4, (T1^-1 * T2^-1)^3, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^3 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 5)(2, 6, 16, 7)(4, 11, 26, 12)(8, 20, 37, 21)(10, 18, 35, 24)(13, 29, 46, 27)(14, 30, 31, 15)(17, 28, 42, 34)(19, 36, 43, 25)(22, 39, 45, 40)(23, 38, 32, 41)(33, 47, 44, 48)(49, 50, 52)(51, 56, 58)(53, 61, 62)(54, 63, 65)(55, 66, 67)(57, 70, 71)(59, 73, 75)(60, 76, 68)(64, 80, 81)(69, 86, 84)(72, 90, 87)(74, 92, 93)(77, 89, 82)(78, 91, 88)(79, 95, 85)(83, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6^3 ), ( 6^4 ) } Outer automorphisms :: reflexible Dual of E3.171 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 48 f = 16 degree seq :: [ 3^16, 4^12 ] E3.171 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 3, 4}) Quotient :: loop Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^4 ] Map:: polyhedral non-degenerate R = (1, 49, 3, 51, 5, 53)(2, 50, 6, 54, 7, 55)(4, 52, 10, 58, 11, 59)(8, 56, 18, 66, 19, 67)(9, 57, 16, 64, 20, 68)(12, 60, 25, 73, 22, 70)(13, 61, 26, 74, 27, 75)(14, 62, 28, 76, 29, 77)(15, 63, 23, 71, 30, 78)(17, 65, 31, 79, 32, 80)(21, 69, 38, 86, 39, 87)(24, 72, 40, 88, 33, 81)(34, 82, 36, 84, 46, 94)(35, 83, 48, 96, 44, 92)(37, 85, 47, 95, 41, 89)(42, 90, 43, 91, 45, 93) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 60)(6, 62)(7, 64)(8, 57)(9, 51)(10, 69)(11, 71)(12, 61)(13, 53)(14, 63)(15, 54)(16, 65)(17, 55)(18, 81)(19, 74)(20, 84)(21, 70)(22, 58)(23, 72)(24, 59)(25, 89)(26, 83)(27, 91)(28, 75)(29, 79)(30, 93)(31, 92)(32, 95)(33, 82)(34, 66)(35, 67)(36, 85)(37, 68)(38, 80)(39, 88)(40, 96)(41, 90)(42, 73)(43, 76)(44, 77)(45, 94)(46, 78)(47, 86)(48, 87) local type(s) :: { ( 3, 4, 3, 4, 3, 4 ) } Outer automorphisms :: reflexible Dual of E3.170 Transitivity :: ET+ VT+ AT Graph:: simple v = 16 e = 48 f = 28 degree seq :: [ 6^16 ] E3.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4}) Quotient :: dipole Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y1^-1 * Y2^-1)^3, (Y2 * Y1^-1)^3, (Y3^-1 * Y1^-1)^3 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 15, 63, 17, 65)(7, 55, 18, 66, 19, 67)(9, 57, 22, 70, 23, 71)(11, 59, 25, 73, 27, 75)(12, 60, 28, 76, 20, 68)(16, 64, 32, 80, 33, 81)(21, 69, 38, 86, 36, 84)(24, 72, 42, 90, 39, 87)(26, 74, 44, 92, 45, 93)(29, 77, 41, 89, 34, 82)(30, 78, 43, 91, 40, 88)(31, 79, 47, 95, 37, 85)(35, 83, 48, 96, 46, 94)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 112, 160, 103, 151)(100, 148, 107, 155, 122, 170, 108, 156)(104, 152, 116, 164, 133, 181, 117, 165)(106, 154, 114, 162, 131, 179, 120, 168)(109, 157, 125, 173, 142, 190, 123, 171)(110, 158, 126, 174, 127, 175, 111, 159)(113, 161, 124, 172, 138, 186, 130, 178)(115, 163, 132, 180, 139, 187, 121, 169)(118, 166, 135, 183, 141, 189, 136, 184)(119, 167, 134, 182, 128, 176, 137, 185)(129, 177, 143, 191, 140, 188, 144, 192) L = (1, 99)(2, 102)(3, 105)(4, 107)(5, 97)(6, 112)(7, 98)(8, 116)(9, 101)(10, 114)(11, 122)(12, 100)(13, 125)(14, 126)(15, 110)(16, 103)(17, 124)(18, 131)(19, 132)(20, 133)(21, 104)(22, 135)(23, 134)(24, 106)(25, 115)(26, 108)(27, 109)(28, 138)(29, 142)(30, 127)(31, 111)(32, 137)(33, 143)(34, 113)(35, 120)(36, 139)(37, 117)(38, 128)(39, 141)(40, 118)(41, 119)(42, 130)(43, 121)(44, 144)(45, 136)(46, 123)(47, 140)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 6, 2, 6, 2, 6 ), ( 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E3.173 Graph:: bipartite v = 28 e = 96 f = 64 degree seq :: [ 6^16, 8^12 ] E3.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4}) Quotient :: dipole Aut^+ = (C4 x C4) : C3 (small group id <48, 3>) Aut = ((C4 x C4) : C3) : C2 (small group id <96, 64>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1)^3, (Y3 * Y2^-1)^3, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 100, 148)(99, 147, 104, 152, 106, 154)(101, 149, 109, 157, 110, 158)(102, 150, 111, 159, 113, 161)(103, 151, 114, 162, 115, 163)(105, 153, 118, 166, 119, 167)(107, 155, 121, 169, 123, 171)(108, 156, 124, 172, 116, 164)(112, 160, 128, 176, 129, 177)(117, 165, 134, 182, 132, 180)(120, 168, 138, 186, 135, 183)(122, 170, 140, 188, 141, 189)(125, 173, 137, 185, 130, 178)(126, 174, 139, 187, 136, 184)(127, 175, 143, 191, 133, 181)(131, 179, 144, 192, 142, 190) L = (1, 99)(2, 102)(3, 105)(4, 107)(5, 97)(6, 112)(7, 98)(8, 116)(9, 101)(10, 114)(11, 122)(12, 100)(13, 125)(14, 126)(15, 110)(16, 103)(17, 124)(18, 131)(19, 132)(20, 133)(21, 104)(22, 135)(23, 134)(24, 106)(25, 115)(26, 108)(27, 109)(28, 138)(29, 142)(30, 127)(31, 111)(32, 137)(33, 143)(34, 113)(35, 120)(36, 139)(37, 117)(38, 128)(39, 141)(40, 118)(41, 119)(42, 130)(43, 121)(44, 144)(45, 136)(46, 123)(47, 140)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8 ), ( 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E3.172 Graph:: simple bipartite v = 64 e = 96 f = 28 degree seq :: [ 2^48, 6^16 ] E3.174 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 6}) Quotient :: regular Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^2 * T2 * T1^-3 * T2 * T1, (T1^-1 * T2)^4, (T2 * T1^-2 * T2 * T1)^2 ] 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, 30, 41, 33, 36, 31)(17, 32, 40, 29, 38, 26)(27, 39, 34, 37, 44, 35)(42, 46, 43, 47, 48, 45) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 29)(18, 33)(19, 34)(20, 30)(23, 35)(24, 36)(25, 37)(28, 40)(31, 42)(32, 43)(38, 45)(39, 46)(41, 47)(44, 48) local type(s) :: { ( 4^6 ) } Outer automorphisms :: reflexible Dual of E3.175 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 24 f = 12 degree seq :: [ 6^8 ] E3.175 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 6}) Quotient :: regular Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2 * T1^-2 * T2 * T1^-1)^2, (T2 * T1 * T2 * T1^-2)^2, (T1 * T2)^6 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 33, 25)(15, 26, 32, 27)(21, 35, 30, 36)(22, 37, 29, 38)(23, 39, 44, 34)(40, 45, 43, 48)(41, 47, 42, 46) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 14)(8, 15)(11, 21)(12, 22)(13, 23)(16, 29)(17, 30)(18, 32)(19, 33)(20, 34)(24, 40)(25, 41)(26, 42)(27, 43)(28, 39)(31, 44)(35, 45)(36, 46)(37, 47)(38, 48) local type(s) :: { ( 6^4 ) } Outer automorphisms :: reflexible Dual of E3.174 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 12 e = 24 f = 8 degree seq :: [ 4^12 ] E3.176 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2 * T1 * T2^-2 * T1)^2, (T2^-2 * T1 * T2^-1 * T1)^2, (T2 * T1)^6, (T2^-1 * T1 * T2 * T1 * T2^-1 * T1)^2 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 30, 40)(25, 41, 28, 42)(31, 44, 38, 45)(33, 46, 36, 47)(49, 50)(51, 55)(52, 57)(53, 58)(54, 60)(56, 63)(59, 68)(61, 71)(62, 73)(64, 76)(65, 78)(66, 79)(67, 81)(69, 84)(70, 86)(72, 83)(74, 85)(75, 80)(77, 82)(87, 92)(88, 95)(89, 94)(90, 93)(91, 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) :: { ( 12, 12 ), ( 12^4 ) } Outer automorphisms :: reflexible Dual of E3.180 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 48 f = 8 degree seq :: [ 2^24, 4^12 ] E3.177 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1 * T2)^2, T2^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 14, 5)(2, 7, 17, 34, 20, 8)(4, 12, 26, 39, 22, 9)(6, 15, 29, 43, 32, 16)(11, 25, 13, 28, 40, 23)(18, 35, 19, 36, 46, 33)(21, 37, 47, 41, 27, 38)(30, 44, 31, 45, 48, 42)(49, 50, 54, 52)(51, 57, 69, 59)(53, 61, 66, 55)(56, 67, 78, 63)(58, 71, 84, 68)(60, 64, 79, 75)(62, 74, 89, 76)(65, 81, 93, 80)(70, 77, 90, 85)(72, 82, 91, 87)(73, 86, 92, 83)(88, 95, 96, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4^4 ), ( 4^6 ) } Outer automorphisms :: reflexible Dual of E3.181 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 48 f = 24 degree seq :: [ 4^12, 6^8 ] E3.178 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 6}) Quotient :: edge Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-3)^2, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-2)^2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 22)(13, 26)(14, 27)(15, 29)(18, 33)(19, 34)(20, 30)(23, 35)(24, 36)(25, 37)(28, 40)(31, 42)(32, 43)(38, 45)(39, 46)(41, 47)(44, 48)(49, 50, 53, 59, 58, 52)(51, 55, 63, 70, 66, 56)(54, 61, 73, 69, 76, 62)(57, 67, 72, 60, 71, 68)(64, 78, 89, 81, 84, 79)(65, 80, 88, 77, 86, 74)(75, 87, 82, 85, 92, 83)(90, 94, 91, 95, 96, 93) 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 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E3.179 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 48 f = 12 degree seq :: [ 2^24, 6^8 ] E3.179 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2 * T1 * T2^-2 * T1)^2, (T2^-2 * T1 * T2^-1 * T1)^2, (T2 * T1)^6, (T2^-1 * T1 * T2 * T1 * T2^-1 * T1)^2 ] Map:: R = (1, 49, 3, 51, 8, 56, 4, 52)(2, 50, 5, 53, 11, 59, 6, 54)(7, 55, 13, 61, 24, 72, 14, 62)(9, 57, 16, 64, 29, 77, 17, 65)(10, 58, 18, 66, 32, 80, 19, 67)(12, 60, 21, 69, 37, 85, 22, 70)(15, 63, 26, 74, 43, 91, 27, 75)(20, 68, 34, 82, 48, 96, 35, 83)(23, 71, 39, 87, 30, 78, 40, 88)(25, 73, 41, 89, 28, 76, 42, 90)(31, 79, 44, 92, 38, 86, 45, 93)(33, 81, 46, 94, 36, 84, 47, 95) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 58)(6, 60)(7, 51)(8, 63)(9, 52)(10, 53)(11, 68)(12, 54)(13, 71)(14, 73)(15, 56)(16, 76)(17, 78)(18, 79)(19, 81)(20, 59)(21, 84)(22, 86)(23, 61)(24, 83)(25, 62)(26, 85)(27, 80)(28, 64)(29, 82)(30, 65)(31, 66)(32, 75)(33, 67)(34, 77)(35, 72)(36, 69)(37, 74)(38, 70)(39, 92)(40, 95)(41, 94)(42, 93)(43, 96)(44, 87)(45, 90)(46, 89)(47, 88)(48, 91) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E3.178 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 32 degree seq :: [ 8^12 ] E3.180 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1 * T2)^2, T2^6 ] Map:: R = (1, 49, 3, 51, 10, 58, 24, 72, 14, 62, 5, 53)(2, 50, 7, 55, 17, 65, 34, 82, 20, 68, 8, 56)(4, 52, 12, 60, 26, 74, 39, 87, 22, 70, 9, 57)(6, 54, 15, 63, 29, 77, 43, 91, 32, 80, 16, 64)(11, 59, 25, 73, 13, 61, 28, 76, 40, 88, 23, 71)(18, 66, 35, 83, 19, 67, 36, 84, 46, 94, 33, 81)(21, 69, 37, 85, 47, 95, 41, 89, 27, 75, 38, 86)(30, 78, 44, 92, 31, 79, 45, 93, 48, 96, 42, 90) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 61)(6, 52)(7, 53)(8, 67)(9, 69)(10, 71)(11, 51)(12, 64)(13, 66)(14, 74)(15, 56)(16, 79)(17, 81)(18, 55)(19, 78)(20, 58)(21, 59)(22, 77)(23, 84)(24, 82)(25, 86)(26, 89)(27, 60)(28, 62)(29, 90)(30, 63)(31, 75)(32, 65)(33, 93)(34, 91)(35, 73)(36, 68)(37, 70)(38, 92)(39, 72)(40, 95)(41, 76)(42, 85)(43, 87)(44, 83)(45, 80)(46, 88)(47, 96)(48, 94) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E3.176 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 36 degree seq :: [ 12^8 ] E3.181 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 6}) Quotient :: loop Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, (T2 * T1^-3)^2, (T2 * T1^-1)^4, (T2 * T1 * T2 * T1^-2)^2 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 17, 65)(10, 58, 21, 69)(11, 59, 22, 70)(13, 61, 26, 74)(14, 62, 27, 75)(15, 63, 29, 77)(18, 66, 33, 81)(19, 67, 34, 82)(20, 68, 30, 78)(23, 71, 35, 83)(24, 72, 36, 84)(25, 73, 37, 85)(28, 76, 40, 88)(31, 79, 42, 90)(32, 80, 43, 91)(38, 86, 45, 93)(39, 87, 46, 94)(41, 89, 47, 95)(44, 92, 48, 96) L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 67)(10, 52)(11, 58)(12, 71)(13, 73)(14, 54)(15, 70)(16, 78)(17, 80)(18, 56)(19, 72)(20, 57)(21, 76)(22, 66)(23, 68)(24, 60)(25, 69)(26, 65)(27, 87)(28, 62)(29, 86)(30, 89)(31, 64)(32, 88)(33, 84)(34, 85)(35, 75)(36, 79)(37, 92)(38, 74)(39, 82)(40, 77)(41, 81)(42, 94)(43, 95)(44, 83)(45, 90)(46, 91)(47, 96)(48, 93) local type(s) :: { ( 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.177 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 24 e = 48 f = 20 degree seq :: [ 4^24 ] E3.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1 * Y2^-1 * Y1)^2, (Y2 * Y1 * Y2^-2 * Y1)^2, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1)^2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 10, 58)(6, 54, 12, 60)(8, 56, 15, 63)(11, 59, 20, 68)(13, 61, 23, 71)(14, 62, 25, 73)(16, 64, 28, 76)(17, 65, 30, 78)(18, 66, 31, 79)(19, 67, 33, 81)(21, 69, 36, 84)(22, 70, 38, 86)(24, 72, 35, 83)(26, 74, 37, 85)(27, 75, 32, 80)(29, 77, 34, 82)(39, 87, 44, 92)(40, 88, 47, 95)(41, 89, 46, 94)(42, 90, 45, 93)(43, 91, 48, 96)(97, 145, 99, 147, 104, 152, 100, 148)(98, 146, 101, 149, 107, 155, 102, 150)(103, 151, 109, 157, 120, 168, 110, 158)(105, 153, 112, 160, 125, 173, 113, 161)(106, 154, 114, 162, 128, 176, 115, 163)(108, 156, 117, 165, 133, 181, 118, 166)(111, 159, 122, 170, 139, 187, 123, 171)(116, 164, 130, 178, 144, 192, 131, 179)(119, 167, 135, 183, 126, 174, 136, 184)(121, 169, 137, 185, 124, 172, 138, 186)(127, 175, 140, 188, 134, 182, 141, 189)(129, 177, 142, 190, 132, 180, 143, 191) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 106)(6, 108)(7, 99)(8, 111)(9, 100)(10, 101)(11, 116)(12, 102)(13, 119)(14, 121)(15, 104)(16, 124)(17, 126)(18, 127)(19, 129)(20, 107)(21, 132)(22, 134)(23, 109)(24, 131)(25, 110)(26, 133)(27, 128)(28, 112)(29, 130)(30, 113)(31, 114)(32, 123)(33, 115)(34, 125)(35, 120)(36, 117)(37, 122)(38, 118)(39, 140)(40, 143)(41, 142)(42, 141)(43, 144)(44, 135)(45, 138)(46, 137)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E3.185 Graph:: bipartite v = 36 e = 96 f = 56 degree seq :: [ 4^24, 8^12 ] E3.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, Y2^6, (Y2^2 * Y1^-1)^2 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 21, 69, 11, 59)(5, 53, 13, 61, 18, 66, 7, 55)(8, 56, 19, 67, 30, 78, 15, 63)(10, 58, 23, 71, 36, 84, 20, 68)(12, 60, 16, 64, 31, 79, 27, 75)(14, 62, 26, 74, 41, 89, 28, 76)(17, 65, 33, 81, 45, 93, 32, 80)(22, 70, 29, 77, 42, 90, 37, 85)(24, 72, 34, 82, 43, 91, 39, 87)(25, 73, 38, 86, 44, 92, 35, 83)(40, 88, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 106, 154, 120, 168, 110, 158, 101, 149)(98, 146, 103, 151, 113, 161, 130, 178, 116, 164, 104, 152)(100, 148, 108, 156, 122, 170, 135, 183, 118, 166, 105, 153)(102, 150, 111, 159, 125, 173, 139, 187, 128, 176, 112, 160)(107, 155, 121, 169, 109, 157, 124, 172, 136, 184, 119, 167)(114, 162, 131, 179, 115, 163, 132, 180, 142, 190, 129, 177)(117, 165, 133, 181, 143, 191, 137, 185, 123, 171, 134, 182)(126, 174, 140, 188, 127, 175, 141, 189, 144, 192, 138, 186) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 111)(7, 113)(8, 98)(9, 100)(10, 120)(11, 121)(12, 122)(13, 124)(14, 101)(15, 125)(16, 102)(17, 130)(18, 131)(19, 132)(20, 104)(21, 133)(22, 105)(23, 107)(24, 110)(25, 109)(26, 135)(27, 134)(28, 136)(29, 139)(30, 140)(31, 141)(32, 112)(33, 114)(34, 116)(35, 115)(36, 142)(37, 143)(38, 117)(39, 118)(40, 119)(41, 123)(42, 126)(43, 128)(44, 127)(45, 144)(46, 129)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E3.184 Graph:: bipartite v = 20 e = 96 f = 72 degree seq :: [ 8^12, 12^8 ] E3.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^6, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, Y3^-2 * Y2 * Y3^3 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 113, 161)(106, 154, 117, 165)(108, 156, 120, 168)(110, 158, 124, 172)(111, 159, 123, 171)(112, 160, 126, 174)(114, 162, 121, 169)(115, 163, 130, 178)(116, 164, 118, 166)(119, 167, 132, 180)(122, 170, 136, 184)(125, 173, 137, 185)(127, 175, 135, 183)(128, 176, 139, 187)(129, 177, 133, 181)(131, 179, 140, 188)(134, 182, 142, 190)(138, 186, 141, 189)(143, 191, 144, 192) L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 111)(8, 114)(9, 115)(10, 100)(11, 118)(12, 121)(13, 122)(14, 102)(15, 125)(16, 103)(17, 128)(18, 106)(19, 129)(20, 105)(21, 127)(22, 131)(23, 107)(24, 134)(25, 110)(26, 135)(27, 109)(28, 133)(29, 117)(30, 138)(31, 112)(32, 116)(33, 113)(34, 137)(35, 124)(36, 141)(37, 119)(38, 123)(39, 120)(40, 140)(41, 143)(42, 130)(43, 126)(44, 144)(45, 136)(46, 132)(47, 139)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E3.183 Graph:: simple bipartite v = 72 e = 96 f = 20 degree seq :: [ 2^48, 4^24 ] E3.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y1^6, Y1 * Y3^-1 * Y1^3 * Y3 * Y1^2, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal R = (1, 49, 2, 50, 5, 53, 11, 59, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 22, 70, 18, 66, 8, 56)(6, 54, 13, 61, 25, 73, 21, 69, 28, 76, 14, 62)(9, 57, 19, 67, 24, 72, 12, 60, 23, 71, 20, 68)(16, 64, 30, 78, 41, 89, 33, 81, 36, 84, 31, 79)(17, 65, 32, 80, 40, 88, 29, 77, 38, 86, 26, 74)(27, 75, 39, 87, 34, 82, 37, 85, 44, 92, 35, 83)(42, 90, 46, 94, 43, 91, 47, 95, 48, 96, 45, 93)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 113)(9, 100)(10, 117)(11, 118)(12, 101)(13, 122)(14, 123)(15, 125)(16, 103)(17, 104)(18, 129)(19, 130)(20, 126)(21, 106)(22, 107)(23, 131)(24, 132)(25, 133)(26, 109)(27, 110)(28, 136)(29, 111)(30, 116)(31, 138)(32, 139)(33, 114)(34, 115)(35, 119)(36, 120)(37, 121)(38, 141)(39, 142)(40, 124)(41, 143)(42, 127)(43, 128)(44, 144)(45, 134)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E3.182 Graph:: simple bipartite v = 56 e = 96 f = 36 degree seq :: [ 2^48, 12^8 ] E3.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y2^-1 * Y1 * Y2^-2)^2, (Y3 * Y2^-1)^4, (Y2^-1 * Y1 * Y2 * Y1 * Y2^-1)^2 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 24, 72)(14, 62, 28, 76)(15, 63, 27, 75)(16, 64, 30, 78)(18, 66, 25, 73)(19, 67, 34, 82)(20, 68, 22, 70)(23, 71, 36, 84)(26, 74, 40, 88)(29, 77, 41, 89)(31, 79, 39, 87)(32, 80, 43, 91)(33, 81, 37, 85)(35, 83, 44, 92)(38, 86, 46, 94)(42, 90, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 121, 169, 110, 158, 102, 150)(103, 151, 111, 159, 125, 173, 117, 165, 127, 175, 112, 160)(105, 153, 115, 163, 129, 177, 113, 161, 128, 176, 116, 164)(107, 155, 118, 166, 131, 179, 124, 172, 133, 181, 119, 167)(109, 157, 122, 170, 135, 183, 120, 168, 134, 182, 123, 171)(126, 174, 138, 186, 130, 178, 137, 185, 143, 191, 139, 187)(132, 180, 141, 189, 136, 184, 140, 188, 144, 192, 142, 190) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 113)(9, 100)(10, 117)(11, 101)(12, 120)(13, 102)(14, 124)(15, 123)(16, 126)(17, 104)(18, 121)(19, 130)(20, 118)(21, 106)(22, 116)(23, 132)(24, 108)(25, 114)(26, 136)(27, 111)(28, 110)(29, 137)(30, 112)(31, 135)(32, 139)(33, 133)(34, 115)(35, 140)(36, 119)(37, 129)(38, 142)(39, 127)(40, 122)(41, 125)(42, 141)(43, 128)(44, 131)(45, 138)(46, 134)(47, 144)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.187 Graph:: bipartite v = 32 e = 96 f = 60 degree seq :: [ 4^24, 12^8 ] E3.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y1^-1 * Y3)^2, (Y3 * Y2^-1)^6 ] Map:: polytopal R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 21, 69, 11, 59)(5, 53, 13, 61, 18, 66, 7, 55)(8, 56, 19, 67, 30, 78, 15, 63)(10, 58, 23, 71, 36, 84, 20, 68)(12, 60, 16, 64, 31, 79, 27, 75)(14, 62, 26, 74, 41, 89, 28, 76)(17, 65, 33, 81, 45, 93, 32, 80)(22, 70, 29, 77, 42, 90, 37, 85)(24, 72, 34, 82, 43, 91, 39, 87)(25, 73, 38, 86, 44, 92, 35, 83)(40, 88, 47, 95, 48, 96, 46, 94)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 111)(7, 113)(8, 98)(9, 100)(10, 120)(11, 121)(12, 122)(13, 124)(14, 101)(15, 125)(16, 102)(17, 130)(18, 131)(19, 132)(20, 104)(21, 133)(22, 105)(23, 107)(24, 110)(25, 109)(26, 135)(27, 134)(28, 136)(29, 139)(30, 140)(31, 141)(32, 112)(33, 114)(34, 116)(35, 115)(36, 142)(37, 143)(38, 117)(39, 118)(40, 119)(41, 123)(42, 126)(43, 128)(44, 127)(45, 144)(46, 129)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E3.186 Graph:: simple bipartite v = 60 e = 96 f = 32 degree seq :: [ 2^48, 8^12 ] E3.188 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 12}) Quotient :: regular Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^12 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 21, 33, 43, 42, 32, 20, 10, 4)(3, 7, 15, 22, 35, 45, 48, 46, 38, 30, 17, 8)(6, 13, 25, 34, 27, 39, 47, 41, 31, 19, 26, 14)(9, 18, 24, 12, 23, 36, 44, 37, 29, 40, 28, 16) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 27)(17, 29)(18, 31)(20, 30)(21, 34)(24, 35)(25, 37)(26, 38)(28, 39)(32, 40)(33, 44)(36, 46)(41, 45)(42, 47)(43, 48) local type(s) :: { ( 3^12 ) } Outer automorphisms :: reflexible Dual of E3.189 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 4 e = 24 f = 16 degree seq :: [ 12^4 ] E3.189 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 12}) Quotient :: regular Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1 * 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, 35, 39)(28, 40, 41)(29, 36, 42)(30, 38, 43)(37, 44, 45)(46, 47, 48) 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, 39)(32, 44)(33, 41)(34, 43)(40, 46)(42, 47)(45, 48) local type(s) :: { ( 12^3 ) } Outer automorphisms :: reflexible Dual of E3.188 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 16 e = 24 f = 4 degree seq :: [ 3^16 ] E3.190 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * 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, 44, 47)(45, 46, 48)(49, 50)(51, 55)(52, 56)(53, 57)(54, 58)(59, 67)(60, 68)(61, 69)(62, 70)(63, 71)(64, 72)(65, 73)(66, 74)(75, 83)(76, 87)(77, 91)(78, 89)(79, 84)(80, 92)(81, 86)(82, 90)(85, 93)(88, 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) :: { ( 24, 24 ), ( 24^3 ) } Outer automorphisms :: reflexible Dual of E3.194 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 48 f = 4 degree seq :: [ 2^24, 3^16 ] E3.191 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^2 * T1^-1 * T2^-4 * T1^-1, T1^-1 * T2^2 * T1^-1 * T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 9, 19, 36, 45, 48, 43, 31, 26, 13, 5)(2, 6, 14, 27, 20, 38, 46, 44, 33, 32, 16, 7)(4, 11, 22, 37, 28, 42, 47, 41, 25, 34, 17, 8)(10, 21, 39, 30, 15, 29, 40, 24, 12, 23, 35, 18)(49, 50, 52)(51, 56, 58)(53, 60, 54)(55, 63, 59)(57, 66, 68)(61, 73, 71)(62, 72, 76)(64, 79, 77)(65, 81, 69)(67, 75, 85)(70, 78, 84)(74, 80, 82)(83, 89, 86)(87, 92, 93)(88, 91, 90)(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) :: { ( 4^3 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E3.195 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 48 f = 24 degree seq :: [ 3^16, 12^4 ] E3.192 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 12}) Quotient :: edge Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^12 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 27)(17, 29)(18, 31)(20, 30)(21, 34)(24, 35)(25, 37)(26, 38)(28, 39)(32, 40)(33, 44)(36, 46)(41, 45)(42, 47)(43, 48)(49, 50, 53, 59, 69, 81, 91, 90, 80, 68, 58, 52)(51, 55, 63, 70, 83, 93, 96, 94, 86, 78, 65, 56)(54, 61, 73, 82, 75, 87, 95, 89, 79, 67, 74, 62)(57, 66, 72, 60, 71, 84, 92, 85, 77, 88, 76, 64) 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) :: { ( 6, 6 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E3.193 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 48 f = 16 degree seq :: [ 2^24, 12^4 ] E3.193 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 49, 3, 51, 4, 52)(2, 50, 5, 53, 6, 54)(7, 55, 11, 59, 12, 60)(8, 56, 13, 61, 14, 62)(9, 57, 15, 63, 16, 64)(10, 58, 17, 65, 18, 66)(19, 67, 27, 75, 28, 76)(20, 68, 29, 77, 30, 78)(21, 69, 31, 79, 32, 80)(22, 70, 33, 81, 34, 82)(23, 71, 35, 83, 36, 84)(24, 72, 37, 85, 38, 86)(25, 73, 39, 87, 40, 88)(26, 74, 41, 89, 42, 90)(43, 91, 44, 92, 47, 95)(45, 93, 46, 94, 48, 96) L = (1, 50)(2, 49)(3, 55)(4, 56)(5, 57)(6, 58)(7, 51)(8, 52)(9, 53)(10, 54)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 83)(28, 87)(29, 91)(30, 89)(31, 84)(32, 92)(33, 86)(34, 90)(35, 75)(36, 79)(37, 93)(38, 81)(39, 76)(40, 94)(41, 78)(42, 82)(43, 77)(44, 80)(45, 85)(46, 88)(47, 96)(48, 95) local type(s) :: { ( 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E3.192 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 48 f = 28 degree seq :: [ 6^16 ] E3.194 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^2 * T1^-1 * T2^-4 * T1^-1, T1^-1 * T2^2 * T1^-1 * T2^8 ] Map:: R = (1, 49, 3, 51, 9, 57, 19, 67, 36, 84, 45, 93, 48, 96, 43, 91, 31, 79, 26, 74, 13, 61, 5, 53)(2, 50, 6, 54, 14, 62, 27, 75, 20, 68, 38, 86, 46, 94, 44, 92, 33, 81, 32, 80, 16, 64, 7, 55)(4, 52, 11, 59, 22, 70, 37, 85, 28, 76, 42, 90, 47, 95, 41, 89, 25, 73, 34, 82, 17, 65, 8, 56)(10, 58, 21, 69, 39, 87, 30, 78, 15, 63, 29, 77, 40, 88, 24, 72, 12, 60, 23, 71, 35, 83, 18, 66) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 60)(6, 53)(7, 63)(8, 58)(9, 66)(10, 51)(11, 55)(12, 54)(13, 73)(14, 72)(15, 59)(16, 79)(17, 81)(18, 68)(19, 75)(20, 57)(21, 65)(22, 78)(23, 61)(24, 76)(25, 71)(26, 80)(27, 85)(28, 62)(29, 64)(30, 84)(31, 77)(32, 82)(33, 69)(34, 74)(35, 89)(36, 70)(37, 67)(38, 83)(39, 92)(40, 91)(41, 86)(42, 88)(43, 90)(44, 93)(45, 87)(46, 95)(47, 96)(48, 94) 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 E3.190 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 48 f = 40 degree seq :: [ 24^4 ] E3.195 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 12}) Quotient :: loop Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^-2 * T2 * T1^3 * T2 * T1^-1, T1^12 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51)(2, 50, 6, 54)(4, 52, 9, 57)(5, 53, 12, 60)(7, 55, 16, 64)(8, 56, 13, 61)(10, 58, 19, 67)(11, 59, 22, 70)(14, 62, 23, 71)(15, 63, 27, 75)(17, 65, 29, 77)(18, 66, 31, 79)(20, 68, 30, 78)(21, 69, 34, 82)(24, 72, 35, 83)(25, 73, 37, 85)(26, 74, 38, 86)(28, 76, 39, 87)(32, 80, 40, 88)(33, 81, 44, 92)(36, 84, 46, 94)(41, 89, 45, 93)(42, 90, 47, 95)(43, 91, 48, 96) L = (1, 50)(2, 53)(3, 55)(4, 49)(5, 59)(6, 61)(7, 63)(8, 51)(9, 66)(10, 52)(11, 69)(12, 71)(13, 73)(14, 54)(15, 70)(16, 57)(17, 56)(18, 72)(19, 74)(20, 58)(21, 81)(22, 83)(23, 84)(24, 60)(25, 82)(26, 62)(27, 87)(28, 64)(29, 88)(30, 65)(31, 67)(32, 68)(33, 91)(34, 75)(35, 93)(36, 92)(37, 77)(38, 78)(39, 95)(40, 76)(41, 79)(42, 80)(43, 90)(44, 85)(45, 96)(46, 86)(47, 89)(48, 94) local type(s) :: { ( 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E3.191 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 48 f = 20 degree seq :: [ 4^24 ] E3.196 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^12 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 19, 67)(12, 60, 20, 68)(13, 61, 21, 69)(14, 62, 22, 70)(15, 63, 23, 71)(16, 64, 24, 72)(17, 65, 25, 73)(18, 66, 26, 74)(27, 75, 35, 83)(28, 76, 39, 87)(29, 77, 43, 91)(30, 78, 41, 89)(31, 79, 36, 84)(32, 80, 44, 92)(33, 81, 38, 86)(34, 82, 42, 90)(37, 85, 45, 93)(40, 88, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 100, 148)(98, 146, 101, 149, 102, 150)(103, 151, 107, 155, 108, 156)(104, 152, 109, 157, 110, 158)(105, 153, 111, 159, 112, 160)(106, 154, 113, 161, 114, 162)(115, 163, 123, 171, 124, 172)(116, 164, 125, 173, 126, 174)(117, 165, 127, 175, 128, 176)(118, 166, 129, 177, 130, 178)(119, 167, 131, 179, 132, 180)(120, 168, 133, 181, 134, 182)(121, 169, 135, 183, 136, 184)(122, 170, 137, 185, 138, 186)(139, 187, 140, 188, 143, 191)(141, 189, 142, 190, 144, 192) L = (1, 98)(2, 97)(3, 103)(4, 104)(5, 105)(6, 106)(7, 99)(8, 100)(9, 101)(10, 102)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 131)(28, 135)(29, 139)(30, 137)(31, 132)(32, 140)(33, 134)(34, 138)(35, 123)(36, 127)(37, 141)(38, 129)(39, 124)(40, 142)(41, 126)(42, 130)(43, 125)(44, 128)(45, 133)(46, 136)(47, 144)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E3.199 Graph:: bipartite v = 40 e = 96 f = 52 degree seq :: [ 4^24, 6^16 ] E3.197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2^2 * Y1 * Y2 * Y1^-1 * Y2, Y1^-1 * Y2^3 * Y1 * Y2^-3, Y2^12 ] Map:: R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 12, 60, 6, 54)(7, 55, 15, 63, 11, 59)(9, 57, 18, 66, 20, 68)(13, 61, 25, 73, 23, 71)(14, 62, 24, 72, 28, 76)(16, 64, 31, 79, 29, 77)(17, 65, 33, 81, 21, 69)(19, 67, 27, 75, 37, 85)(22, 70, 30, 78, 36, 84)(26, 74, 32, 80, 34, 82)(35, 83, 41, 89, 38, 86)(39, 87, 44, 92, 45, 93)(40, 88, 43, 91, 42, 90)(46, 94, 47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 115, 163, 132, 180, 141, 189, 144, 192, 139, 187, 127, 175, 122, 170, 109, 157, 101, 149)(98, 146, 102, 150, 110, 158, 123, 171, 116, 164, 134, 182, 142, 190, 140, 188, 129, 177, 128, 176, 112, 160, 103, 151)(100, 148, 107, 155, 118, 166, 133, 181, 124, 172, 138, 186, 143, 191, 137, 185, 121, 169, 130, 178, 113, 161, 104, 152)(106, 154, 117, 165, 135, 183, 126, 174, 111, 159, 125, 173, 136, 184, 120, 168, 108, 156, 119, 167, 131, 179, 114, 162) L = (1, 99)(2, 102)(3, 105)(4, 107)(5, 97)(6, 110)(7, 98)(8, 100)(9, 115)(10, 117)(11, 118)(12, 119)(13, 101)(14, 123)(15, 125)(16, 103)(17, 104)(18, 106)(19, 132)(20, 134)(21, 135)(22, 133)(23, 131)(24, 108)(25, 130)(26, 109)(27, 116)(28, 138)(29, 136)(30, 111)(31, 122)(32, 112)(33, 128)(34, 113)(35, 114)(36, 141)(37, 124)(38, 142)(39, 126)(40, 120)(41, 121)(42, 143)(43, 127)(44, 129)(45, 144)(46, 140)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E3.198 Graph:: bipartite v = 20 e = 96 f = 72 degree seq :: [ 6^16, 24^4 ] E3.198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^-1 * Y2 * Y3^3 * Y2 * Y3^-2, (Y3^-1 * Y1^-1)^12 ] Map:: polytopal R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146)(99, 147, 103, 151)(100, 148, 105, 153)(101, 149, 107, 155)(102, 150, 109, 157)(104, 152, 112, 160)(106, 154, 115, 163)(108, 156, 118, 166)(110, 158, 121, 169)(111, 159, 123, 171)(113, 161, 119, 167)(114, 162, 127, 175)(116, 164, 122, 170)(117, 165, 129, 177)(120, 168, 133, 181)(124, 172, 134, 182)(125, 173, 132, 180)(126, 174, 131, 179)(128, 176, 130, 178)(135, 183, 142, 190)(136, 184, 141, 189)(137, 185, 140, 188)(138, 186, 139, 187)(143, 191, 144, 192) L = (1, 99)(2, 101)(3, 104)(4, 97)(5, 108)(6, 98)(7, 109)(8, 113)(9, 114)(10, 100)(11, 105)(12, 119)(13, 120)(14, 102)(15, 103)(16, 123)(17, 126)(18, 125)(19, 124)(20, 106)(21, 107)(22, 129)(23, 132)(24, 131)(25, 130)(26, 110)(27, 135)(28, 111)(29, 112)(30, 136)(31, 115)(32, 116)(33, 139)(34, 117)(35, 118)(36, 140)(37, 121)(38, 122)(39, 141)(40, 143)(41, 127)(42, 128)(43, 137)(44, 144)(45, 133)(46, 134)(47, 138)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 24 ), ( 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E3.197 Graph:: simple bipartite v = 72 e = 96 f = 20 degree seq :: [ 2^48, 4^24 ] E3.199 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |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 * Y1^3 * Y3^-1 * Y1^-3, Y1^12 ] Map:: polytopal R = (1, 49, 2, 50, 5, 53, 11, 59, 21, 69, 33, 81, 43, 91, 42, 90, 32, 80, 20, 68, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 22, 70, 35, 83, 45, 93, 48, 96, 46, 94, 38, 86, 30, 78, 17, 65, 8, 56)(6, 54, 13, 61, 25, 73, 34, 82, 27, 75, 39, 87, 47, 95, 41, 89, 31, 79, 19, 67, 26, 74, 14, 62)(9, 57, 18, 66, 24, 72, 12, 60, 23, 71, 36, 84, 44, 92, 37, 85, 29, 77, 40, 88, 28, 76, 16, 64)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 102)(3, 97)(4, 105)(5, 108)(6, 98)(7, 112)(8, 109)(9, 100)(10, 115)(11, 118)(12, 101)(13, 104)(14, 119)(15, 123)(16, 103)(17, 125)(18, 127)(19, 106)(20, 126)(21, 130)(22, 107)(23, 110)(24, 131)(25, 133)(26, 134)(27, 111)(28, 135)(29, 113)(30, 116)(31, 114)(32, 136)(33, 140)(34, 117)(35, 120)(36, 142)(37, 121)(38, 122)(39, 124)(40, 128)(41, 141)(42, 143)(43, 144)(44, 129)(45, 137)(46, 132)(47, 138)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E3.196 Graph:: simple bipartite v = 52 e = 96 f = 40 degree seq :: [ 2^48, 24^4 ] E3.200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-1, Y2^12 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 16, 64)(10, 58, 19, 67)(12, 60, 22, 70)(14, 62, 25, 73)(15, 63, 27, 75)(17, 65, 23, 71)(18, 66, 31, 79)(20, 68, 26, 74)(21, 69, 33, 81)(24, 72, 37, 85)(28, 76, 38, 86)(29, 77, 36, 84)(30, 78, 35, 83)(32, 80, 34, 82)(39, 87, 46, 94)(40, 88, 45, 93)(41, 89, 44, 92)(42, 90, 43, 91)(47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 113, 161, 126, 174, 136, 184, 143, 191, 138, 186, 128, 176, 116, 164, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 119, 167, 132, 180, 140, 188, 144, 192, 142, 190, 134, 182, 122, 170, 110, 158, 102, 150)(103, 151, 109, 157, 120, 168, 131, 179, 118, 166, 129, 177, 139, 187, 137, 185, 127, 175, 115, 163, 124, 172, 111, 159)(105, 153, 114, 162, 125, 173, 112, 160, 123, 171, 135, 183, 141, 189, 133, 181, 121, 169, 130, 178, 117, 165, 107, 155) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 112)(9, 100)(10, 115)(11, 101)(12, 118)(13, 102)(14, 121)(15, 123)(16, 104)(17, 119)(18, 127)(19, 106)(20, 122)(21, 129)(22, 108)(23, 113)(24, 133)(25, 110)(26, 116)(27, 111)(28, 134)(29, 132)(30, 131)(31, 114)(32, 130)(33, 117)(34, 128)(35, 126)(36, 125)(37, 120)(38, 124)(39, 142)(40, 141)(41, 140)(42, 139)(43, 138)(44, 137)(45, 136)(46, 135)(47, 144)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 2, 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 E3.201 Graph:: bipartite v = 28 e = 96 f = 64 degree seq :: [ 4^24, 24^4 ] E3.201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-1 * Y3^2 * Y1^-1 * Y3^-2, (Y3 * Y2^-1)^12 ] Map:: polytopal R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 12, 60, 6, 54)(7, 55, 15, 63, 11, 59)(9, 57, 18, 66, 20, 68)(13, 61, 25, 73, 23, 71)(14, 62, 24, 72, 28, 76)(16, 64, 31, 79, 29, 77)(17, 65, 33, 81, 21, 69)(19, 67, 27, 75, 37, 85)(22, 70, 30, 78, 36, 84)(26, 74, 32, 80, 34, 82)(35, 83, 41, 89, 38, 86)(39, 87, 44, 92, 45, 93)(40, 88, 43, 91, 42, 90)(46, 94, 47, 95, 48, 96)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(132, 180)(133, 181)(134, 182)(135, 183)(136, 184)(137, 185)(138, 186)(139, 187)(140, 188)(141, 189)(142, 190)(143, 191)(144, 192) L = (1, 99)(2, 102)(3, 105)(4, 107)(5, 97)(6, 110)(7, 98)(8, 100)(9, 115)(10, 117)(11, 118)(12, 119)(13, 101)(14, 123)(15, 125)(16, 103)(17, 104)(18, 106)(19, 132)(20, 134)(21, 135)(22, 133)(23, 131)(24, 108)(25, 130)(26, 109)(27, 116)(28, 138)(29, 136)(30, 111)(31, 122)(32, 112)(33, 128)(34, 113)(35, 114)(36, 141)(37, 124)(38, 142)(39, 126)(40, 120)(41, 121)(42, 143)(43, 127)(44, 129)(45, 144)(46, 140)(47, 137)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E3.200 Graph:: simple bipartite v = 64 e = 96 f = 28 degree seq :: [ 2^48, 6^16 ] E3.202 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 8}) Quotient :: regular Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^8, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, (T2 * T1^3 * T2 * T1^-2)^2 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 21, 20, 10, 4)(3, 7, 15, 27, 45, 31, 17, 8)(6, 13, 25, 41, 66, 44, 26, 14)(9, 18, 32, 52, 75, 49, 29, 16)(12, 23, 39, 62, 85, 65, 40, 24)(19, 34, 55, 79, 89, 67, 54, 33)(22, 37, 60, 51, 76, 84, 61, 38)(28, 47, 63, 43, 69, 83, 74, 48)(30, 50, 64, 86, 78, 53, 68, 42)(35, 57, 80, 87, 73, 46, 72, 56)(36, 58, 81, 70, 90, 77, 82, 59)(71, 91, 94, 93, 96, 88, 95, 92) 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, 36)(24, 37)(25, 42)(26, 43)(27, 46)(29, 47)(31, 51)(32, 53)(34, 56)(38, 58)(39, 63)(40, 64)(41, 67)(44, 70)(45, 71)(48, 72)(49, 62)(50, 60)(52, 77)(54, 68)(55, 74)(57, 59)(61, 83)(65, 87)(66, 88)(69, 81)(73, 91)(75, 93)(76, 92)(78, 82)(79, 84)(80, 86)(85, 94)(89, 95)(90, 96) local type(s) :: { ( 3^8 ) } Outer automorphisms :: reflexible Dual of E3.203 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 12 e = 48 f = 32 degree seq :: [ 8^12 ] E3.203 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 8}) Quotient :: regular Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2 * T1 * T2 * T1^-1)^3, (T1^-1 * T2)^8 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 37, 41)(29, 42, 43)(30, 44, 45)(35, 49, 50)(36, 47, 51)(38, 52, 53)(46, 60, 61)(48, 62, 63)(54, 69, 70)(55, 58, 71)(56, 72, 73)(57, 74, 75)(59, 76, 64)(65, 67, 80)(66, 81, 82)(68, 83, 77)(78, 79, 91)(84, 86, 94)(85, 96, 92)(87, 95, 88)(89, 90, 93) 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, 77)(61, 78)(62, 79)(63, 69)(70, 84)(71, 85)(72, 86)(73, 87)(74, 88)(75, 89)(76, 90)(80, 92)(81, 93)(82, 94)(83, 95)(91, 96) local type(s) :: { ( 8^3 ) } Outer automorphisms :: reflexible Dual of E3.202 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 32 e = 48 f = 12 degree seq :: [ 3^32 ] E3.204 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1 * T2^-1)^3, (T2^-1 * T1)^8 ] 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, 75, 87)(74, 88, 89)(76, 90, 77)(78, 79, 91)(80, 82, 92)(81, 93, 94)(83, 95, 84)(85, 86, 96)(97, 98)(99, 103)(100, 104)(101, 105)(102, 106)(107, 115)(108, 116)(109, 117)(110, 118)(111, 119)(112, 120)(113, 121)(114, 122)(123, 139)(124, 140)(125, 133)(126, 141)(127, 142)(128, 136)(129, 143)(130, 144)(131, 145)(132, 146)(134, 147)(135, 148)(137, 149)(138, 150)(151, 168)(152, 169)(153, 170)(154, 171)(155, 172)(156, 173)(157, 174)(158, 175)(159, 160)(161, 176)(162, 177)(163, 178)(164, 179)(165, 180)(166, 181)(167, 182)(183, 190)(184, 192)(185, 188)(186, 191)(187, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16, 16 ), ( 16^3 ) } Outer automorphisms :: reflexible Dual of E3.208 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 96 f = 12 degree seq :: [ 2^48, 3^32 ] E3.205 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^8, (T2^2 * T1^-1)^3, T2 * T1^-1 * T2^-3 * T1^2 * T2^-2 * T1 * T2^2 * T1^-1 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 37, 26, 13, 5)(2, 6, 14, 27, 49, 32, 16, 7)(4, 11, 22, 41, 58, 34, 17, 8)(10, 21, 40, 64, 82, 59, 35, 18)(12, 23, 43, 67, 88, 68, 44, 24)(15, 29, 52, 74, 94, 75, 53, 30)(20, 39, 31, 54, 76, 83, 60, 36)(25, 45, 69, 90, 87, 65, 42, 46)(28, 51, 33, 56, 78, 91, 71, 48)(38, 63, 57, 79, 95, 89, 84, 61)(47, 62, 85, 81, 92, 72, 50, 70)(55, 73, 93, 86, 96, 80, 66, 77)(97, 98, 100)(99, 104, 106)(101, 108, 102)(103, 111, 107)(105, 114, 116)(109, 121, 119)(110, 120, 124)(112, 127, 125)(113, 129, 117)(115, 132, 134)(118, 126, 138)(122, 143, 141)(123, 144, 146)(128, 151, 150)(130, 153, 152)(131, 148, 135)(133, 157, 158)(136, 147, 140)(137, 161, 162)(139, 142, 149)(145, 168, 169)(154, 176, 175)(155, 177, 170)(156, 174, 159)(160, 164, 182)(163, 171, 185)(165, 166, 167)(172, 173, 183)(178, 189, 188)(179, 186, 187)(180, 190, 181)(184, 191, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4^3 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E3.209 Transitivity :: ET+ Graph:: simple bipartite v = 44 e = 96 f = 48 degree seq :: [ 3^32, 8^12 ] E3.206 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 8}) Quotient :: edge Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^8, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, (T2 * T1^3 * T2 * T1^-2)^2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 22)(14, 23)(15, 28)(17, 30)(18, 33)(20, 35)(21, 36)(24, 37)(25, 42)(26, 43)(27, 46)(29, 47)(31, 51)(32, 53)(34, 56)(38, 58)(39, 63)(40, 64)(41, 67)(44, 70)(45, 71)(48, 72)(49, 62)(50, 60)(52, 77)(54, 68)(55, 74)(57, 59)(61, 83)(65, 87)(66, 88)(69, 81)(73, 91)(75, 93)(76, 92)(78, 82)(79, 84)(80, 86)(85, 94)(89, 95)(90, 96)(97, 98, 101, 107, 117, 116, 106, 100)(99, 103, 111, 123, 141, 127, 113, 104)(102, 109, 121, 137, 162, 140, 122, 110)(105, 114, 128, 148, 171, 145, 125, 112)(108, 119, 135, 158, 181, 161, 136, 120)(115, 130, 151, 175, 185, 163, 150, 129)(118, 133, 156, 147, 172, 180, 157, 134)(124, 143, 159, 139, 165, 179, 170, 144)(126, 146, 160, 182, 174, 149, 164, 138)(131, 153, 176, 183, 169, 142, 168, 152)(132, 154, 177, 166, 186, 173, 178, 155)(167, 187, 190, 189, 192, 184, 191, 188) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 6 ), ( 6^8 ) } Outer automorphisms :: reflexible Dual of E3.207 Transitivity :: ET+ Graph:: simple bipartite v = 60 e = 96 f = 32 degree seq :: [ 2^48, 8^12 ] E3.207 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1 * T2^-1)^3, (T2^-1 * T1)^8 ] Map:: R = (1, 97, 3, 99, 4, 100)(2, 98, 5, 101, 6, 102)(7, 103, 11, 107, 12, 108)(8, 104, 13, 109, 14, 110)(9, 105, 15, 111, 16, 112)(10, 106, 17, 113, 18, 114)(19, 115, 27, 123, 28, 124)(20, 116, 29, 125, 30, 126)(21, 117, 31, 127, 32, 128)(22, 118, 33, 129, 34, 130)(23, 119, 35, 131, 36, 132)(24, 120, 37, 133, 38, 134)(25, 121, 39, 135, 40, 136)(26, 122, 41, 137, 42, 138)(43, 139, 55, 151, 56, 152)(44, 140, 47, 143, 57, 153)(45, 141, 58, 154, 59, 155)(46, 142, 60, 156, 61, 157)(48, 144, 62, 158, 63, 159)(49, 145, 64, 160, 65, 161)(50, 146, 53, 149, 66, 162)(51, 147, 67, 163, 68, 164)(52, 148, 69, 165, 70, 166)(54, 150, 71, 167, 72, 168)(73, 169, 75, 171, 87, 183)(74, 170, 88, 184, 89, 185)(76, 172, 90, 186, 77, 173)(78, 174, 79, 175, 91, 187)(80, 176, 82, 178, 92, 188)(81, 177, 93, 189, 94, 190)(83, 179, 95, 191, 84, 180)(85, 181, 86, 182, 96, 192) L = (1, 98)(2, 97)(3, 103)(4, 104)(5, 105)(6, 106)(7, 99)(8, 100)(9, 101)(10, 102)(11, 115)(12, 116)(13, 117)(14, 118)(15, 119)(16, 120)(17, 121)(18, 122)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 139)(28, 140)(29, 133)(30, 141)(31, 142)(32, 136)(33, 143)(34, 144)(35, 145)(36, 146)(37, 125)(38, 147)(39, 148)(40, 128)(41, 149)(42, 150)(43, 123)(44, 124)(45, 126)(46, 127)(47, 129)(48, 130)(49, 131)(50, 132)(51, 134)(52, 135)(53, 137)(54, 138)(55, 168)(56, 169)(57, 170)(58, 171)(59, 172)(60, 173)(61, 174)(62, 175)(63, 160)(64, 159)(65, 176)(66, 177)(67, 178)(68, 179)(69, 180)(70, 181)(71, 182)(72, 151)(73, 152)(74, 153)(75, 154)(76, 155)(77, 156)(78, 157)(79, 158)(80, 161)(81, 162)(82, 163)(83, 164)(84, 165)(85, 166)(86, 167)(87, 190)(88, 192)(89, 188)(90, 191)(91, 189)(92, 185)(93, 187)(94, 183)(95, 186)(96, 184) local type(s) :: { ( 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E3.206 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 32 e = 96 f = 60 degree seq :: [ 6^32 ] E3.208 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ F^2, T1^3, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T2^8, (T2^2 * T1^-1)^3, T2 * T1^-1 * T2^-3 * T1^2 * T2^-2 * T1 * T2^2 * T1^-1 ] Map:: R = (1, 97, 3, 99, 9, 105, 19, 115, 37, 133, 26, 122, 13, 109, 5, 101)(2, 98, 6, 102, 14, 110, 27, 123, 49, 145, 32, 128, 16, 112, 7, 103)(4, 100, 11, 107, 22, 118, 41, 137, 58, 154, 34, 130, 17, 113, 8, 104)(10, 106, 21, 117, 40, 136, 64, 160, 82, 178, 59, 155, 35, 131, 18, 114)(12, 108, 23, 119, 43, 139, 67, 163, 88, 184, 68, 164, 44, 140, 24, 120)(15, 111, 29, 125, 52, 148, 74, 170, 94, 190, 75, 171, 53, 149, 30, 126)(20, 116, 39, 135, 31, 127, 54, 150, 76, 172, 83, 179, 60, 156, 36, 132)(25, 121, 45, 141, 69, 165, 90, 186, 87, 183, 65, 161, 42, 138, 46, 142)(28, 124, 51, 147, 33, 129, 56, 152, 78, 174, 91, 187, 71, 167, 48, 144)(38, 134, 63, 159, 57, 153, 79, 175, 95, 191, 89, 185, 84, 180, 61, 157)(47, 143, 62, 158, 85, 181, 81, 177, 92, 188, 72, 168, 50, 146, 70, 166)(55, 151, 73, 169, 93, 189, 86, 182, 96, 192, 80, 176, 66, 162, 77, 173) L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 108)(6, 101)(7, 111)(8, 106)(9, 114)(10, 99)(11, 103)(12, 102)(13, 121)(14, 120)(15, 107)(16, 127)(17, 129)(18, 116)(19, 132)(20, 105)(21, 113)(22, 126)(23, 109)(24, 124)(25, 119)(26, 143)(27, 144)(28, 110)(29, 112)(30, 138)(31, 125)(32, 151)(33, 117)(34, 153)(35, 148)(36, 134)(37, 157)(38, 115)(39, 131)(40, 147)(41, 161)(42, 118)(43, 142)(44, 136)(45, 122)(46, 149)(47, 141)(48, 146)(49, 168)(50, 123)(51, 140)(52, 135)(53, 139)(54, 128)(55, 150)(56, 130)(57, 152)(58, 176)(59, 177)(60, 174)(61, 158)(62, 133)(63, 156)(64, 164)(65, 162)(66, 137)(67, 171)(68, 182)(69, 166)(70, 167)(71, 165)(72, 169)(73, 145)(74, 155)(75, 185)(76, 173)(77, 183)(78, 159)(79, 154)(80, 175)(81, 170)(82, 189)(83, 186)(84, 190)(85, 180)(86, 160)(87, 172)(88, 191)(89, 163)(90, 187)(91, 179)(92, 178)(93, 188)(94, 181)(95, 192)(96, 184) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E3.204 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 80 degree seq :: [ 16^12 ] E3.209 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 8}) Quotient :: loop Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^8, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-2, (T2 * T1^3 * T2 * T1^-2)^2 ] Map:: polyhedral non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 13, 109)(10, 106, 19, 115)(11, 107, 22, 118)(14, 110, 23, 119)(15, 111, 28, 124)(17, 113, 30, 126)(18, 114, 33, 129)(20, 116, 35, 131)(21, 117, 36, 132)(24, 120, 37, 133)(25, 121, 42, 138)(26, 122, 43, 139)(27, 123, 46, 142)(29, 125, 47, 143)(31, 127, 51, 147)(32, 128, 53, 149)(34, 130, 56, 152)(38, 134, 58, 154)(39, 135, 63, 159)(40, 136, 64, 160)(41, 137, 67, 163)(44, 140, 70, 166)(45, 141, 71, 167)(48, 144, 72, 168)(49, 145, 62, 158)(50, 146, 60, 156)(52, 148, 77, 173)(54, 150, 68, 164)(55, 151, 74, 170)(57, 153, 59, 155)(61, 157, 83, 179)(65, 161, 87, 183)(66, 162, 88, 184)(69, 165, 81, 177)(73, 169, 91, 187)(75, 171, 93, 189)(76, 172, 92, 188)(78, 174, 82, 178)(79, 175, 84, 180)(80, 176, 86, 182)(85, 181, 94, 190)(89, 185, 95, 191)(90, 186, 96, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 117)(12, 119)(13, 121)(14, 102)(15, 123)(16, 105)(17, 104)(18, 128)(19, 130)(20, 106)(21, 116)(22, 133)(23, 135)(24, 108)(25, 137)(26, 110)(27, 141)(28, 143)(29, 112)(30, 146)(31, 113)(32, 148)(33, 115)(34, 151)(35, 153)(36, 154)(37, 156)(38, 118)(39, 158)(40, 120)(41, 162)(42, 126)(43, 165)(44, 122)(45, 127)(46, 168)(47, 159)(48, 124)(49, 125)(50, 160)(51, 172)(52, 171)(53, 164)(54, 129)(55, 175)(56, 131)(57, 176)(58, 177)(59, 132)(60, 147)(61, 134)(62, 181)(63, 139)(64, 182)(65, 136)(66, 140)(67, 150)(68, 138)(69, 179)(70, 186)(71, 187)(72, 152)(73, 142)(74, 144)(75, 145)(76, 180)(77, 178)(78, 149)(79, 185)(80, 183)(81, 166)(82, 155)(83, 170)(84, 157)(85, 161)(86, 174)(87, 169)(88, 191)(89, 163)(90, 173)(91, 190)(92, 167)(93, 192)(94, 189)(95, 188)(96, 184) local type(s) :: { ( 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E3.205 Transitivity :: ET+ VT+ AT Graph:: simple v = 48 e = 96 f = 44 degree seq :: [ 4^48 ] E3.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2 * Y1 * Y2^-1)^3, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 8, 104)(5, 101, 9, 105)(6, 102, 10, 106)(11, 107, 19, 115)(12, 108, 20, 116)(13, 109, 21, 117)(14, 110, 22, 118)(15, 111, 23, 119)(16, 112, 24, 120)(17, 113, 25, 121)(18, 114, 26, 122)(27, 123, 43, 139)(28, 124, 44, 140)(29, 125, 37, 133)(30, 126, 45, 141)(31, 127, 46, 142)(32, 128, 40, 136)(33, 129, 47, 143)(34, 130, 48, 144)(35, 131, 49, 145)(36, 132, 50, 146)(38, 134, 51, 147)(39, 135, 52, 148)(41, 137, 53, 149)(42, 138, 54, 150)(55, 151, 72, 168)(56, 152, 73, 169)(57, 153, 74, 170)(58, 154, 75, 171)(59, 155, 76, 172)(60, 156, 77, 173)(61, 157, 78, 174)(62, 158, 79, 175)(63, 159, 64, 160)(65, 161, 80, 176)(66, 162, 81, 177)(67, 163, 82, 178)(68, 164, 83, 179)(69, 165, 84, 180)(70, 166, 85, 181)(71, 167, 86, 182)(87, 183, 94, 190)(88, 184, 96, 192)(89, 185, 92, 188)(90, 186, 95, 191)(91, 187, 93, 189)(193, 289, 195, 291, 196, 292)(194, 290, 197, 293, 198, 294)(199, 295, 203, 299, 204, 300)(200, 296, 205, 301, 206, 302)(201, 297, 207, 303, 208, 304)(202, 298, 209, 305, 210, 306)(211, 307, 219, 315, 220, 316)(212, 308, 221, 317, 222, 318)(213, 309, 223, 319, 224, 320)(214, 310, 225, 321, 226, 322)(215, 311, 227, 323, 228, 324)(216, 312, 229, 325, 230, 326)(217, 313, 231, 327, 232, 328)(218, 314, 233, 329, 234, 330)(235, 331, 247, 343, 248, 344)(236, 332, 239, 335, 249, 345)(237, 333, 250, 346, 251, 347)(238, 334, 252, 348, 253, 349)(240, 336, 254, 350, 255, 351)(241, 337, 256, 352, 257, 353)(242, 338, 245, 341, 258, 354)(243, 339, 259, 355, 260, 356)(244, 340, 261, 357, 262, 358)(246, 342, 263, 359, 264, 360)(265, 361, 267, 363, 279, 375)(266, 362, 280, 376, 281, 377)(268, 364, 282, 378, 269, 365)(270, 366, 271, 367, 283, 379)(272, 368, 274, 370, 284, 380)(273, 369, 285, 381, 286, 382)(275, 371, 287, 383, 276, 372)(277, 373, 278, 374, 288, 384) L = (1, 194)(2, 193)(3, 199)(4, 200)(5, 201)(6, 202)(7, 195)(8, 196)(9, 197)(10, 198)(11, 211)(12, 212)(13, 213)(14, 214)(15, 215)(16, 216)(17, 217)(18, 218)(19, 203)(20, 204)(21, 205)(22, 206)(23, 207)(24, 208)(25, 209)(26, 210)(27, 235)(28, 236)(29, 229)(30, 237)(31, 238)(32, 232)(33, 239)(34, 240)(35, 241)(36, 242)(37, 221)(38, 243)(39, 244)(40, 224)(41, 245)(42, 246)(43, 219)(44, 220)(45, 222)(46, 223)(47, 225)(48, 226)(49, 227)(50, 228)(51, 230)(52, 231)(53, 233)(54, 234)(55, 264)(56, 265)(57, 266)(58, 267)(59, 268)(60, 269)(61, 270)(62, 271)(63, 256)(64, 255)(65, 272)(66, 273)(67, 274)(68, 275)(69, 276)(70, 277)(71, 278)(72, 247)(73, 248)(74, 249)(75, 250)(76, 251)(77, 252)(78, 253)(79, 254)(80, 257)(81, 258)(82, 259)(83, 260)(84, 261)(85, 262)(86, 263)(87, 286)(88, 288)(89, 284)(90, 287)(91, 285)(92, 281)(93, 283)(94, 279)(95, 282)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E3.213 Graph:: bipartite v = 80 e = 192 f = 108 degree seq :: [ 4^48, 6^32 ] E3.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^8, (Y1 * Y2^-2)^3, Y2 * Y1^-1 * Y2^-3 * Y1^2 * Y2^-2 * Y1 * Y2^2 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 12, 108, 6, 102)(7, 103, 15, 111, 11, 107)(9, 105, 18, 114, 20, 116)(13, 109, 25, 121, 23, 119)(14, 110, 24, 120, 28, 124)(16, 112, 31, 127, 29, 125)(17, 113, 33, 129, 21, 117)(19, 115, 36, 132, 38, 134)(22, 118, 30, 126, 42, 138)(26, 122, 47, 143, 45, 141)(27, 123, 48, 144, 50, 146)(32, 128, 55, 151, 54, 150)(34, 130, 57, 153, 56, 152)(35, 131, 52, 148, 39, 135)(37, 133, 61, 157, 62, 158)(40, 136, 51, 147, 44, 140)(41, 137, 65, 161, 66, 162)(43, 139, 46, 142, 53, 149)(49, 145, 72, 168, 73, 169)(58, 154, 80, 176, 79, 175)(59, 155, 81, 177, 74, 170)(60, 156, 78, 174, 63, 159)(64, 160, 68, 164, 86, 182)(67, 163, 75, 171, 89, 185)(69, 165, 70, 166, 71, 167)(76, 172, 77, 173, 87, 183)(82, 178, 93, 189, 92, 188)(83, 179, 90, 186, 91, 187)(84, 180, 94, 190, 85, 181)(88, 184, 95, 191, 96, 192)(193, 289, 195, 291, 201, 297, 211, 307, 229, 325, 218, 314, 205, 301, 197, 293)(194, 290, 198, 294, 206, 302, 219, 315, 241, 337, 224, 320, 208, 304, 199, 295)(196, 292, 203, 299, 214, 310, 233, 329, 250, 346, 226, 322, 209, 305, 200, 296)(202, 298, 213, 309, 232, 328, 256, 352, 274, 370, 251, 347, 227, 323, 210, 306)(204, 300, 215, 311, 235, 331, 259, 355, 280, 376, 260, 356, 236, 332, 216, 312)(207, 303, 221, 317, 244, 340, 266, 362, 286, 382, 267, 363, 245, 341, 222, 318)(212, 308, 231, 327, 223, 319, 246, 342, 268, 364, 275, 371, 252, 348, 228, 324)(217, 313, 237, 333, 261, 357, 282, 378, 279, 375, 257, 353, 234, 330, 238, 334)(220, 316, 243, 339, 225, 321, 248, 344, 270, 366, 283, 379, 263, 359, 240, 336)(230, 326, 255, 351, 249, 345, 271, 367, 287, 383, 281, 377, 276, 372, 253, 349)(239, 335, 254, 350, 277, 373, 273, 369, 284, 380, 264, 360, 242, 338, 262, 358)(247, 343, 265, 361, 285, 381, 278, 374, 288, 384, 272, 368, 258, 354, 269, 365) L = (1, 195)(2, 198)(3, 201)(4, 203)(5, 193)(6, 206)(7, 194)(8, 196)(9, 211)(10, 213)(11, 214)(12, 215)(13, 197)(14, 219)(15, 221)(16, 199)(17, 200)(18, 202)(19, 229)(20, 231)(21, 232)(22, 233)(23, 235)(24, 204)(25, 237)(26, 205)(27, 241)(28, 243)(29, 244)(30, 207)(31, 246)(32, 208)(33, 248)(34, 209)(35, 210)(36, 212)(37, 218)(38, 255)(39, 223)(40, 256)(41, 250)(42, 238)(43, 259)(44, 216)(45, 261)(46, 217)(47, 254)(48, 220)(49, 224)(50, 262)(51, 225)(52, 266)(53, 222)(54, 268)(55, 265)(56, 270)(57, 271)(58, 226)(59, 227)(60, 228)(61, 230)(62, 277)(63, 249)(64, 274)(65, 234)(66, 269)(67, 280)(68, 236)(69, 282)(70, 239)(71, 240)(72, 242)(73, 285)(74, 286)(75, 245)(76, 275)(77, 247)(78, 283)(79, 287)(80, 258)(81, 284)(82, 251)(83, 252)(84, 253)(85, 273)(86, 288)(87, 257)(88, 260)(89, 276)(90, 279)(91, 263)(92, 264)(93, 278)(94, 267)(95, 281)(96, 272)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) 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 ) } Outer automorphisms :: reflexible Dual of E3.212 Graph:: bipartite v = 44 e = 192 f = 144 degree seq :: [ 6^32, 16^12 ] E3.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y3^-3 * Y2)^3, (Y3^2 * Y2 * Y3^-3 * Y2)^2, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 208, 304)(202, 298, 211, 307)(204, 300, 214, 310)(206, 302, 217, 313)(207, 303, 219, 315)(209, 305, 222, 318)(210, 306, 224, 320)(212, 308, 227, 323)(213, 309, 228, 324)(215, 311, 231, 327)(216, 312, 233, 329)(218, 314, 236, 332)(220, 316, 238, 334)(221, 317, 240, 336)(223, 319, 243, 339)(225, 321, 245, 341)(226, 322, 247, 343)(229, 325, 251, 347)(230, 326, 253, 349)(232, 328, 256, 352)(234, 330, 258, 354)(235, 331, 260, 356)(237, 333, 250, 346)(239, 335, 264, 360)(241, 337, 261, 357)(242, 338, 266, 362)(244, 340, 257, 353)(246, 342, 270, 366)(248, 344, 254, 350)(249, 345, 268, 364)(252, 348, 274, 370)(255, 351, 276, 372)(259, 355, 280, 376)(262, 358, 278, 374)(263, 359, 283, 379)(265, 361, 277, 373)(267, 363, 275, 371)(269, 365, 285, 381)(271, 367, 282, 378)(272, 368, 281, 377)(273, 369, 286, 382)(279, 375, 288, 384)(284, 380, 287, 383) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 205)(8, 209)(9, 210)(10, 196)(11, 201)(12, 215)(13, 216)(14, 198)(15, 199)(16, 219)(17, 223)(18, 225)(19, 226)(20, 202)(21, 203)(22, 228)(23, 232)(24, 234)(25, 235)(26, 206)(27, 237)(28, 207)(29, 208)(30, 240)(31, 212)(32, 211)(33, 246)(34, 248)(35, 249)(36, 250)(37, 213)(38, 214)(39, 253)(40, 218)(41, 217)(42, 259)(43, 261)(44, 262)(45, 251)(46, 263)(47, 220)(48, 260)(49, 221)(50, 222)(51, 266)(52, 224)(53, 257)(54, 252)(55, 227)(56, 271)(57, 272)(58, 238)(59, 273)(60, 229)(61, 247)(62, 230)(63, 231)(64, 276)(65, 233)(66, 244)(67, 239)(68, 236)(69, 281)(70, 282)(71, 275)(72, 284)(73, 241)(74, 283)(75, 242)(76, 243)(77, 245)(78, 285)(79, 279)(80, 277)(81, 265)(82, 287)(83, 254)(84, 286)(85, 255)(86, 256)(87, 258)(88, 288)(89, 269)(90, 267)(91, 264)(92, 270)(93, 268)(94, 274)(95, 280)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 6, 16 ), ( 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E3.211 Graph:: simple bipartite v = 144 e = 192 f = 44 degree seq :: [ 2^96, 4^48 ] E3.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |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, Y1^8, Y3 * Y1^-3 * Y3^-1 * Y1^-2 * Y3 * Y1 * Y3^-1 * Y1^-2, 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 ] Map:: polytopal R = (1, 97, 2, 98, 5, 101, 11, 107, 21, 117, 20, 116, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 27, 123, 45, 141, 31, 127, 17, 113, 8, 104)(6, 102, 13, 109, 25, 121, 41, 137, 66, 162, 44, 140, 26, 122, 14, 110)(9, 105, 18, 114, 32, 128, 52, 148, 75, 171, 49, 145, 29, 125, 16, 112)(12, 108, 23, 119, 39, 135, 62, 158, 85, 181, 65, 161, 40, 136, 24, 120)(19, 115, 34, 130, 55, 151, 79, 175, 89, 185, 67, 163, 54, 150, 33, 129)(22, 118, 37, 133, 60, 156, 51, 147, 76, 172, 84, 180, 61, 157, 38, 134)(28, 124, 47, 143, 63, 159, 43, 139, 69, 165, 83, 179, 74, 170, 48, 144)(30, 126, 50, 146, 64, 160, 86, 182, 78, 174, 53, 149, 68, 164, 42, 138)(35, 131, 57, 153, 80, 176, 87, 183, 73, 169, 46, 142, 72, 168, 56, 152)(36, 132, 58, 154, 81, 177, 70, 166, 90, 186, 77, 173, 82, 178, 59, 155)(71, 167, 91, 187, 94, 190, 93, 189, 96, 192, 88, 184, 95, 191, 92, 188)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 205)(9, 196)(10, 211)(11, 214)(12, 197)(13, 200)(14, 215)(15, 220)(16, 199)(17, 222)(18, 225)(19, 202)(20, 227)(21, 228)(22, 203)(23, 206)(24, 229)(25, 234)(26, 235)(27, 238)(28, 207)(29, 239)(30, 209)(31, 243)(32, 245)(33, 210)(34, 248)(35, 212)(36, 213)(37, 216)(38, 250)(39, 255)(40, 256)(41, 259)(42, 217)(43, 218)(44, 262)(45, 263)(46, 219)(47, 221)(48, 264)(49, 254)(50, 252)(51, 223)(52, 269)(53, 224)(54, 260)(55, 266)(56, 226)(57, 251)(58, 230)(59, 249)(60, 242)(61, 275)(62, 241)(63, 231)(64, 232)(65, 279)(66, 280)(67, 233)(68, 246)(69, 273)(70, 236)(71, 237)(72, 240)(73, 283)(74, 247)(75, 285)(76, 284)(77, 244)(78, 274)(79, 276)(80, 278)(81, 261)(82, 270)(83, 253)(84, 271)(85, 286)(86, 272)(87, 257)(88, 258)(89, 287)(90, 288)(91, 265)(92, 268)(93, 267)(94, 277)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.210 Graph:: simple bipartite v = 108 e = 192 f = 80 degree seq :: [ 2^96, 16^12 ] E3.214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^3, (Y3 * Y2^-1)^3, Y2^8, (Y2^2 * Y1 * Y2)^3, (Y2^2 * Y1 * Y2^-3 * Y1)^2 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 16, 112)(10, 106, 19, 115)(12, 108, 22, 118)(14, 110, 25, 121)(15, 111, 27, 123)(17, 113, 30, 126)(18, 114, 32, 128)(20, 116, 35, 131)(21, 117, 36, 132)(23, 119, 39, 135)(24, 120, 41, 137)(26, 122, 44, 140)(28, 124, 46, 142)(29, 125, 48, 144)(31, 127, 51, 147)(33, 129, 53, 149)(34, 130, 55, 151)(37, 133, 59, 155)(38, 134, 61, 157)(40, 136, 64, 160)(42, 138, 66, 162)(43, 139, 68, 164)(45, 141, 58, 154)(47, 143, 72, 168)(49, 145, 69, 165)(50, 146, 74, 170)(52, 148, 65, 161)(54, 150, 78, 174)(56, 152, 62, 158)(57, 153, 76, 172)(60, 156, 82, 178)(63, 159, 84, 180)(67, 163, 88, 184)(70, 166, 86, 182)(71, 167, 91, 187)(73, 169, 85, 181)(75, 171, 83, 179)(77, 173, 93, 189)(79, 175, 90, 186)(80, 176, 89, 185)(81, 177, 94, 190)(87, 183, 96, 192)(92, 188, 95, 191)(193, 289, 195, 291, 200, 296, 209, 305, 223, 319, 212, 308, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 215, 311, 232, 328, 218, 314, 206, 302, 198, 294)(199, 295, 205, 301, 216, 312, 234, 330, 259, 355, 239, 335, 220, 316, 207, 303)(201, 297, 210, 306, 225, 321, 246, 342, 252, 348, 229, 325, 213, 309, 203, 299)(208, 304, 219, 315, 237, 333, 251, 347, 273, 369, 265, 361, 241, 337, 221, 317)(211, 307, 226, 322, 248, 344, 271, 367, 279, 375, 258, 354, 244, 340, 224, 320)(214, 310, 228, 324, 250, 346, 238, 334, 263, 359, 275, 371, 254, 350, 230, 326)(217, 313, 235, 331, 261, 357, 281, 377, 269, 365, 245, 341, 257, 353, 233, 329)(222, 318, 240, 336, 260, 356, 236, 332, 262, 358, 282, 378, 267, 363, 242, 338)(227, 323, 249, 345, 272, 368, 277, 373, 255, 351, 231, 327, 253, 349, 247, 343)(243, 339, 266, 362, 283, 379, 264, 360, 284, 380, 270, 366, 285, 381, 268, 364)(256, 352, 276, 372, 286, 382, 274, 370, 287, 383, 280, 376, 288, 384, 278, 374) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 208)(9, 196)(10, 211)(11, 197)(12, 214)(13, 198)(14, 217)(15, 219)(16, 200)(17, 222)(18, 224)(19, 202)(20, 227)(21, 228)(22, 204)(23, 231)(24, 233)(25, 206)(26, 236)(27, 207)(28, 238)(29, 240)(30, 209)(31, 243)(32, 210)(33, 245)(34, 247)(35, 212)(36, 213)(37, 251)(38, 253)(39, 215)(40, 256)(41, 216)(42, 258)(43, 260)(44, 218)(45, 250)(46, 220)(47, 264)(48, 221)(49, 261)(50, 266)(51, 223)(52, 257)(53, 225)(54, 270)(55, 226)(56, 254)(57, 268)(58, 237)(59, 229)(60, 274)(61, 230)(62, 248)(63, 276)(64, 232)(65, 244)(66, 234)(67, 280)(68, 235)(69, 241)(70, 278)(71, 283)(72, 239)(73, 277)(74, 242)(75, 275)(76, 249)(77, 285)(78, 246)(79, 282)(80, 281)(81, 286)(82, 252)(83, 267)(84, 255)(85, 265)(86, 262)(87, 288)(88, 259)(89, 272)(90, 271)(91, 263)(92, 287)(93, 269)(94, 273)(95, 284)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) 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 E3.215 Graph:: bipartite v = 60 e = 192 f = 128 degree seq :: [ 4^48, 16^12 ] E3.215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8}) Quotient :: dipole Aut^+ = ((C4 x C4) : C3) : C2 (small group id <96, 64>) Aut = (((C4 x C4) : C3) : C2) : C2 (small group id <192, 956>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y1^-1)^3, Y3 * Y1^-1 * Y3^-3 * Y1 * Y3^2 * Y1^-1 * Y3^-4 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 4, 100)(3, 99, 8, 104, 10, 106)(5, 101, 12, 108, 6, 102)(7, 103, 15, 111, 11, 107)(9, 105, 18, 114, 20, 116)(13, 109, 25, 121, 23, 119)(14, 110, 24, 120, 28, 124)(16, 112, 31, 127, 29, 125)(17, 113, 33, 129, 21, 117)(19, 115, 36, 132, 38, 134)(22, 118, 30, 126, 42, 138)(26, 122, 47, 143, 45, 141)(27, 123, 48, 144, 50, 146)(32, 128, 55, 151, 54, 150)(34, 130, 57, 153, 56, 152)(35, 131, 52, 148, 39, 135)(37, 133, 61, 157, 62, 158)(40, 136, 51, 147, 44, 140)(41, 137, 65, 161, 66, 162)(43, 139, 46, 142, 53, 149)(49, 145, 72, 168, 73, 169)(58, 154, 80, 176, 79, 175)(59, 155, 81, 177, 74, 170)(60, 156, 78, 174, 63, 159)(64, 160, 68, 164, 86, 182)(67, 163, 75, 171, 89, 185)(69, 165, 70, 166, 71, 167)(76, 172, 77, 173, 87, 183)(82, 178, 93, 189, 92, 188)(83, 179, 90, 186, 91, 187)(84, 180, 94, 190, 85, 181)(88, 184, 95, 191, 96, 192)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 198)(3, 201)(4, 203)(5, 193)(6, 206)(7, 194)(8, 196)(9, 211)(10, 213)(11, 214)(12, 215)(13, 197)(14, 219)(15, 221)(16, 199)(17, 200)(18, 202)(19, 229)(20, 231)(21, 232)(22, 233)(23, 235)(24, 204)(25, 237)(26, 205)(27, 241)(28, 243)(29, 244)(30, 207)(31, 246)(32, 208)(33, 248)(34, 209)(35, 210)(36, 212)(37, 218)(38, 255)(39, 223)(40, 256)(41, 250)(42, 238)(43, 259)(44, 216)(45, 261)(46, 217)(47, 254)(48, 220)(49, 224)(50, 262)(51, 225)(52, 266)(53, 222)(54, 268)(55, 265)(56, 270)(57, 271)(58, 226)(59, 227)(60, 228)(61, 230)(62, 277)(63, 249)(64, 274)(65, 234)(66, 269)(67, 280)(68, 236)(69, 282)(70, 239)(71, 240)(72, 242)(73, 285)(74, 286)(75, 245)(76, 275)(77, 247)(78, 283)(79, 287)(80, 258)(81, 284)(82, 251)(83, 252)(84, 253)(85, 273)(86, 288)(87, 257)(88, 260)(89, 276)(90, 279)(91, 263)(92, 264)(93, 278)(94, 267)(95, 281)(96, 272)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E3.214 Graph:: simple bipartite v = 128 e = 192 f = 60 degree seq :: [ 2^96, 6^32 ] E3.216 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-3 ] Map:: polyhedral non-degenerate R = (1, 2, 5, 11, 20, 10, 4)(3, 7, 15, 26, 30, 17, 8)(6, 13, 24, 39, 42, 25, 14)(9, 18, 31, 49, 46, 28, 16)(12, 22, 37, 57, 60, 38, 23)(19, 33, 52, 77, 76, 51, 32)(21, 35, 55, 81, 84, 56, 36)(27, 44, 67, 97, 100, 68, 45)(29, 47, 70, 102, 91, 62, 40)(34, 54, 80, 115, 114, 79, 53)(41, 63, 92, 130, 123, 86, 58)(43, 65, 95, 134, 137, 96, 66)(48, 72, 105, 143, 117, 104, 71)(50, 74, 108, 129, 148, 109, 75)(59, 87, 124, 142, 103, 118, 82)(61, 89, 127, 110, 149, 128, 90)(64, 94, 133, 160, 153, 132, 93)(69, 101, 140, 122, 85, 121, 98)(73, 106, 145, 120, 155, 146, 107)(78, 112, 135, 99, 138, 152, 113)(83, 119, 147, 159, 131, 154, 116)(88, 126, 156, 151, 111, 150, 125)(136, 161, 157, 167, 163, 166, 144)(139, 158, 168, 165, 141, 164, 162) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 123)(100, 139)(101, 107)(102, 141)(104, 118)(105, 144)(108, 127)(109, 147)(113, 150)(114, 134)(115, 153)(119, 145)(122, 126)(124, 152)(128, 157)(130, 158)(132, 154)(133, 161)(137, 160)(138, 162)(140, 163)(142, 164)(143, 155)(146, 166)(148, 165)(149, 151)(156, 167)(159, 168) local type(s) :: { ( 3^7 ) } Outer automorphisms :: reflexible Dual of E3.217 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 24 e = 84 f = 56 degree seq :: [ 7^24 ] E3.217 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 3, 7}) Quotient :: regular Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1^-1 * T2)^7, (T2 * T1 * T2 * T1^-1)^4 ] Map:: polyhedral non-degenerate R = (1, 2, 4)(3, 6, 7)(5, 9, 10)(8, 13, 14)(11, 17, 18)(12, 19, 20)(15, 23, 24)(16, 25, 26)(21, 31, 32)(22, 33, 34)(27, 39, 40)(28, 41, 42)(29, 43, 44)(30, 45, 46)(35, 51, 52)(36, 53, 54)(37, 55, 56)(38, 57, 58)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 59)(60, 79, 80)(61, 81, 77)(62, 82, 83)(63, 84, 85)(64, 86, 87)(65, 88, 89)(73, 95, 96)(74, 97, 93)(75, 98, 99)(76, 100, 101)(78, 102, 103)(90, 112, 113)(91, 114, 115)(92, 116, 117)(94, 118, 119)(104, 127, 111)(105, 128, 129)(106, 130, 131)(107, 132, 133)(108, 134, 135)(109, 136, 137)(110, 138, 139)(120, 146, 126)(121, 147, 148)(122, 149, 150)(123, 151, 152)(124, 153, 154)(125, 155, 156)(140, 162, 145)(141, 163, 161)(142, 160, 164)(143, 158, 165)(144, 166, 159)(157, 168, 167) 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, 47)(32, 48)(33, 49)(34, 50)(39, 59)(40, 60)(41, 61)(42, 62)(43, 63)(44, 64)(45, 65)(46, 51)(52, 73)(53, 74)(54, 75)(55, 76)(56, 77)(57, 78)(58, 66)(67, 90)(68, 86)(69, 91)(70, 92)(71, 93)(72, 94)(79, 104)(80, 105)(81, 106)(82, 107)(83, 84)(85, 108)(87, 109)(88, 110)(89, 111)(95, 120)(96, 121)(97, 122)(98, 123)(99, 100)(101, 124)(102, 125)(103, 126)(112, 140)(113, 141)(114, 142)(115, 116)(117, 143)(118, 144)(119, 145)(127, 157)(128, 158)(129, 130)(131, 155)(132, 154)(133, 159)(134, 147)(135, 160)(136, 161)(137, 138)(139, 152)(146, 167)(148, 149)(150, 166)(151, 165)(153, 163)(156, 164)(162, 168) local type(s) :: { ( 7^3 ) } Outer automorphisms :: reflexible Dual of E3.216 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 56 e = 84 f = 24 degree seq :: [ 3^56 ] E3.218 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, (T1 * T2^-1 * T1 * T2)^4 ] 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, 58, 59)(44, 60, 61)(45, 62, 63)(46, 64, 65)(47, 66, 67)(48, 68, 69)(49, 70, 71)(50, 72, 51)(52, 73, 74)(53, 75, 76)(54, 77, 78)(55, 79, 80)(56, 81, 82)(57, 83, 84)(85, 103, 104)(86, 105, 93)(87, 106, 107)(88, 108, 109)(89, 110, 111)(90, 112, 113)(91, 114, 115)(92, 116, 117)(94, 118, 119)(95, 120, 102)(96, 121, 122)(97, 123, 124)(98, 125, 126)(99, 127, 128)(100, 129, 130)(101, 131, 132)(133, 155, 139)(134, 151, 156)(135, 157, 158)(136, 159, 154)(137, 160, 149)(138, 148, 161)(140, 162, 145)(141, 163, 153)(142, 152, 164)(143, 147, 165)(144, 166, 150)(146, 167, 168)(169, 170)(171, 175)(172, 176)(173, 177)(174, 178)(179, 187)(180, 188)(181, 189)(182, 190)(183, 191)(184, 192)(185, 193)(186, 194)(195, 211)(196, 212)(197, 213)(198, 214)(199, 215)(200, 216)(201, 217)(202, 218)(203, 219)(204, 220)(205, 221)(206, 222)(207, 223)(208, 224)(209, 225)(210, 226)(227, 253)(228, 254)(229, 255)(230, 256)(231, 244)(232, 257)(233, 234)(235, 258)(236, 249)(237, 259)(238, 260)(239, 261)(240, 262)(241, 263)(242, 264)(243, 265)(245, 266)(246, 247)(248, 267)(250, 268)(251, 269)(252, 270)(271, 301)(272, 302)(273, 303)(274, 304)(275, 276)(277, 305)(278, 306)(279, 307)(280, 308)(281, 309)(282, 310)(283, 284)(285, 311)(286, 312)(287, 313)(288, 314)(289, 315)(290, 291)(292, 316)(293, 317)(294, 318)(295, 319)(296, 320)(297, 321)(298, 299)(300, 322)(323, 336)(324, 325)(326, 334)(327, 333)(328, 331)(329, 332)(330, 335) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 14, 14 ), ( 14^3 ) } Outer automorphisms :: reflexible Dual of E3.222 Transitivity :: ET+ Graph:: simple bipartite v = 140 e = 168 f = 24 degree seq :: [ 2^84, 3^56 ] E3.219 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^7, (T1 * T2^-2)^4 ] Map:: polyhedral non-degenerate R = (1, 3, 9, 19, 26, 13, 5)(2, 6, 14, 27, 32, 16, 7)(4, 11, 22, 40, 34, 17, 8)(10, 21, 39, 63, 59, 35, 18)(12, 23, 42, 68, 71, 43, 24)(15, 29, 50, 78, 81, 51, 30)(20, 38, 62, 94, 92, 60, 36)(25, 44, 72, 106, 108, 73, 45)(28, 49, 77, 113, 111, 75, 47)(31, 52, 82, 118, 120, 83, 53)(33, 55, 85, 122, 124, 86, 56)(37, 61, 93, 131, 109, 74, 46)(41, 67, 100, 138, 136, 98, 65)(48, 76, 112, 149, 121, 84, 54)(57, 66, 99, 137, 160, 125, 87)(58, 88, 126, 151, 114, 79, 89)(64, 97, 70, 104, 141, 133, 95)(69, 103, 80, 116, 153, 139, 101)(90, 96, 134, 164, 146, 144, 127)(91, 128, 162, 168, 158, 123, 129)(102, 140, 130, 132, 156, 142, 105)(107, 145, 110, 147, 167, 161, 143)(115, 152, 148, 150, 159, 154, 117)(119, 157, 135, 165, 163, 166, 155)(169, 170, 172)(171, 176, 178)(173, 180, 174)(175, 183, 179)(177, 186, 188)(181, 193, 191)(182, 192, 196)(184, 199, 197)(185, 201, 189)(187, 204, 205)(190, 198, 209)(194, 214, 212)(195, 215, 216)(200, 222, 220)(202, 225, 223)(203, 226, 206)(207, 224, 232)(208, 233, 234)(210, 213, 237)(211, 238, 217)(218, 221, 247)(219, 248, 235)(227, 258, 256)(228, 259, 229)(230, 257, 251)(231, 263, 264)(236, 269, 270)(239, 273, 272)(240, 242, 275)(241, 268, 271)(243, 278, 244)(245, 265, 254)(246, 282, 283)(249, 285, 284)(250, 252, 287)(253, 255, 291)(260, 298, 296)(261, 297, 293)(262, 288, 300)(266, 303, 267)(274, 311, 312)(276, 314, 306)(277, 280, 313)(279, 316, 315)(281, 292, 318)(286, 323, 324)(289, 305, 325)(290, 326, 327)(294, 295, 329)(299, 328, 317)(301, 331, 302)(304, 332, 333)(307, 330, 308)(309, 310, 334)(319, 335, 320)(321, 322, 336) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 4^3 ), ( 4^7 ) } Outer automorphisms :: reflexible Dual of E3.223 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 168 f = 84 degree seq :: [ 3^56, 7^24 ] E3.220 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 3, 7}) Quotient :: edge Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-3 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 13)(10, 19)(11, 21)(14, 22)(15, 27)(17, 29)(18, 32)(20, 34)(23, 35)(24, 40)(25, 41)(26, 43)(28, 44)(30, 48)(31, 50)(33, 53)(36, 54)(37, 58)(38, 59)(39, 61)(42, 64)(45, 65)(46, 69)(47, 71)(49, 73)(51, 74)(52, 78)(55, 82)(56, 83)(57, 85)(60, 88)(62, 89)(63, 93)(66, 72)(67, 98)(68, 99)(70, 103)(75, 106)(76, 110)(77, 111)(79, 112)(80, 116)(81, 117)(84, 120)(86, 121)(87, 125)(90, 94)(91, 129)(92, 131)(95, 135)(96, 136)(97, 123)(100, 139)(101, 107)(102, 141)(104, 118)(105, 144)(108, 127)(109, 147)(113, 150)(114, 134)(115, 153)(119, 145)(122, 126)(124, 152)(128, 157)(130, 158)(132, 154)(133, 161)(137, 160)(138, 162)(140, 163)(142, 164)(143, 155)(146, 166)(148, 165)(149, 151)(156, 167)(159, 168)(169, 170, 173, 179, 188, 178, 172)(171, 175, 183, 194, 198, 185, 176)(174, 181, 192, 207, 210, 193, 182)(177, 186, 199, 217, 214, 196, 184)(180, 190, 205, 225, 228, 206, 191)(187, 201, 220, 245, 244, 219, 200)(189, 203, 223, 249, 252, 224, 204)(195, 212, 235, 265, 268, 236, 213)(197, 215, 238, 270, 259, 230, 208)(202, 222, 248, 283, 282, 247, 221)(209, 231, 260, 298, 291, 254, 226)(211, 233, 263, 302, 305, 264, 234)(216, 240, 273, 311, 285, 272, 239)(218, 242, 276, 297, 316, 277, 243)(227, 255, 292, 310, 271, 286, 250)(229, 257, 295, 278, 317, 296, 258)(232, 262, 301, 328, 321, 300, 261)(237, 269, 308, 290, 253, 289, 266)(241, 274, 313, 288, 323, 314, 275)(246, 280, 303, 267, 306, 320, 281)(251, 287, 315, 327, 299, 322, 284)(256, 294, 324, 319, 279, 318, 293)(304, 329, 325, 335, 331, 334, 312)(307, 326, 336, 333, 309, 332, 330) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336) local type(s) :: { ( 6, 6 ), ( 6^7 ) } Outer automorphisms :: reflexible Dual of E3.221 Transitivity :: ET+ Graph:: simple bipartite v = 108 e = 168 f = 56 degree seq :: [ 2^84, 7^24 ] E3.221 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1)^7, (T1 * T2^-1 * T1 * T2)^4 ] Map:: R = (1, 169, 3, 171, 4, 172)(2, 170, 5, 173, 6, 174)(7, 175, 11, 179, 12, 180)(8, 176, 13, 181, 14, 182)(9, 177, 15, 183, 16, 184)(10, 178, 17, 185, 18, 186)(19, 187, 27, 195, 28, 196)(20, 188, 29, 197, 30, 198)(21, 189, 31, 199, 32, 200)(22, 190, 33, 201, 34, 202)(23, 191, 35, 203, 36, 204)(24, 192, 37, 205, 38, 206)(25, 193, 39, 207, 40, 208)(26, 194, 41, 209, 42, 210)(43, 211, 58, 226, 59, 227)(44, 212, 60, 228, 61, 229)(45, 213, 62, 230, 63, 231)(46, 214, 64, 232, 65, 233)(47, 215, 66, 234, 67, 235)(48, 216, 68, 236, 69, 237)(49, 217, 70, 238, 71, 239)(50, 218, 72, 240, 51, 219)(52, 220, 73, 241, 74, 242)(53, 221, 75, 243, 76, 244)(54, 222, 77, 245, 78, 246)(55, 223, 79, 247, 80, 248)(56, 224, 81, 249, 82, 250)(57, 225, 83, 251, 84, 252)(85, 253, 103, 271, 104, 272)(86, 254, 105, 273, 93, 261)(87, 255, 106, 274, 107, 275)(88, 256, 108, 276, 109, 277)(89, 257, 110, 278, 111, 279)(90, 258, 112, 280, 113, 281)(91, 259, 114, 282, 115, 283)(92, 260, 116, 284, 117, 285)(94, 262, 118, 286, 119, 287)(95, 263, 120, 288, 102, 270)(96, 264, 121, 289, 122, 290)(97, 265, 123, 291, 124, 292)(98, 266, 125, 293, 126, 294)(99, 267, 127, 295, 128, 296)(100, 268, 129, 297, 130, 298)(101, 269, 131, 299, 132, 300)(133, 301, 155, 323, 139, 307)(134, 302, 151, 319, 156, 324)(135, 303, 157, 325, 158, 326)(136, 304, 159, 327, 154, 322)(137, 305, 160, 328, 149, 317)(138, 306, 148, 316, 161, 329)(140, 308, 162, 330, 145, 313)(141, 309, 163, 331, 153, 321)(142, 310, 152, 320, 164, 332)(143, 311, 147, 315, 165, 333)(144, 312, 166, 334, 150, 318)(146, 314, 167, 335, 168, 336) L = (1, 170)(2, 169)(3, 175)(4, 176)(5, 177)(6, 178)(7, 171)(8, 172)(9, 173)(10, 174)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 179)(20, 180)(21, 181)(22, 182)(23, 183)(24, 184)(25, 185)(26, 186)(27, 211)(28, 212)(29, 213)(30, 214)(31, 215)(32, 216)(33, 217)(34, 218)(35, 219)(36, 220)(37, 221)(38, 222)(39, 223)(40, 224)(41, 225)(42, 226)(43, 195)(44, 196)(45, 197)(46, 198)(47, 199)(48, 200)(49, 201)(50, 202)(51, 203)(52, 204)(53, 205)(54, 206)(55, 207)(56, 208)(57, 209)(58, 210)(59, 253)(60, 254)(61, 255)(62, 256)(63, 244)(64, 257)(65, 234)(66, 233)(67, 258)(68, 249)(69, 259)(70, 260)(71, 261)(72, 262)(73, 263)(74, 264)(75, 265)(76, 231)(77, 266)(78, 247)(79, 246)(80, 267)(81, 236)(82, 268)(83, 269)(84, 270)(85, 227)(86, 228)(87, 229)(88, 230)(89, 232)(90, 235)(91, 237)(92, 238)(93, 239)(94, 240)(95, 241)(96, 242)(97, 243)(98, 245)(99, 248)(100, 250)(101, 251)(102, 252)(103, 301)(104, 302)(105, 303)(106, 304)(107, 276)(108, 275)(109, 305)(110, 306)(111, 307)(112, 308)(113, 309)(114, 310)(115, 284)(116, 283)(117, 311)(118, 312)(119, 313)(120, 314)(121, 315)(122, 291)(123, 290)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 299)(131, 298)(132, 322)(133, 271)(134, 272)(135, 273)(136, 274)(137, 277)(138, 278)(139, 279)(140, 280)(141, 281)(142, 282)(143, 285)(144, 286)(145, 287)(146, 288)(147, 289)(148, 292)(149, 293)(150, 294)(151, 295)(152, 296)(153, 297)(154, 300)(155, 336)(156, 325)(157, 324)(158, 334)(159, 333)(160, 331)(161, 332)(162, 335)(163, 328)(164, 329)(165, 327)(166, 326)(167, 330)(168, 323) local type(s) :: { ( 2, 7, 2, 7, 2, 7 ) } Outer automorphisms :: reflexible Dual of E3.220 Transitivity :: ET+ VT+ AT Graph:: v = 56 e = 168 f = 108 degree seq :: [ 6^56 ] E3.222 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^7, (T1 * T2^-2)^4 ] Map:: R = (1, 169, 3, 171, 9, 177, 19, 187, 26, 194, 13, 181, 5, 173)(2, 170, 6, 174, 14, 182, 27, 195, 32, 200, 16, 184, 7, 175)(4, 172, 11, 179, 22, 190, 40, 208, 34, 202, 17, 185, 8, 176)(10, 178, 21, 189, 39, 207, 63, 231, 59, 227, 35, 203, 18, 186)(12, 180, 23, 191, 42, 210, 68, 236, 71, 239, 43, 211, 24, 192)(15, 183, 29, 197, 50, 218, 78, 246, 81, 249, 51, 219, 30, 198)(20, 188, 38, 206, 62, 230, 94, 262, 92, 260, 60, 228, 36, 204)(25, 193, 44, 212, 72, 240, 106, 274, 108, 276, 73, 241, 45, 213)(28, 196, 49, 217, 77, 245, 113, 281, 111, 279, 75, 243, 47, 215)(31, 199, 52, 220, 82, 250, 118, 286, 120, 288, 83, 251, 53, 221)(33, 201, 55, 223, 85, 253, 122, 290, 124, 292, 86, 254, 56, 224)(37, 205, 61, 229, 93, 261, 131, 299, 109, 277, 74, 242, 46, 214)(41, 209, 67, 235, 100, 268, 138, 306, 136, 304, 98, 266, 65, 233)(48, 216, 76, 244, 112, 280, 149, 317, 121, 289, 84, 252, 54, 222)(57, 225, 66, 234, 99, 267, 137, 305, 160, 328, 125, 293, 87, 255)(58, 226, 88, 256, 126, 294, 151, 319, 114, 282, 79, 247, 89, 257)(64, 232, 97, 265, 70, 238, 104, 272, 141, 309, 133, 301, 95, 263)(69, 237, 103, 271, 80, 248, 116, 284, 153, 321, 139, 307, 101, 269)(90, 258, 96, 264, 134, 302, 164, 332, 146, 314, 144, 312, 127, 295)(91, 259, 128, 296, 162, 330, 168, 336, 158, 326, 123, 291, 129, 297)(102, 270, 140, 308, 130, 298, 132, 300, 156, 324, 142, 310, 105, 273)(107, 275, 145, 313, 110, 278, 147, 315, 167, 335, 161, 329, 143, 311)(115, 283, 152, 320, 148, 316, 150, 318, 159, 327, 154, 322, 117, 285)(119, 287, 157, 325, 135, 303, 165, 333, 163, 331, 166, 334, 155, 323) L = (1, 170)(2, 172)(3, 176)(4, 169)(5, 180)(6, 173)(7, 183)(8, 178)(9, 186)(10, 171)(11, 175)(12, 174)(13, 193)(14, 192)(15, 179)(16, 199)(17, 201)(18, 188)(19, 204)(20, 177)(21, 185)(22, 198)(23, 181)(24, 196)(25, 191)(26, 214)(27, 215)(28, 182)(29, 184)(30, 209)(31, 197)(32, 222)(33, 189)(34, 225)(35, 226)(36, 205)(37, 187)(38, 203)(39, 224)(40, 233)(41, 190)(42, 213)(43, 238)(44, 194)(45, 237)(46, 212)(47, 216)(48, 195)(49, 211)(50, 221)(51, 248)(52, 200)(53, 247)(54, 220)(55, 202)(56, 232)(57, 223)(58, 206)(59, 258)(60, 259)(61, 228)(62, 257)(63, 263)(64, 207)(65, 234)(66, 208)(67, 219)(68, 269)(69, 210)(70, 217)(71, 273)(72, 242)(73, 268)(74, 275)(75, 278)(76, 243)(77, 265)(78, 282)(79, 218)(80, 235)(81, 285)(82, 252)(83, 230)(84, 287)(85, 255)(86, 245)(87, 291)(88, 227)(89, 251)(90, 256)(91, 229)(92, 298)(93, 297)(94, 288)(95, 264)(96, 231)(97, 254)(98, 303)(99, 266)(100, 271)(101, 270)(102, 236)(103, 241)(104, 239)(105, 272)(106, 311)(107, 240)(108, 314)(109, 280)(110, 244)(111, 316)(112, 313)(113, 292)(114, 283)(115, 246)(116, 249)(117, 284)(118, 323)(119, 250)(120, 300)(121, 305)(122, 326)(123, 253)(124, 318)(125, 261)(126, 295)(127, 329)(128, 260)(129, 293)(130, 296)(131, 328)(132, 262)(133, 331)(134, 301)(135, 267)(136, 332)(137, 325)(138, 276)(139, 330)(140, 307)(141, 310)(142, 334)(143, 312)(144, 274)(145, 277)(146, 306)(147, 279)(148, 315)(149, 299)(150, 281)(151, 335)(152, 319)(153, 322)(154, 336)(155, 324)(156, 286)(157, 289)(158, 327)(159, 290)(160, 317)(161, 294)(162, 308)(163, 302)(164, 333)(165, 304)(166, 309)(167, 320)(168, 321) local type(s) :: { ( 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3 ) } Outer automorphisms :: reflexible Dual of E3.218 Transitivity :: ET+ VT+ AT Graph:: v = 24 e = 168 f = 140 degree seq :: [ 14^24 ] E3.223 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 3, 7}) Quotient :: loop Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^3, T1^7, T2 * T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-2 * T2 * T1^-3 ] Map:: polyhedral non-degenerate R = (1, 169, 3, 171)(2, 170, 6, 174)(4, 172, 9, 177)(5, 173, 12, 180)(7, 175, 16, 184)(8, 176, 13, 181)(10, 178, 19, 187)(11, 179, 21, 189)(14, 182, 22, 190)(15, 183, 27, 195)(17, 185, 29, 197)(18, 186, 32, 200)(20, 188, 34, 202)(23, 191, 35, 203)(24, 192, 40, 208)(25, 193, 41, 209)(26, 194, 43, 211)(28, 196, 44, 212)(30, 198, 48, 216)(31, 199, 50, 218)(33, 201, 53, 221)(36, 204, 54, 222)(37, 205, 58, 226)(38, 206, 59, 227)(39, 207, 61, 229)(42, 210, 64, 232)(45, 213, 65, 233)(46, 214, 69, 237)(47, 215, 71, 239)(49, 217, 73, 241)(51, 219, 74, 242)(52, 220, 78, 246)(55, 223, 82, 250)(56, 224, 83, 251)(57, 225, 85, 253)(60, 228, 88, 256)(62, 230, 89, 257)(63, 231, 93, 261)(66, 234, 72, 240)(67, 235, 98, 266)(68, 236, 99, 267)(70, 238, 103, 271)(75, 243, 106, 274)(76, 244, 110, 278)(77, 245, 111, 279)(79, 247, 112, 280)(80, 248, 116, 284)(81, 249, 117, 285)(84, 252, 120, 288)(86, 254, 121, 289)(87, 255, 125, 293)(90, 258, 94, 262)(91, 259, 129, 297)(92, 260, 131, 299)(95, 263, 135, 303)(96, 264, 136, 304)(97, 265, 123, 291)(100, 268, 139, 307)(101, 269, 107, 275)(102, 270, 141, 309)(104, 272, 118, 286)(105, 273, 144, 312)(108, 276, 127, 295)(109, 277, 147, 315)(113, 281, 150, 318)(114, 282, 134, 302)(115, 283, 153, 321)(119, 287, 145, 313)(122, 290, 126, 294)(124, 292, 152, 320)(128, 296, 157, 325)(130, 298, 158, 326)(132, 300, 154, 322)(133, 301, 161, 329)(137, 305, 160, 328)(138, 306, 162, 330)(140, 308, 163, 331)(142, 310, 164, 332)(143, 311, 155, 323)(146, 314, 166, 334)(148, 316, 165, 333)(149, 317, 151, 319)(156, 324, 167, 335)(159, 327, 168, 336) L = (1, 170)(2, 173)(3, 175)(4, 169)(5, 179)(6, 181)(7, 183)(8, 171)(9, 186)(10, 172)(11, 188)(12, 190)(13, 192)(14, 174)(15, 194)(16, 177)(17, 176)(18, 199)(19, 201)(20, 178)(21, 203)(22, 205)(23, 180)(24, 207)(25, 182)(26, 198)(27, 212)(28, 184)(29, 215)(30, 185)(31, 217)(32, 187)(33, 220)(34, 222)(35, 223)(36, 189)(37, 225)(38, 191)(39, 210)(40, 197)(41, 231)(42, 193)(43, 233)(44, 235)(45, 195)(46, 196)(47, 238)(48, 240)(49, 214)(50, 242)(51, 200)(52, 245)(53, 202)(54, 248)(55, 249)(56, 204)(57, 228)(58, 209)(59, 255)(60, 206)(61, 257)(62, 208)(63, 260)(64, 262)(65, 263)(66, 211)(67, 265)(68, 213)(69, 269)(70, 270)(71, 216)(72, 273)(73, 274)(74, 276)(75, 218)(76, 219)(77, 244)(78, 280)(79, 221)(80, 283)(81, 252)(82, 227)(83, 287)(84, 224)(85, 289)(86, 226)(87, 292)(88, 294)(89, 295)(90, 229)(91, 230)(92, 298)(93, 232)(94, 301)(95, 302)(96, 234)(97, 268)(98, 237)(99, 306)(100, 236)(101, 308)(102, 259)(103, 286)(104, 239)(105, 311)(106, 313)(107, 241)(108, 297)(109, 243)(110, 317)(111, 318)(112, 303)(113, 246)(114, 247)(115, 282)(116, 251)(117, 272)(118, 250)(119, 315)(120, 323)(121, 266)(122, 253)(123, 254)(124, 310)(125, 256)(126, 324)(127, 278)(128, 258)(129, 316)(130, 291)(131, 322)(132, 261)(133, 328)(134, 305)(135, 267)(136, 329)(137, 264)(138, 320)(139, 326)(140, 290)(141, 332)(142, 271)(143, 285)(144, 304)(145, 288)(146, 275)(147, 327)(148, 277)(149, 296)(150, 293)(151, 279)(152, 281)(153, 300)(154, 284)(155, 314)(156, 319)(157, 335)(158, 336)(159, 299)(160, 321)(161, 325)(162, 307)(163, 334)(164, 330)(165, 309)(166, 312)(167, 331)(168, 333) local type(s) :: { ( 3, 7, 3, 7 ) } Outer automorphisms :: reflexible Dual of E3.219 Transitivity :: ET+ VT+ AT Graph:: simple v = 84 e = 168 f = 80 degree seq :: [ 4^84 ] E3.224 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^7, (Y3 * Y2^-1)^7, (Y1 * Y2 * Y1 * Y2^-1)^4 ] Map:: R = (1, 169, 2, 170)(3, 171, 7, 175)(4, 172, 8, 176)(5, 173, 9, 177)(6, 174, 10, 178)(11, 179, 19, 187)(12, 180, 20, 188)(13, 181, 21, 189)(14, 182, 22, 190)(15, 183, 23, 191)(16, 184, 24, 192)(17, 185, 25, 193)(18, 186, 26, 194)(27, 195, 43, 211)(28, 196, 44, 212)(29, 197, 45, 213)(30, 198, 46, 214)(31, 199, 47, 215)(32, 200, 48, 216)(33, 201, 49, 217)(34, 202, 50, 218)(35, 203, 51, 219)(36, 204, 52, 220)(37, 205, 53, 221)(38, 206, 54, 222)(39, 207, 55, 223)(40, 208, 56, 224)(41, 209, 57, 225)(42, 210, 58, 226)(59, 227, 85, 253)(60, 228, 86, 254)(61, 229, 87, 255)(62, 230, 88, 256)(63, 231, 76, 244)(64, 232, 89, 257)(65, 233, 66, 234)(67, 235, 90, 258)(68, 236, 81, 249)(69, 237, 91, 259)(70, 238, 92, 260)(71, 239, 93, 261)(72, 240, 94, 262)(73, 241, 95, 263)(74, 242, 96, 264)(75, 243, 97, 265)(77, 245, 98, 266)(78, 246, 79, 247)(80, 248, 99, 267)(82, 250, 100, 268)(83, 251, 101, 269)(84, 252, 102, 270)(103, 271, 133, 301)(104, 272, 134, 302)(105, 273, 135, 303)(106, 274, 136, 304)(107, 275, 108, 276)(109, 277, 137, 305)(110, 278, 138, 306)(111, 279, 139, 307)(112, 280, 140, 308)(113, 281, 141, 309)(114, 282, 142, 310)(115, 283, 116, 284)(117, 285, 143, 311)(118, 286, 144, 312)(119, 287, 145, 313)(120, 288, 146, 314)(121, 289, 147, 315)(122, 290, 123, 291)(124, 292, 148, 316)(125, 293, 149, 317)(126, 294, 150, 318)(127, 295, 151, 319)(128, 296, 152, 320)(129, 297, 153, 321)(130, 298, 131, 299)(132, 300, 154, 322)(155, 323, 168, 336)(156, 324, 157, 325)(158, 326, 166, 334)(159, 327, 165, 333)(160, 328, 163, 331)(161, 329, 164, 332)(162, 330, 167, 335)(337, 505, 339, 507, 340, 508)(338, 506, 341, 509, 342, 510)(343, 511, 347, 515, 348, 516)(344, 512, 349, 517, 350, 518)(345, 513, 351, 519, 352, 520)(346, 514, 353, 521, 354, 522)(355, 523, 363, 531, 364, 532)(356, 524, 365, 533, 366, 534)(357, 525, 367, 535, 368, 536)(358, 526, 369, 537, 370, 538)(359, 527, 371, 539, 372, 540)(360, 528, 373, 541, 374, 542)(361, 529, 375, 543, 376, 544)(362, 530, 377, 545, 378, 546)(379, 547, 394, 562, 395, 563)(380, 548, 396, 564, 397, 565)(381, 549, 398, 566, 399, 567)(382, 550, 400, 568, 401, 569)(383, 551, 402, 570, 403, 571)(384, 552, 404, 572, 405, 573)(385, 553, 406, 574, 407, 575)(386, 554, 408, 576, 387, 555)(388, 556, 409, 577, 410, 578)(389, 557, 411, 579, 412, 580)(390, 558, 413, 581, 414, 582)(391, 559, 415, 583, 416, 584)(392, 560, 417, 585, 418, 586)(393, 561, 419, 587, 420, 588)(421, 589, 439, 607, 440, 608)(422, 590, 441, 609, 429, 597)(423, 591, 442, 610, 443, 611)(424, 592, 444, 612, 445, 613)(425, 593, 446, 614, 447, 615)(426, 594, 448, 616, 449, 617)(427, 595, 450, 618, 451, 619)(428, 596, 452, 620, 453, 621)(430, 598, 454, 622, 455, 623)(431, 599, 456, 624, 438, 606)(432, 600, 457, 625, 458, 626)(433, 601, 459, 627, 460, 628)(434, 602, 461, 629, 462, 630)(435, 603, 463, 631, 464, 632)(436, 604, 465, 633, 466, 634)(437, 605, 467, 635, 468, 636)(469, 637, 491, 659, 475, 643)(470, 638, 487, 655, 492, 660)(471, 639, 493, 661, 494, 662)(472, 640, 495, 663, 490, 658)(473, 641, 496, 664, 485, 653)(474, 642, 484, 652, 497, 665)(476, 644, 498, 666, 481, 649)(477, 645, 499, 667, 489, 657)(478, 646, 488, 656, 500, 668)(479, 647, 483, 651, 501, 669)(480, 648, 502, 670, 486, 654)(482, 650, 503, 671, 504, 672) L = (1, 338)(2, 337)(3, 343)(4, 344)(5, 345)(6, 346)(7, 339)(8, 340)(9, 341)(10, 342)(11, 355)(12, 356)(13, 357)(14, 358)(15, 359)(16, 360)(17, 361)(18, 362)(19, 347)(20, 348)(21, 349)(22, 350)(23, 351)(24, 352)(25, 353)(26, 354)(27, 379)(28, 380)(29, 381)(30, 382)(31, 383)(32, 384)(33, 385)(34, 386)(35, 387)(36, 388)(37, 389)(38, 390)(39, 391)(40, 392)(41, 393)(42, 394)(43, 363)(44, 364)(45, 365)(46, 366)(47, 367)(48, 368)(49, 369)(50, 370)(51, 371)(52, 372)(53, 373)(54, 374)(55, 375)(56, 376)(57, 377)(58, 378)(59, 421)(60, 422)(61, 423)(62, 424)(63, 412)(64, 425)(65, 402)(66, 401)(67, 426)(68, 417)(69, 427)(70, 428)(71, 429)(72, 430)(73, 431)(74, 432)(75, 433)(76, 399)(77, 434)(78, 415)(79, 414)(80, 435)(81, 404)(82, 436)(83, 437)(84, 438)(85, 395)(86, 396)(87, 397)(88, 398)(89, 400)(90, 403)(91, 405)(92, 406)(93, 407)(94, 408)(95, 409)(96, 410)(97, 411)(98, 413)(99, 416)(100, 418)(101, 419)(102, 420)(103, 469)(104, 470)(105, 471)(106, 472)(107, 444)(108, 443)(109, 473)(110, 474)(111, 475)(112, 476)(113, 477)(114, 478)(115, 452)(116, 451)(117, 479)(118, 480)(119, 481)(120, 482)(121, 483)(122, 459)(123, 458)(124, 484)(125, 485)(126, 486)(127, 487)(128, 488)(129, 489)(130, 467)(131, 466)(132, 490)(133, 439)(134, 440)(135, 441)(136, 442)(137, 445)(138, 446)(139, 447)(140, 448)(141, 449)(142, 450)(143, 453)(144, 454)(145, 455)(146, 456)(147, 457)(148, 460)(149, 461)(150, 462)(151, 463)(152, 464)(153, 465)(154, 468)(155, 504)(156, 493)(157, 492)(158, 502)(159, 501)(160, 499)(161, 500)(162, 503)(163, 496)(164, 497)(165, 495)(166, 494)(167, 498)(168, 491)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 2, 14, 2, 14 ), ( 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E3.227 Graph:: bipartite v = 140 e = 336 f = 192 degree seq :: [ 4^84, 6^56 ] E3.225 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y2^7, (Y1 * Y2^-2)^4 ] Map:: R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 10, 178)(5, 173, 12, 180, 6, 174)(7, 175, 15, 183, 11, 179)(9, 177, 18, 186, 20, 188)(13, 181, 25, 193, 23, 191)(14, 182, 24, 192, 28, 196)(16, 184, 31, 199, 29, 197)(17, 185, 33, 201, 21, 189)(19, 187, 36, 204, 37, 205)(22, 190, 30, 198, 41, 209)(26, 194, 46, 214, 44, 212)(27, 195, 47, 215, 48, 216)(32, 200, 54, 222, 52, 220)(34, 202, 57, 225, 55, 223)(35, 203, 58, 226, 38, 206)(39, 207, 56, 224, 64, 232)(40, 208, 65, 233, 66, 234)(42, 210, 45, 213, 69, 237)(43, 211, 70, 238, 49, 217)(50, 218, 53, 221, 79, 247)(51, 219, 80, 248, 67, 235)(59, 227, 90, 258, 88, 256)(60, 228, 91, 259, 61, 229)(62, 230, 89, 257, 83, 251)(63, 231, 95, 263, 96, 264)(68, 236, 101, 269, 102, 270)(71, 239, 105, 273, 104, 272)(72, 240, 74, 242, 107, 275)(73, 241, 100, 268, 103, 271)(75, 243, 110, 278, 76, 244)(77, 245, 97, 265, 86, 254)(78, 246, 114, 282, 115, 283)(81, 249, 117, 285, 116, 284)(82, 250, 84, 252, 119, 287)(85, 253, 87, 255, 123, 291)(92, 260, 130, 298, 128, 296)(93, 261, 129, 297, 125, 293)(94, 262, 120, 288, 132, 300)(98, 266, 135, 303, 99, 267)(106, 274, 143, 311, 144, 312)(108, 276, 146, 314, 138, 306)(109, 277, 112, 280, 145, 313)(111, 279, 148, 316, 147, 315)(113, 281, 124, 292, 150, 318)(118, 286, 155, 323, 156, 324)(121, 289, 137, 305, 157, 325)(122, 290, 158, 326, 159, 327)(126, 294, 127, 295, 161, 329)(131, 299, 160, 328, 149, 317)(133, 301, 163, 331, 134, 302)(136, 304, 164, 332, 165, 333)(139, 307, 162, 330, 140, 308)(141, 309, 142, 310, 166, 334)(151, 319, 167, 335, 152, 320)(153, 321, 154, 322, 168, 336)(337, 505, 339, 507, 345, 513, 355, 523, 362, 530, 349, 517, 341, 509)(338, 506, 342, 510, 350, 518, 363, 531, 368, 536, 352, 520, 343, 511)(340, 508, 347, 515, 358, 526, 376, 544, 370, 538, 353, 521, 344, 512)(346, 514, 357, 525, 375, 543, 399, 567, 395, 563, 371, 539, 354, 522)(348, 516, 359, 527, 378, 546, 404, 572, 407, 575, 379, 547, 360, 528)(351, 519, 365, 533, 386, 554, 414, 582, 417, 585, 387, 555, 366, 534)(356, 524, 374, 542, 398, 566, 430, 598, 428, 596, 396, 564, 372, 540)(361, 529, 380, 548, 408, 576, 442, 610, 444, 612, 409, 577, 381, 549)(364, 532, 385, 553, 413, 581, 449, 617, 447, 615, 411, 579, 383, 551)(367, 535, 388, 556, 418, 586, 454, 622, 456, 624, 419, 587, 389, 557)(369, 537, 391, 559, 421, 589, 458, 626, 460, 628, 422, 590, 392, 560)(373, 541, 397, 565, 429, 597, 467, 635, 445, 613, 410, 578, 382, 550)(377, 545, 403, 571, 436, 604, 474, 642, 472, 640, 434, 602, 401, 569)(384, 552, 412, 580, 448, 616, 485, 653, 457, 625, 420, 588, 390, 558)(393, 561, 402, 570, 435, 603, 473, 641, 496, 664, 461, 629, 423, 591)(394, 562, 424, 592, 462, 630, 487, 655, 450, 618, 415, 583, 425, 593)(400, 568, 433, 601, 406, 574, 440, 608, 477, 645, 469, 637, 431, 599)(405, 573, 439, 607, 416, 584, 452, 620, 489, 657, 475, 643, 437, 605)(426, 594, 432, 600, 470, 638, 500, 668, 482, 650, 480, 648, 463, 631)(427, 595, 464, 632, 498, 666, 504, 672, 494, 662, 459, 627, 465, 633)(438, 606, 476, 644, 466, 634, 468, 636, 492, 660, 478, 646, 441, 609)(443, 611, 481, 649, 446, 614, 483, 651, 503, 671, 497, 665, 479, 647)(451, 619, 488, 656, 484, 652, 486, 654, 495, 663, 490, 658, 453, 621)(455, 623, 493, 661, 471, 639, 501, 669, 499, 667, 502, 670, 491, 659) L = (1, 339)(2, 342)(3, 345)(4, 347)(5, 337)(6, 350)(7, 338)(8, 340)(9, 355)(10, 357)(11, 358)(12, 359)(13, 341)(14, 363)(15, 365)(16, 343)(17, 344)(18, 346)(19, 362)(20, 374)(21, 375)(22, 376)(23, 378)(24, 348)(25, 380)(26, 349)(27, 368)(28, 385)(29, 386)(30, 351)(31, 388)(32, 352)(33, 391)(34, 353)(35, 354)(36, 356)(37, 397)(38, 398)(39, 399)(40, 370)(41, 403)(42, 404)(43, 360)(44, 408)(45, 361)(46, 373)(47, 364)(48, 412)(49, 413)(50, 414)(51, 366)(52, 418)(53, 367)(54, 384)(55, 421)(56, 369)(57, 402)(58, 424)(59, 371)(60, 372)(61, 429)(62, 430)(63, 395)(64, 433)(65, 377)(66, 435)(67, 436)(68, 407)(69, 439)(70, 440)(71, 379)(72, 442)(73, 381)(74, 382)(75, 383)(76, 448)(77, 449)(78, 417)(79, 425)(80, 452)(81, 387)(82, 454)(83, 389)(84, 390)(85, 458)(86, 392)(87, 393)(88, 462)(89, 394)(90, 432)(91, 464)(92, 396)(93, 467)(94, 428)(95, 400)(96, 470)(97, 406)(98, 401)(99, 473)(100, 474)(101, 405)(102, 476)(103, 416)(104, 477)(105, 438)(106, 444)(107, 481)(108, 409)(109, 410)(110, 483)(111, 411)(112, 485)(113, 447)(114, 415)(115, 488)(116, 489)(117, 451)(118, 456)(119, 493)(120, 419)(121, 420)(122, 460)(123, 465)(124, 422)(125, 423)(126, 487)(127, 426)(128, 498)(129, 427)(130, 468)(131, 445)(132, 492)(133, 431)(134, 500)(135, 501)(136, 434)(137, 496)(138, 472)(139, 437)(140, 466)(141, 469)(142, 441)(143, 443)(144, 463)(145, 446)(146, 480)(147, 503)(148, 486)(149, 457)(150, 495)(151, 450)(152, 484)(153, 475)(154, 453)(155, 455)(156, 478)(157, 471)(158, 459)(159, 490)(160, 461)(161, 479)(162, 504)(163, 502)(164, 482)(165, 499)(166, 491)(167, 497)(168, 494)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) 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 E3.226 Graph:: bipartite v = 80 e = 336 f = 252 degree seq :: [ 6^56, 14^24 ] E3.226 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^7, (Y3^-1 * Y1^-1)^7, Y3^2 * Y2 * Y3^2 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 ] Map:: polytopal R = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(85, 253)(86, 254)(87, 255)(88, 256)(89, 257)(90, 258)(91, 259)(92, 260)(93, 261)(94, 262)(95, 263)(96, 264)(97, 265)(98, 266)(99, 267)(100, 268)(101, 269)(102, 270)(103, 271)(104, 272)(105, 273)(106, 274)(107, 275)(108, 276)(109, 277)(110, 278)(111, 279)(112, 280)(113, 281)(114, 282)(115, 283)(116, 284)(117, 285)(118, 286)(119, 287)(120, 288)(121, 289)(122, 290)(123, 291)(124, 292)(125, 293)(126, 294)(127, 295)(128, 296)(129, 297)(130, 298)(131, 299)(132, 300)(133, 301)(134, 302)(135, 303)(136, 304)(137, 305)(138, 306)(139, 307)(140, 308)(141, 309)(142, 310)(143, 311)(144, 312)(145, 313)(146, 314)(147, 315)(148, 316)(149, 317)(150, 318)(151, 319)(152, 320)(153, 321)(154, 322)(155, 323)(156, 324)(157, 325)(158, 326)(159, 327)(160, 328)(161, 329)(162, 330)(163, 331)(164, 332)(165, 333)(166, 334)(167, 335)(168, 336)(337, 505, 338, 506)(339, 507, 343, 511)(340, 508, 345, 513)(341, 509, 347, 515)(342, 510, 349, 517)(344, 512, 352, 520)(346, 514, 355, 523)(348, 516, 358, 526)(350, 518, 361, 529)(351, 519, 363, 531)(353, 521, 366, 534)(354, 522, 367, 535)(356, 524, 370, 538)(357, 525, 371, 539)(359, 527, 374, 542)(360, 528, 375, 543)(362, 530, 378, 546)(364, 532, 380, 548)(365, 533, 382, 550)(368, 536, 386, 554)(369, 537, 388, 556)(372, 540, 392, 560)(373, 541, 393, 561)(376, 544, 397, 565)(377, 545, 398, 566)(379, 547, 401, 569)(381, 549, 404, 572)(383, 551, 406, 574)(384, 552, 390, 558)(385, 553, 409, 577)(387, 555, 412, 580)(389, 557, 414, 582)(391, 559, 417, 585)(394, 562, 421, 589)(395, 563, 400, 568)(396, 564, 424, 592)(399, 567, 428, 596)(402, 570, 432, 600)(403, 571, 433, 601)(405, 573, 436, 604)(407, 575, 439, 607)(408, 576, 440, 608)(410, 578, 443, 611)(411, 579, 444, 612)(413, 581, 447, 615)(415, 583, 450, 618)(416, 584, 451, 619)(418, 586, 454, 622)(419, 587, 446, 614)(420, 588, 456, 624)(422, 590, 459, 627)(423, 591, 460, 628)(425, 593, 463, 631)(426, 594, 435, 603)(427, 595, 465, 633)(429, 597, 468, 636)(430, 598, 469, 637)(431, 599, 453, 621)(434, 602, 473, 641)(437, 605, 466, 634)(438, 606, 476, 644)(441, 609, 480, 648)(442, 610, 462, 630)(445, 613, 483, 651)(448, 616, 457, 625)(449, 617, 486, 654)(452, 620, 490, 658)(455, 623, 491, 659)(458, 626, 492, 660)(461, 629, 495, 663)(464, 632, 496, 664)(467, 635, 497, 665)(470, 638, 500, 668)(471, 639, 478, 646)(472, 640, 489, 657)(474, 642, 493, 661)(475, 643, 494, 662)(477, 645, 487, 655)(479, 647, 482, 650)(481, 649, 488, 656)(484, 652, 498, 666)(485, 653, 499, 667)(501, 669, 504, 672)(502, 670, 503, 671) L = (1, 339)(2, 341)(3, 344)(4, 337)(5, 348)(6, 338)(7, 349)(8, 353)(9, 354)(10, 340)(11, 345)(12, 359)(13, 360)(14, 342)(15, 343)(16, 363)(17, 356)(18, 368)(19, 369)(20, 346)(21, 347)(22, 371)(23, 362)(24, 376)(25, 377)(26, 350)(27, 379)(28, 351)(29, 352)(30, 382)(31, 355)(32, 387)(33, 389)(34, 390)(35, 391)(36, 357)(37, 358)(38, 393)(39, 361)(40, 381)(41, 399)(42, 400)(43, 402)(44, 403)(45, 364)(46, 405)(47, 365)(48, 366)(49, 367)(50, 409)(51, 372)(52, 370)(53, 415)(54, 416)(55, 418)(56, 419)(57, 420)(58, 373)(59, 374)(60, 375)(61, 424)(62, 378)(63, 429)(64, 430)(65, 380)(66, 407)(67, 434)(68, 435)(69, 437)(70, 438)(71, 383)(72, 384)(73, 442)(74, 385)(75, 386)(76, 444)(77, 388)(78, 447)(79, 410)(80, 452)(81, 392)(82, 422)(83, 455)(84, 457)(85, 458)(86, 394)(87, 395)(88, 462)(89, 396)(90, 397)(91, 398)(92, 465)(93, 425)(94, 470)(95, 401)(96, 453)(97, 404)(98, 474)(99, 475)(100, 406)(101, 441)(102, 477)(103, 478)(104, 479)(105, 408)(106, 463)(107, 481)(108, 482)(109, 411)(110, 412)(111, 456)(112, 413)(113, 414)(114, 486)(115, 440)(116, 448)(117, 417)(118, 431)(119, 471)(120, 421)(121, 461)(122, 487)(123, 493)(124, 494)(125, 423)(126, 443)(127, 484)(128, 426)(129, 436)(130, 427)(131, 428)(132, 497)(133, 460)(134, 466)(135, 432)(136, 433)(137, 489)(138, 454)(139, 495)(140, 439)(141, 467)(142, 502)(143, 483)(144, 500)(145, 464)(146, 480)(147, 501)(148, 445)(149, 446)(150, 476)(151, 449)(152, 450)(153, 451)(154, 472)(155, 499)(156, 459)(157, 504)(158, 496)(159, 490)(160, 503)(161, 492)(162, 468)(163, 469)(164, 485)(165, 473)(166, 488)(167, 491)(168, 498)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 6, 14 ), ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E3.225 Graph:: simple bipartite v = 252 e = 336 f = 80 degree seq :: [ 2^168, 4^84 ] E3.227 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |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^-1)^3, Y1^7, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3 * Y1^-2 ] Map:: polytopal R = (1, 169, 2, 170, 5, 173, 11, 179, 20, 188, 10, 178, 4, 172)(3, 171, 7, 175, 15, 183, 26, 194, 30, 198, 17, 185, 8, 176)(6, 174, 13, 181, 24, 192, 39, 207, 42, 210, 25, 193, 14, 182)(9, 177, 18, 186, 31, 199, 49, 217, 46, 214, 28, 196, 16, 184)(12, 180, 22, 190, 37, 205, 57, 225, 60, 228, 38, 206, 23, 191)(19, 187, 33, 201, 52, 220, 77, 245, 76, 244, 51, 219, 32, 200)(21, 189, 35, 203, 55, 223, 81, 249, 84, 252, 56, 224, 36, 204)(27, 195, 44, 212, 67, 235, 97, 265, 100, 268, 68, 236, 45, 213)(29, 197, 47, 215, 70, 238, 102, 270, 91, 259, 62, 230, 40, 208)(34, 202, 54, 222, 80, 248, 115, 283, 114, 282, 79, 247, 53, 221)(41, 209, 63, 231, 92, 260, 130, 298, 123, 291, 86, 254, 58, 226)(43, 211, 65, 233, 95, 263, 134, 302, 137, 305, 96, 264, 66, 234)(48, 216, 72, 240, 105, 273, 143, 311, 117, 285, 104, 272, 71, 239)(50, 218, 74, 242, 108, 276, 129, 297, 148, 316, 109, 277, 75, 243)(59, 227, 87, 255, 124, 292, 142, 310, 103, 271, 118, 286, 82, 250)(61, 229, 89, 257, 127, 295, 110, 278, 149, 317, 128, 296, 90, 258)(64, 232, 94, 262, 133, 301, 160, 328, 153, 321, 132, 300, 93, 261)(69, 237, 101, 269, 140, 308, 122, 290, 85, 253, 121, 289, 98, 266)(73, 241, 106, 274, 145, 313, 120, 288, 155, 323, 146, 314, 107, 275)(78, 246, 112, 280, 135, 303, 99, 267, 138, 306, 152, 320, 113, 281)(83, 251, 119, 287, 147, 315, 159, 327, 131, 299, 154, 322, 116, 284)(88, 256, 126, 294, 156, 324, 151, 319, 111, 279, 150, 318, 125, 293)(136, 304, 161, 329, 157, 325, 167, 335, 163, 331, 166, 334, 144, 312)(139, 307, 158, 326, 168, 336, 165, 333, 141, 309, 164, 332, 162, 330)(337, 505)(338, 506)(339, 507)(340, 508)(341, 509)(342, 510)(343, 511)(344, 512)(345, 513)(346, 514)(347, 515)(348, 516)(349, 517)(350, 518)(351, 519)(352, 520)(353, 521)(354, 522)(355, 523)(356, 524)(357, 525)(358, 526)(359, 527)(360, 528)(361, 529)(362, 530)(363, 531)(364, 532)(365, 533)(366, 534)(367, 535)(368, 536)(369, 537)(370, 538)(371, 539)(372, 540)(373, 541)(374, 542)(375, 543)(376, 544)(377, 545)(378, 546)(379, 547)(380, 548)(381, 549)(382, 550)(383, 551)(384, 552)(385, 553)(386, 554)(387, 555)(388, 556)(389, 557)(390, 558)(391, 559)(392, 560)(393, 561)(394, 562)(395, 563)(396, 564)(397, 565)(398, 566)(399, 567)(400, 568)(401, 569)(402, 570)(403, 571)(404, 572)(405, 573)(406, 574)(407, 575)(408, 576)(409, 577)(410, 578)(411, 579)(412, 580)(413, 581)(414, 582)(415, 583)(416, 584)(417, 585)(418, 586)(419, 587)(420, 588)(421, 589)(422, 590)(423, 591)(424, 592)(425, 593)(426, 594)(427, 595)(428, 596)(429, 597)(430, 598)(431, 599)(432, 600)(433, 601)(434, 602)(435, 603)(436, 604)(437, 605)(438, 606)(439, 607)(440, 608)(441, 609)(442, 610)(443, 611)(444, 612)(445, 613)(446, 614)(447, 615)(448, 616)(449, 617)(450, 618)(451, 619)(452, 620)(453, 621)(454, 622)(455, 623)(456, 624)(457, 625)(458, 626)(459, 627)(460, 628)(461, 629)(462, 630)(463, 631)(464, 632)(465, 633)(466, 634)(467, 635)(468, 636)(469, 637)(470, 638)(471, 639)(472, 640)(473, 641)(474, 642)(475, 643)(476, 644)(477, 645)(478, 646)(479, 647)(480, 648)(481, 649)(482, 650)(483, 651)(484, 652)(485, 653)(486, 654)(487, 655)(488, 656)(489, 657)(490, 658)(491, 659)(492, 660)(493, 661)(494, 662)(495, 663)(496, 664)(497, 665)(498, 666)(499, 667)(500, 668)(501, 669)(502, 670)(503, 671)(504, 672) L = (1, 339)(2, 342)(3, 337)(4, 345)(5, 348)(6, 338)(7, 352)(8, 349)(9, 340)(10, 355)(11, 357)(12, 341)(13, 344)(14, 358)(15, 363)(16, 343)(17, 365)(18, 368)(19, 346)(20, 370)(21, 347)(22, 350)(23, 371)(24, 376)(25, 377)(26, 379)(27, 351)(28, 380)(29, 353)(30, 384)(31, 386)(32, 354)(33, 389)(34, 356)(35, 359)(36, 390)(37, 394)(38, 395)(39, 397)(40, 360)(41, 361)(42, 400)(43, 362)(44, 364)(45, 401)(46, 405)(47, 407)(48, 366)(49, 409)(50, 367)(51, 410)(52, 414)(53, 369)(54, 372)(55, 418)(56, 419)(57, 421)(58, 373)(59, 374)(60, 424)(61, 375)(62, 425)(63, 429)(64, 378)(65, 381)(66, 408)(67, 434)(68, 435)(69, 382)(70, 439)(71, 383)(72, 402)(73, 385)(74, 387)(75, 442)(76, 446)(77, 447)(78, 388)(79, 448)(80, 452)(81, 453)(82, 391)(83, 392)(84, 456)(85, 393)(86, 457)(87, 461)(88, 396)(89, 398)(90, 430)(91, 465)(92, 467)(93, 399)(94, 426)(95, 471)(96, 472)(97, 459)(98, 403)(99, 404)(100, 475)(101, 443)(102, 477)(103, 406)(104, 454)(105, 480)(106, 411)(107, 437)(108, 463)(109, 483)(110, 412)(111, 413)(112, 415)(113, 486)(114, 470)(115, 489)(116, 416)(117, 417)(118, 440)(119, 481)(120, 420)(121, 422)(122, 462)(123, 433)(124, 488)(125, 423)(126, 458)(127, 444)(128, 493)(129, 427)(130, 494)(131, 428)(132, 490)(133, 497)(134, 450)(135, 431)(136, 432)(137, 496)(138, 498)(139, 436)(140, 499)(141, 438)(142, 500)(143, 491)(144, 441)(145, 455)(146, 502)(147, 445)(148, 501)(149, 487)(150, 449)(151, 485)(152, 460)(153, 451)(154, 468)(155, 479)(156, 503)(157, 464)(158, 466)(159, 504)(160, 473)(161, 469)(162, 474)(163, 476)(164, 478)(165, 484)(166, 482)(167, 492)(168, 495)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E3.224 Graph:: simple bipartite v = 192 e = 336 f = 140 degree seq :: [ 2^168, 14^24 ] E3.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^3, (Y3 * Y2^-1)^3, Y2^7, Y1 * Y2^-3 * Y1 * Y2^-2 * Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2^-3 ] Map:: R = (1, 169, 2, 170)(3, 171, 7, 175)(4, 172, 9, 177)(5, 173, 11, 179)(6, 174, 13, 181)(8, 176, 16, 184)(10, 178, 19, 187)(12, 180, 22, 190)(14, 182, 25, 193)(15, 183, 27, 195)(17, 185, 30, 198)(18, 186, 31, 199)(20, 188, 34, 202)(21, 189, 35, 203)(23, 191, 38, 206)(24, 192, 39, 207)(26, 194, 42, 210)(28, 196, 44, 212)(29, 197, 46, 214)(32, 200, 50, 218)(33, 201, 52, 220)(36, 204, 56, 224)(37, 205, 57, 225)(40, 208, 61, 229)(41, 209, 62, 230)(43, 211, 65, 233)(45, 213, 68, 236)(47, 215, 70, 238)(48, 216, 54, 222)(49, 217, 73, 241)(51, 219, 76, 244)(53, 221, 78, 246)(55, 223, 81, 249)(58, 226, 85, 253)(59, 227, 64, 232)(60, 228, 88, 256)(63, 231, 92, 260)(66, 234, 96, 264)(67, 235, 97, 265)(69, 237, 100, 268)(71, 239, 103, 271)(72, 240, 104, 272)(74, 242, 107, 275)(75, 243, 108, 276)(77, 245, 111, 279)(79, 247, 114, 282)(80, 248, 115, 283)(82, 250, 118, 286)(83, 251, 110, 278)(84, 252, 120, 288)(86, 254, 123, 291)(87, 255, 124, 292)(89, 257, 127, 295)(90, 258, 99, 267)(91, 259, 129, 297)(93, 261, 132, 300)(94, 262, 133, 301)(95, 263, 117, 285)(98, 266, 137, 305)(101, 269, 130, 298)(102, 270, 140, 308)(105, 273, 144, 312)(106, 274, 126, 294)(109, 277, 147, 315)(112, 280, 121, 289)(113, 281, 150, 318)(116, 284, 154, 322)(119, 287, 155, 323)(122, 290, 156, 324)(125, 293, 159, 327)(128, 296, 160, 328)(131, 299, 161, 329)(134, 302, 164, 332)(135, 303, 142, 310)(136, 304, 153, 321)(138, 306, 157, 325)(139, 307, 158, 326)(141, 309, 151, 319)(143, 311, 146, 314)(145, 313, 152, 320)(148, 316, 162, 330)(149, 317, 163, 331)(165, 333, 168, 336)(166, 334, 167, 335)(337, 505, 339, 507, 344, 512, 353, 521, 356, 524, 346, 514, 340, 508)(338, 506, 341, 509, 348, 516, 359, 527, 362, 530, 350, 518, 342, 510)(343, 511, 349, 517, 360, 528, 376, 544, 381, 549, 364, 532, 351, 519)(345, 513, 354, 522, 368, 536, 387, 555, 372, 540, 357, 525, 347, 515)(352, 520, 363, 531, 379, 547, 402, 570, 407, 575, 383, 551, 365, 533)(355, 523, 369, 537, 389, 557, 415, 583, 410, 578, 385, 553, 367, 535)(358, 526, 371, 539, 391, 559, 418, 586, 422, 590, 394, 562, 373, 541)(361, 529, 377, 545, 399, 567, 429, 597, 425, 593, 396, 564, 375, 543)(366, 534, 382, 550, 405, 573, 437, 605, 441, 609, 408, 576, 384, 552)(370, 538, 390, 558, 416, 584, 452, 620, 448, 616, 413, 581, 388, 556)(374, 542, 393, 561, 420, 588, 457, 625, 461, 629, 423, 591, 395, 563)(378, 546, 400, 568, 430, 598, 470, 638, 466, 634, 427, 595, 398, 566)(380, 548, 403, 571, 434, 602, 474, 642, 454, 622, 431, 599, 401, 569)(386, 554, 409, 577, 442, 610, 463, 631, 484, 652, 445, 613, 411, 579)(392, 560, 419, 587, 455, 623, 471, 639, 432, 600, 453, 621, 417, 585)(397, 565, 424, 592, 462, 630, 443, 611, 481, 649, 464, 632, 426, 594)(404, 572, 435, 603, 475, 643, 495, 663, 490, 658, 472, 640, 433, 601)(406, 574, 438, 606, 477, 645, 467, 635, 428, 596, 465, 633, 436, 604)(412, 580, 444, 612, 482, 650, 480, 648, 500, 668, 485, 653, 446, 614)(414, 582, 447, 615, 456, 624, 421, 589, 458, 626, 487, 655, 449, 617)(439, 607, 478, 646, 502, 670, 488, 656, 450, 618, 486, 654, 476, 644)(440, 608, 479, 647, 483, 651, 501, 669, 473, 641, 489, 657, 451, 619)(459, 627, 493, 661, 504, 672, 498, 666, 468, 636, 497, 665, 492, 660)(460, 628, 494, 662, 496, 664, 503, 671, 491, 659, 499, 667, 469, 637) L = (1, 338)(2, 337)(3, 343)(4, 345)(5, 347)(6, 349)(7, 339)(8, 352)(9, 340)(10, 355)(11, 341)(12, 358)(13, 342)(14, 361)(15, 363)(16, 344)(17, 366)(18, 367)(19, 346)(20, 370)(21, 371)(22, 348)(23, 374)(24, 375)(25, 350)(26, 378)(27, 351)(28, 380)(29, 382)(30, 353)(31, 354)(32, 386)(33, 388)(34, 356)(35, 357)(36, 392)(37, 393)(38, 359)(39, 360)(40, 397)(41, 398)(42, 362)(43, 401)(44, 364)(45, 404)(46, 365)(47, 406)(48, 390)(49, 409)(50, 368)(51, 412)(52, 369)(53, 414)(54, 384)(55, 417)(56, 372)(57, 373)(58, 421)(59, 400)(60, 424)(61, 376)(62, 377)(63, 428)(64, 395)(65, 379)(66, 432)(67, 433)(68, 381)(69, 436)(70, 383)(71, 439)(72, 440)(73, 385)(74, 443)(75, 444)(76, 387)(77, 447)(78, 389)(79, 450)(80, 451)(81, 391)(82, 454)(83, 446)(84, 456)(85, 394)(86, 459)(87, 460)(88, 396)(89, 463)(90, 435)(91, 465)(92, 399)(93, 468)(94, 469)(95, 453)(96, 402)(97, 403)(98, 473)(99, 426)(100, 405)(101, 466)(102, 476)(103, 407)(104, 408)(105, 480)(106, 462)(107, 410)(108, 411)(109, 483)(110, 419)(111, 413)(112, 457)(113, 486)(114, 415)(115, 416)(116, 490)(117, 431)(118, 418)(119, 491)(120, 420)(121, 448)(122, 492)(123, 422)(124, 423)(125, 495)(126, 442)(127, 425)(128, 496)(129, 427)(130, 437)(131, 497)(132, 429)(133, 430)(134, 500)(135, 478)(136, 489)(137, 434)(138, 493)(139, 494)(140, 438)(141, 487)(142, 471)(143, 482)(144, 441)(145, 488)(146, 479)(147, 445)(148, 498)(149, 499)(150, 449)(151, 477)(152, 481)(153, 472)(154, 452)(155, 455)(156, 458)(157, 474)(158, 475)(159, 461)(160, 464)(161, 467)(162, 484)(163, 485)(164, 470)(165, 504)(166, 503)(167, 502)(168, 501)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) 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 E3.229 Graph:: bipartite v = 108 e = 336 f = 224 degree seq :: [ 4^84, 14^24 ] E3.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 7}) Quotient :: dipole Aut^+ = PSL(3,2) (small group id <168, 42>) Aut = PSL(3,2) : C2 (small group id <336, 208>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^7, (Y3^-2 * Y1)^4, (Y3 * Y2^-1)^7 ] Map:: polytopal R = (1, 169, 2, 170, 4, 172)(3, 171, 8, 176, 10, 178)(5, 173, 12, 180, 6, 174)(7, 175, 15, 183, 11, 179)(9, 177, 18, 186, 20, 188)(13, 181, 25, 193, 23, 191)(14, 182, 24, 192, 28, 196)(16, 184, 31, 199, 29, 197)(17, 185, 33, 201, 21, 189)(19, 187, 36, 204, 37, 205)(22, 190, 30, 198, 41, 209)(26, 194, 46, 214, 44, 212)(27, 195, 47, 215, 48, 216)(32, 200, 54, 222, 52, 220)(34, 202, 57, 225, 55, 223)(35, 203, 58, 226, 38, 206)(39, 207, 56, 224, 64, 232)(40, 208, 65, 233, 66, 234)(42, 210, 45, 213, 69, 237)(43, 211, 70, 238, 49, 217)(50, 218, 53, 221, 79, 247)(51, 219, 80, 248, 67, 235)(59, 227, 90, 258, 88, 256)(60, 228, 91, 259, 61, 229)(62, 230, 89, 257, 83, 251)(63, 231, 95, 263, 96, 264)(68, 236, 101, 269, 102, 270)(71, 239, 105, 273, 104, 272)(72, 240, 74, 242, 107, 275)(73, 241, 100, 268, 103, 271)(75, 243, 110, 278, 76, 244)(77, 245, 97, 265, 86, 254)(78, 246, 114, 282, 115, 283)(81, 249, 117, 285, 116, 284)(82, 250, 84, 252, 119, 287)(85, 253, 87, 255, 123, 291)(92, 260, 130, 298, 128, 296)(93, 261, 129, 297, 125, 293)(94, 262, 120, 288, 132, 300)(98, 266, 135, 303, 99, 267)(106, 274, 143, 311, 144, 312)(108, 276, 146, 314, 138, 306)(109, 277, 112, 280, 145, 313)(111, 279, 148, 316, 147, 315)(113, 281, 124, 292, 150, 318)(118, 286, 155, 323, 156, 324)(121, 289, 137, 305, 157, 325)(122, 290, 158, 326, 159, 327)(126, 294, 127, 295, 161, 329)(131, 299, 160, 328, 149, 317)(133, 301, 163, 331, 134, 302)(136, 304, 164, 332, 165, 333)(139, 307, 162, 330, 140, 308)(141, 309, 142, 310, 166, 334)(151, 319, 167, 335, 152, 320)(153, 321, 154, 322, 168, 336)(337, 505)(338, 506)(339, 507)(340, 508)(341, 509)(342, 510)(343, 511)(344, 512)(345, 513)(346, 514)(347, 515)(348, 516)(349, 517)(350, 518)(351, 519)(352, 520)(353, 521)(354, 522)(355, 523)(356, 524)(357, 525)(358, 526)(359, 527)(360, 528)(361, 529)(362, 530)(363, 531)(364, 532)(365, 533)(366, 534)(367, 535)(368, 536)(369, 537)(370, 538)(371, 539)(372, 540)(373, 541)(374, 542)(375, 543)(376, 544)(377, 545)(378, 546)(379, 547)(380, 548)(381, 549)(382, 550)(383, 551)(384, 552)(385, 553)(386, 554)(387, 555)(388, 556)(389, 557)(390, 558)(391, 559)(392, 560)(393, 561)(394, 562)(395, 563)(396, 564)(397, 565)(398, 566)(399, 567)(400, 568)(401, 569)(402, 570)(403, 571)(404, 572)(405, 573)(406, 574)(407, 575)(408, 576)(409, 577)(410, 578)(411, 579)(412, 580)(413, 581)(414, 582)(415, 583)(416, 584)(417, 585)(418, 586)(419, 587)(420, 588)(421, 589)(422, 590)(423, 591)(424, 592)(425, 593)(426, 594)(427, 595)(428, 596)(429, 597)(430, 598)(431, 599)(432, 600)(433, 601)(434, 602)(435, 603)(436, 604)(437, 605)(438, 606)(439, 607)(440, 608)(441, 609)(442, 610)(443, 611)(444, 612)(445, 613)(446, 614)(447, 615)(448, 616)(449, 617)(450, 618)(451, 619)(452, 620)(453, 621)(454, 622)(455, 623)(456, 624)(457, 625)(458, 626)(459, 627)(460, 628)(461, 629)(462, 630)(463, 631)(464, 632)(465, 633)(466, 634)(467, 635)(468, 636)(469, 637)(470, 638)(471, 639)(472, 640)(473, 641)(474, 642)(475, 643)(476, 644)(477, 645)(478, 646)(479, 647)(480, 648)(481, 649)(482, 650)(483, 651)(484, 652)(485, 653)(486, 654)(487, 655)(488, 656)(489, 657)(490, 658)(491, 659)(492, 660)(493, 661)(494, 662)(495, 663)(496, 664)(497, 665)(498, 666)(499, 667)(500, 668)(501, 669)(502, 670)(503, 671)(504, 672) L = (1, 339)(2, 342)(3, 345)(4, 347)(5, 337)(6, 350)(7, 338)(8, 340)(9, 355)(10, 357)(11, 358)(12, 359)(13, 341)(14, 363)(15, 365)(16, 343)(17, 344)(18, 346)(19, 362)(20, 374)(21, 375)(22, 376)(23, 378)(24, 348)(25, 380)(26, 349)(27, 368)(28, 385)(29, 386)(30, 351)(31, 388)(32, 352)(33, 391)(34, 353)(35, 354)(36, 356)(37, 397)(38, 398)(39, 399)(40, 370)(41, 403)(42, 404)(43, 360)(44, 408)(45, 361)(46, 373)(47, 364)(48, 412)(49, 413)(50, 414)(51, 366)(52, 418)(53, 367)(54, 384)(55, 421)(56, 369)(57, 402)(58, 424)(59, 371)(60, 372)(61, 429)(62, 430)(63, 395)(64, 433)(65, 377)(66, 435)(67, 436)(68, 407)(69, 439)(70, 440)(71, 379)(72, 442)(73, 381)(74, 382)(75, 383)(76, 448)(77, 449)(78, 417)(79, 425)(80, 452)(81, 387)(82, 454)(83, 389)(84, 390)(85, 458)(86, 392)(87, 393)(88, 462)(89, 394)(90, 432)(91, 464)(92, 396)(93, 467)(94, 428)(95, 400)(96, 470)(97, 406)(98, 401)(99, 473)(100, 474)(101, 405)(102, 476)(103, 416)(104, 477)(105, 438)(106, 444)(107, 481)(108, 409)(109, 410)(110, 483)(111, 411)(112, 485)(113, 447)(114, 415)(115, 488)(116, 489)(117, 451)(118, 456)(119, 493)(120, 419)(121, 420)(122, 460)(123, 465)(124, 422)(125, 423)(126, 487)(127, 426)(128, 498)(129, 427)(130, 468)(131, 445)(132, 492)(133, 431)(134, 500)(135, 501)(136, 434)(137, 496)(138, 472)(139, 437)(140, 466)(141, 469)(142, 441)(143, 443)(144, 463)(145, 446)(146, 480)(147, 503)(148, 486)(149, 457)(150, 495)(151, 450)(152, 484)(153, 475)(154, 453)(155, 455)(156, 478)(157, 471)(158, 459)(159, 490)(160, 461)(161, 479)(162, 504)(163, 502)(164, 482)(165, 499)(166, 491)(167, 497)(168, 494)(169, 505)(170, 506)(171, 507)(172, 508)(173, 509)(174, 510)(175, 511)(176, 512)(177, 513)(178, 514)(179, 515)(180, 516)(181, 517)(182, 518)(183, 519)(184, 520)(185, 521)(186, 522)(187, 523)(188, 524)(189, 525)(190, 526)(191, 527)(192, 528)(193, 529)(194, 530)(195, 531)(196, 532)(197, 533)(198, 534)(199, 535)(200, 536)(201, 537)(202, 538)(203, 539)(204, 540)(205, 541)(206, 542)(207, 543)(208, 544)(209, 545)(210, 546)(211, 547)(212, 548)(213, 549)(214, 550)(215, 551)(216, 552)(217, 553)(218, 554)(219, 555)(220, 556)(221, 557)(222, 558)(223, 559)(224, 560)(225, 561)(226, 562)(227, 563)(228, 564)(229, 565)(230, 566)(231, 567)(232, 568)(233, 569)(234, 570)(235, 571)(236, 572)(237, 573)(238, 574)(239, 575)(240, 576)(241, 577)(242, 578)(243, 579)(244, 580)(245, 581)(246, 582)(247, 583)(248, 584)(249, 585)(250, 586)(251, 587)(252, 588)(253, 589)(254, 590)(255, 591)(256, 592)(257, 593)(258, 594)(259, 595)(260, 596)(261, 597)(262, 598)(263, 599)(264, 600)(265, 601)(266, 602)(267, 603)(268, 604)(269, 605)(270, 606)(271, 607)(272, 608)(273, 609)(274, 610)(275, 611)(276, 612)(277, 613)(278, 614)(279, 615)(280, 616)(281, 617)(282, 618)(283, 619)(284, 620)(285, 621)(286, 622)(287, 623)(288, 624)(289, 625)(290, 626)(291, 627)(292, 628)(293, 629)(294, 630)(295, 631)(296, 632)(297, 633)(298, 634)(299, 635)(300, 636)(301, 637)(302, 638)(303, 639)(304, 640)(305, 641)(306, 642)(307, 643)(308, 644)(309, 645)(310, 646)(311, 647)(312, 648)(313, 649)(314, 650)(315, 651)(316, 652)(317, 653)(318, 654)(319, 655)(320, 656)(321, 657)(322, 658)(323, 659)(324, 660)(325, 661)(326, 662)(327, 663)(328, 664)(329, 665)(330, 666)(331, 667)(332, 668)(333, 669)(334, 670)(335, 671)(336, 672) local type(s) :: { ( 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E3.228 Graph:: simple bipartite v = 224 e = 336 f = 108 degree seq :: [ 2^168, 6^56 ] ## Checksum: 229 records. ## Written on: Tue Oct 15 10:01:58 CEST 2019