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On this page are computer-accessible forms for the graph C4[ 120, 10 ] = PS(12,20;3).

(I) Following is a form readable by MAGMA:

g:=Graph<120|{ {20, 22}, {60, 62}, {100, 102}, {27, 31}, {107, 111}, {40, 44}, {67, 71}, {80, 84}, {26, 31}, {106, 111}, {66, 71}, {19, 21}, {59, 61}, {99, 101}, {40, 47}, {80, 87}, {2, 11}, {54, 63}, {52, 61}, {50, 59}, {48, 57}, {4, 13}, {6, 15}, {16, 25}, {18, 27}, {20, 29}, {35, 42}, {37, 44}, {39, 46}, {82, 91}, {84, 93}, {86, 95}, {96, 105}, {98, 107}, {100, 109}, {1, 11}, {49, 59}, {48, 58}, {4, 14}, {5, 15}, {81, 91}, {84, 94}, {85, 95}, {5, 14}, {53, 62}, {49, 58}, {17, 26}, {34, 41}, {38, 45}, {67, 72}, {85, 94}, {97, 106}, {16, 28}, {51, 63}, {17, 29}, {18, 30}, {37, 41}, {38, 42}, {39, 43}, {68, 72}, {69, 73}, {70, 74}, {96, 108}, {97, 109}, {98, 110}, {68, 73}, {70, 75}, {2, 12}, {64, 78}, {50, 60}, {3, 13}, {32, 46}, {33, 47}, {65, 79}, {82, 92}, {83, 93}, {3, 12}, {19, 28}, {36, 43}, {64, 79}, {69, 74}, {83, 92}, {99, 108}, {32, 49}, {65, 80}, {72, 89}, {101, 116}, {103, 118}, {105, 120}, {34, 48}, {106, 120}, {35, 49}, {66, 80}, {71, 85}, {74, 88}, {75, 89}, {102, 116}, {103, 117}, {33, 50}, {73, 90}, {102, 117}, {12, 24}, {13, 25}, {14, 26}, {15, 27}, {1, 20}, {41, 60}, {11, 30}, {6, 16}, {47, 57}, {46, 56}, {7, 17}, {36, 50}, {76, 90}, {101, 115}, {7, 16}, {47, 56}, {15, 24}, {8, 17}, {46, 55}, {44, 53}, {42, 51}, {10, 19}, {12, 21}, {14, 23}, {75, 82}, {77, 84}, {79, 86}, {8, 18}, {45, 55}, {44, 54}, {9, 19}, {41, 51}, {9, 18}, {107, 112}, {45, 54}, {13, 22}, {74, 81}, {78, 85}, {11, 23}, {110, 114}, {109, 113}, {108, 112}, {77, 81}, {78, 82}, {79, 83}, {108, 113}, {110, 115}, {10, 20}, {43, 53}, {42, 52}, {72, 86}, {73, 87}, {104, 118}, {105, 119}, {43, 52}, {109, 114}, {71, 88}, {76, 83}, {104, 119}, {31, 48}, {21, 36}, {23, 38}, {25, 40}, {22, 36}, {23, 37}, {26, 40}, {31, 45}, {22, 37}, {92, 104}, {93, 105}, {94, 106}, {95, 107}, {81, 100}, {91, 110}, {21, 35}, {86, 96}, {87, 97}, {87, 96}, {95, 104}, {88, 97}, {90, 99}, {92, 101}, {94, 103}, {88, 98}, {89, 99}, {27, 32}, {89, 98}, {93, 102}, {28, 32}, {29, 33}, {30, 34}, {91, 103}, {28, 33}, {30, 35}, {24, 38}, {25, 39}, {90, 100}, {24, 39}, {29, 34}, {8, 111}, {5, 111}, {2, 115}, {63, 78}, {61, 76}, {4, 117}, {6, 119}, {62, 76}, {63, 77}, {1, 114}, {62, 77}, {5, 118}, {1, 117}, {55, 67}, {54, 66}, {53, 65}, {52, 64}, {2, 118}, {3, 119}, {51, 70}, {6, 112}, {61, 75}, {7, 113}, {3, 116}, {55, 64}, {9, 112}, {60, 69}, {58, 67}, {56, 65}, {8, 114}, {9, 115}, {10, 113}, {57, 66}, {4, 120}, {58, 70}, {57, 69}, {56, 68}, {10, 116}, {7, 120}, {59, 68} }>;

(II) A more general form is to represent the graph as the orbit of {20, 22} under the group generated by the following permutations:

a: (2, 8, 10, 4)(3, 5, 9, 7)(11, 114, 20, 117)(12, 111, 19, 120)(13, 118, 18, 113)(14, 115, 17, 116)(15, 112, 16, 119)(21, 106)(22, 103, 30, 109)(23, 110, 29, 102)(24, 107, 28, 105)(25, 104, 27, 108)(26, 101)(31, 99, 40, 92)(32, 96, 39, 95)(33, 93, 38, 98)(34, 100, 37, 91)(35, 97, 36, 94)(41, 81)(42, 88, 50, 84)(43, 85, 49, 87)(44, 82, 48, 90)(45, 89, 47, 83)(46, 86)(51, 74, 60, 77)(52, 71, 59, 80)(53, 78, 58, 73)(54, 75, 57, 76)(55, 72, 56, 79)(61, 66)(62, 63, 70, 69)(64, 67, 68, 65)
b: (1, 11, 30, 34, 41, 51, 70, 74, 81, 91, 110, 114)(2, 18, 29, 37, 42, 58, 69, 77, 82, 98, 109, 117)(3, 15, 28, 40, 43, 55, 68, 80, 83, 95, 108, 120)(4, 12, 27, 33, 44, 52, 67, 73, 84, 92, 107, 113)(5, 19, 26, 36, 45, 59, 66, 76, 85, 99, 106, 116)(6, 16, 25, 39, 46, 56, 65, 79, 86, 96, 105, 119)(7, 13, 24, 32, 47, 53, 64, 72, 87, 93, 104, 112)(8, 20, 23, 35, 48, 60, 63, 75, 88, 100, 103, 115)(9, 17, 22, 38, 49, 57, 62, 78, 89, 97, 102, 118)(10, 14, 21, 31, 50, 54, 61, 71, 90, 94, 101, 111)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)(11, 12, 13, 14, 15, 16, 17, 18, 19, 20)(21, 22, 23, 24, 25, 26, 27, 28, 29, 30)(31, 32, 33, 34, 35, 36, 37, 38, 39, 40)(41, 42, 43, 44, 45, 46, 47, 48, 49, 50)(51, 52, 53, 54, 55, 56, 57, 58, 59, 60)(61, 62, 63, 64, 65, 66, 67, 68, 69, 70)(71, 72, 73, 74, 75, 76, 77, 78, 79, 80)(81, 82, 83, 84, 85, 86, 87, 88, 89, 90)(91, 92, 93, 94, 95, 96, 97, 98, 99, 100)(101, 102, 103, 104, 105, 106, 107, 108, 109, 110)(111, 112, 113, 114, 115, 116, 117, 118, 119, 120)
d: (2, 10)(3, 9)(4, 8)(5, 7)(11, 20)(12, 19)(13, 18)(14, 17)(15, 16)(22, 30)(23, 29)(24, 28)(25, 27)(31, 40)(32, 39)(33, 38)(34, 37)(35, 36)(42, 50)(43, 49)(44, 48)(45, 47)(51, 60)(52, 59)(53, 58)(54, 57)(55, 56)(62, 70)(63, 69)(64, 68)(65, 67)(71, 80)(72, 79)(73, 78)(74, 77)(75, 76)(82, 90)(83, 89)(84, 88)(85, 87)(91, 100)(92, 99)(93, 98)(94, 97)(95, 96)(102, 110)(103, 109)(104, 108)(105, 107)(111, 120)(112, 119)(113, 118)(114, 117)(115, 116)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 120, 10 ]
120
-1 11 114 117 20
-2 11 12 115 118
-3 12 13 116 119
-4 13 14 117 120
-5 111 14 15 118
-6 112 15 16 119
-7 113 16 17 120
-8 111 114 17 18
-9 112 115 18 19
-10 113 116 19 20
-11 1 23 2 30
-12 2 24 3 21
-13 22 3 25 4
-14 23 4 26 5
-15 24 5 27 6
-16 25 6 28 7
-17 26 7 29 8
-18 27 8 30 9
-19 28 9 10 21
-20 22 1 29 10
-21 12 35 36 19
-22 13 36 37 20
-23 11 14 37 38
-24 12 15 38 39
-25 13 16 39 40
-26 14 17 40 31
-27 15 18 31 32
-28 33 16 19 32
-29 33 34 17 20
-30 11 34 35 18
-31 45 26 48 27
-32 46 27 49 28
-33 47 28 50 29
-34 48 29 30 41
-35 49 30 42 21
-36 22 50 21 43
-37 22 44 23 41
-38 23 45 24 42
-39 24 46 25 43
-40 44 25 47 26
-41 34 37 60 51
-42 35 38 51 52
-43 36 39 52 53
-44 37 40 53 54
-45 55 38 31 54
-46 55 56 39 32
-47 33 56 57 40
-48 34 57 58 31
-49 35 58 59 32
-50 33 36 59 60
-51 70 41 63 42
-52 61 42 64 43
-53 44 62 43 65
-54 44 66 45 63
-55 45 67 46 64
-56 46 68 47 65
-57 66 47 69 48
-58 67 48 70 49
-59 68 49 50 61
-60 69 50 62 41
-61 59 52 75 76
-62 77 60 53 76
-63 77 78 51 54
-64 55 78 79 52
-65 56 79 80 53
-66 57 80 71 54
-67 55 58 71 72
-68 56 59 72 73
-69 57 60 73 74
-70 58 51 74 75
-71 66 88 67 85
-72 67 89 68 86
-73 68 90 69 87
-74 88 69 70 81
-75 89 70 82 61
-76 90 61 83 62
-77 81 62 84 63
-78 82 63 85 64
-79 83 64 86 65
-80 66 84 65 87
-81 77 100 91 74
-82 78 91 92 75
-83 79 92 93 76
-84 77 80 93 94
-85 78 71 94 95
-86 79 72 95 96
-87 80 73 96 97
-88 71 74 97 98
-89 99 72 75 98
-90 99 100 73 76
-91 110 81 103 82
-92 101 82 104 83
-93 102 83 105 84
-94 103 84 106 85
-95 104 85 107 86
-96 105 86 108 87
-97 88 106 87 109
-98 88 110 89 107
-99 89 90 101 108
-100 90 102 81 109
-101 99 92 115 116
-102 100 93 116 117
-103 91 94 117 118
-104 92 95 118 119
-105 93 96 119 120
-106 111 94 97 120
-107 111 112 95 98
-108 99 112 113 96
-109 100 113 114 97
-110 91 114 115 98
-111 5 106 8 107
-112 6 107 9 108
-113 7 108 10 109
-114 110 1 8 109
-115 110 2 101 9
-116 101 3 102 10
-117 1 102 4 103
-118 2 103 5 104
-119 3 104 6 105
-120 4 105 7 106
0

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