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On this page are computer-accessible forms for the graph C4[ 144, 20 ] = PL(MSY(6,12,5,6)).

(I) Following is a form readable by MAGMA:

g:=Graph<144|{ {68, 78}, {68, 79}, {67, 79}, {67, 78}, {68, 90}, {69, 91}, {68, 91}, {69, 90}, {70, 102}, {64, 97}, {70, 103}, {69, 103}, {69, 102}, {64, 108}, {65, 109}, {64, 109}, {70, 114}, {71, 115}, {70, 115}, {71, 114}, {72, 126}, {72, 127}, {64, 120}, {71, 127}, {65, 121}, {65, 120}, {71, 126}, {66, 121}, {35, 99}, {36, 100}, {19, 81}, {58, 120}, {39, 101}, {19, 80}, {59, 120}, {39, 100}, {14, 74}, {58, 126}, {57, 125}, {25, 93}, {20, 80}, {46, 106}, {53, 113}, {14, 75}, {20, 81}, {46, 107}, {52, 113}, {13, 75}, {30, 88}, {45, 107}, {52, 114}, {8, 79}, {58, 125}, {57, 126}, {36, 99}, {35, 100}, {31, 88}, {25, 94}, {13, 74}, {45, 106}, {53, 114}, {1, 73}, {31, 87}, {21, 93}, {20, 92}, {7, 79}, {2, 74}, {20, 93}, {30, 87}, {21, 92}, {1, 74}, {2, 73}, {40, 100}, {59, 119}, {31, 82}, {58, 119}, {40, 101}, {31, 81}, {6, 86}, {12, 92}, {7, 86}, {26, 75}, {49, 96}, {7, 85}, {25, 75}, {6, 85}, {63, 108}, {34, 118}, {41, 125}, {25, 76}, {35, 118}, {41, 124}, {26, 76}, {35, 117}, {42, 124}, {7, 80}, {34, 117}, {12, 91}, {42, 125}, {8, 80}, {15, 87}, {14, 86}, {40, 112}, {41, 113}, {46, 118}, {47, 119}, {14, 87}, {60, 101}, {34, 123}, {15, 86}, {40, 113}, {41, 112}, {46, 119}, {47, 118}, {53, 108}, {1, 91}, {60, 102}, {33, 123}, {54, 108}, {60, 96}, {1, 92}, {59, 102}, {33, 124}, {54, 107}, {34, 124}, {63, 97}, {62, 96}, {59, 101}, {53, 107}, {63, 96}, {6, 103}, {5, 103}, {23, 117}, {22, 116}, {22, 117}, {60, 95}, {23, 116}, {55, 84}, {55, 83}, {5, 109}, {37, 77}, {18, 122}, {4, 109}, {61, 84}, {37, 76}, {18, 123}, {11, 98}, {4, 110}, {63, 85}, {62, 84}, {38, 76}, {17, 123}, {11, 97}, {5, 110}, {62, 85}, {56, 83}, {17, 122}, {38, 77}, {15, 99}, {56, 84}, {28, 112}, {54, 90}, {5, 104}, {29, 112}, {15, 98}, {12, 97}, {55, 90}, {6, 104}, {12, 98}, {49, 95}, {55, 89}, {54, 89}, {9, 121}, {10, 122}, {32, 81}, {16, 98}, {32, 82}, {29, 111}, {44, 94}, {45, 95}, {9, 122}, {28, 111}, {16, 99}, {10, 121}, {44, 95}, {45, 94}, {29, 105}, {61, 73}, {30, 106}, {29, 106}, {62, 73}, {30, 105}, {11, 115}, {43, 83}, {10, 115}, {36, 93}, {43, 82}, {36, 94}, {4, 127}, {3, 127}, {21, 105}, {49, 77}, {50, 78}, {21, 104}, {10, 116}, {22, 104}, {17, 111}, {16, 110}, {38, 88}, {39, 89}, {44, 82}, {11, 116}, {22, 105}, {17, 110}, {16, 111}, {38, 89}, {39, 88}, {44, 83}, {49, 78}, {50, 77}, {13, 141}, {13, 140}, {9, 139}, {3, 128}, {8, 139}, {2, 134}, {8, 140}, {4, 128}, {3, 134}, {9, 140}, {3, 133}, {2, 133}, {26, 136}, {27, 136}, {18, 134}, {24, 140}, {19, 135}, {18, 135}, {24, 141}, {19, 134}, {23, 129}, {23, 128}, {24, 128}, {24, 129}, {27, 130}, {27, 129}, {27, 135}, {26, 135}, {28, 129}, {28, 130}, {42, 136}, {43, 137}, {42, 137}, {43, 136}, {56, 144}, {57, 144}, {37, 143}, {37, 142}, {33, 141}, {47, 131}, {32, 141}, {47, 130}, {32, 142}, {33, 142}, {51, 131}, {52, 132}, {48, 130}, {48, 131}, {57, 143}, {61, 139}, {51, 132}, {61, 138}, {56, 143}, {52, 131}, {50, 138}, {51, 138}, {51, 137}, {50, 137}, {48, 142}, {48, 143}, {72, 138}, {72, 139}, {65, 132}, {66, 132}, {67, 133}, {66, 133}, {66, 144}, {67, 144} }>;

(II) A more general form is to represent the graph as the orbit of {68, 78} under the group generated by the following permutations:

a: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)(13, 66, 23, 64, 21, 62, 19, 72, 17, 70, 15, 68)(14, 67, 24, 65, 22, 63, 20, 61, 18, 71, 16, 69)(25, 56, 27, 58, 29, 60, 31, 50, 33, 52, 35, 54)(26, 57, 28, 59, 30, 49, 32, 51, 34, 53, 36, 55)(37, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38)(73, 134, 127, 110, 103, 86, 79, 140, 121, 116, 97, 92)(74, 133, 128, 109, 104, 85, 80, 139, 122, 115, 98, 91)(75, 144, 129, 120, 105, 96, 81, 138, 123, 114, 99, 90)(76, 143, 130, 119, 106, 95, 82, 137, 124, 113, 100, 89)(77, 142, 131, 118, 107, 94, 83, 136, 125, 112, 101, 88)(78, 141, 132, 117, 108, 93, 84, 135, 126, 111, 102, 87)
b: (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, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(31, 49)(32, 50)(33, 51)(34, 52)(35, 53)(36, 54)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(73, 74)(75, 84)(76, 83)(77, 82)(78, 81)(79, 80)(85, 86)(87, 96)(88, 95)(89, 94)(90, 93)(91, 92)(97, 98)(99, 108)(100, 107)(101, 106)(102, 105)(103, 104)(109, 110)(111, 120)(112, 119)(113, 118)(114, 117)(115, 116)(121, 122)(123, 132)(124, 131)(125, 130)(126, 129)(127, 128)(133, 134)(135, 144)(136, 143)(137, 142)(138, 141)(139, 140)
c: (2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(13, 21)(14, 20)(15, 19)(16, 18)(22, 24)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(37, 45)(38, 44)(39, 43)(40, 42)(46, 48)(50, 60)(51, 59)(52, 58)(53, 57)(54, 56)(61, 69)(62, 68)(63, 67)(64, 66)(70, 72)(73, 91)(74, 92)(75, 93)(76, 94)(77, 95)(78, 96)(79, 85)(80, 86)(81, 87)(82, 88)(83, 89)(84, 90)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144)(109, 121)(110, 122)(111, 123)(112, 124)(113, 125)(114, 126)(115, 127)(116, 128)(117, 129)(118, 130)(119, 131)(120, 132)
d: (1, 13, 9, 17, 5, 21)(2, 24, 10, 16, 6, 20)(3, 23, 11, 15, 7, 19)(4, 22, 12, 14, 8, 18)(25, 61, 33, 65, 29, 69)(26, 72, 34, 64, 30, 68)(27, 71, 35, 63, 31, 67)(28, 70, 36, 62, 32, 66)(37, 51, 41, 59, 45, 55)(38, 50, 42, 58, 46, 54)(39, 49, 43, 57, 47, 53)(40, 60, 44, 56, 48, 52)(73, 141, 121, 111, 103, 93)(74, 140, 122, 110, 104, 92)(75, 139, 123, 109, 105, 91)(76, 138, 124, 120, 106, 90)(77, 137, 125, 119, 107, 89)(78, 136, 126, 118, 108, 88)(79, 135, 127, 117, 97, 87)(80, 134, 128, 116, 98, 86)(81, 133, 129, 115, 99, 85)(82, 144, 130, 114, 100, 96)(83, 143, 131, 113, 101, 95)(84, 142, 132, 112, 102, 94)
e: (1, 73, 61, 138, 51, 131, 47, 118, 35, 99, 15, 86, 7, 79, 67, 144, 57, 125, 41, 112, 29, 105, 21, 92)(2, 84, 72, 137, 52, 130, 46, 117, 36, 98, 14, 85, 8, 78, 66, 143, 58, 124, 40, 111, 30, 104, 20, 91)(3, 83, 71, 136, 53, 129, 45, 116, 25, 97, 13, 96, 9, 77, 65, 142, 59, 123, 39, 110, 31, 103, 19, 90)(4, 82, 70, 135, 54, 128, 44, 115, 26, 108, 24, 95, 10, 76, 64, 141, 60, 122, 38, 109, 32, 102, 18, 89)(5, 81, 69, 134, 55, 127, 43, 114, 27, 107, 23, 94, 11, 75, 63, 140, 49, 121, 37, 120, 33, 101, 17, 88)(6, 80, 68, 133, 56, 126, 42, 113, 28, 106, 22, 93, 12, 74, 62, 139, 50, 132, 48, 119, 34, 100, 16, 87)

(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[ 144, 20 ]
144
-1 91 92 73 74
-2 133 134 73 74
-3 133 134 127 128
-4 110 127 128 109
-5 110 103 104 109
-6 103 104 85 86
-7 79 80 85 86
-8 79 80 139 140
-9 121 122 139 140
-10 121 122 115 116
-11 115 116 97 98
-12 91 92 97 98
-13 74 140 75 141
-14 74 75 86 87
-15 99 86 87 98
-16 99 110 111 98
-17 110 111 122 123
-18 122 123 134 135
-19 134 80 135 81
-20 80 81 92 93
-21 92 93 104 105
-22 104 105 116 117
-23 116 117 128 129
-24 128 129 140 141
-25 93 94 75 76
-26 135 136 75 76
-27 135 136 129 130
-28 111 112 129 130
-29 111 112 105 106
-30 88 105 106 87
-31 88 81 82 87
-32 81 82 141 142
-33 123 124 141 142
-34 123 124 117 118
-35 99 100 117 118
-36 99 100 93 94
-37 77 143 76 142
-38 77 88 89 76
-39 88 89 100 101
-40 100 101 112 113
-41 112 113 124 125
-42 124 125 136 137
-43 136 82 137 83
-44 82 83 94 95
-45 94 95 106 107
-46 106 107 118 119
-47 118 119 130 131
-48 143 130 131 142
-49 77 78 95 96
-50 77 78 137 138
-51 132 137 138 131
-52 132 113 114 131
-53 113 114 107 108
-54 89 90 107 108
-55 89 90 83 84
-56 143 144 83 84
-57 143 144 125 126
-58 125 126 119 120
-59 101 102 119 120
-60 101 102 95 96
-61 138 73 84 139
-62 73 84 85 96
-63 85 96 97 108
-64 97 108 109 120
-65 121 132 109 120
-66 121 132 133 144
-67 78 133 144 79
-68 78 79 90 91
-69 90 91 102 103
-70 102 103 114 115
-71 114 115 126 127
-72 126 127 138 139
-73 1 2 61 62
-74 1 2 13 14
-75 13 14 25 26
-76 25 26 37 38
-77 37 38 49 50
-78 67 68 49 50
-79 67 68 7 8
-80 7 8 19 20
-81 19 20 31 32
-82 44 31 32 43
-83 44 55 56 43
-84 55 56 61 62
-85 6 7 62 63
-86 14 15 6 7
-87 14 15 30 31
-88 38 39 30 31
-89 55 38 39 54
-90 55 68 69 54
-91 1 12 68 69
-92 1 12 20 21
-93 25 36 20 21
-94 44 45 25 36
-95 44 45 49 60
-96 49 60 62 63
-97 11 12 63 64
-98 11 12 15 16
-99 35 36 15 16
-100 35 36 39 40
-101 59 60 39 40
-102 69 59 70 60
-103 69 70 5 6
-104 22 5 6 21
-105 22 29 30 21
-106 45 46 29 30
-107 45 46 53 54
-108 63 53 64 54
-109 4 5 64 65
-110 4 5 16 17
-111 16 17 28 29
-112 28 29 40 41
-113 40 41 52 53
-114 70 71 52 53
-115 11 70 71 10
-116 11 22 23 10
-117 22 23 34 35
-118 34 35 46 47
-119 46 47 58 59
-120 58 59 64 65
-121 66 9 10 65
-122 17 18 9 10
-123 33 34 17 18
-124 33 34 41 42
-125 57 58 41 42
-126 57 58 71 72
-127 3 4 71 72
-128 23 24 3 4
-129 23 24 27 28
-130 47 48 27 28
-131 47 48 51 52
-132 66 51 52 65
-133 66 67 2 3
-134 2 3 18 19
-135 26 27 18 19
-136 26 27 42 43
-137 50 51 42 43
-138 50 61 72 51
-139 61 72 8 9
-140 13 24 8 9
-141 33 13 24 32
-142 33 37 48 32
-143 56 57 37 48
-144 66 56 67 57
0

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