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On this page are computer-accessible forms for the graph C4[ 180, 11 ] = PS(12,15;4).

(I) Following is a form readable by MAGMA:

g:=Graph<180|{ {45, 46}, {165, 166}, {105, 106}, {27, 31}, {147, 151}, {59, 63}, {58, 62}, {57, 61}, {88, 92}, {89, 93}, {90, 94}, {120, 124}, {75, 76}, {20, 31}, {148, 159}, {144, 155}, {52, 63}, {80, 91}, {84, 95}, {112, 123}, {116, 127}, {87, 91}, {150, 154}, {149, 153}, {148, 152}, {117, 121}, {118, 122}, {119, 123}, {51, 62}, {147, 158}, {145, 156}, {81, 92}, {83, 94}, {113, 124}, {115, 126}, {32, 46}, {161, 175}, {160, 174}, {65, 79}, {64, 78}, {33, 47}, {96, 110}, {97, 111}, {128, 142}, {129, 143}, {50, 61}, {146, 157}, {82, 93}, {114, 125}, {135, 136}, {1, 17}, {164, 180}, {163, 179}, {162, 178}, {161, 177}, {160, 176}, {74, 90}, {73, 89}, {72, 88}, {71, 87}, {70, 86}, {69, 85}, {68, 84}, {67, 83}, {66, 82}, {65, 81}, {64, 80}, {44, 60}, {43, 59}, {42, 58}, {41, 57}, {40, 56}, {39, 55}, {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}, {32, 48}, {33, 49}, {34, 50}, {35, 51}, {36, 52}, {37, 53}, {38, 54}, {96, 112}, {97, 113}, {98, 114}, {99, 115}, {100, 116}, {101, 117}, {102, 118}, {103, 119}, {104, 120}, {128, 144}, {129, 145}, {130, 146}, {131, 147}, {132, 148}, {133, 149}, {134, 150}, {2, 16}, {163, 177}, {162, 176}, {75, 89}, {74, 88}, {71, 85}, {70, 84}, {67, 81}, {66, 80}, {43, 57}, {42, 56}, {39, 53}, {3, 17}, {6, 20}, {7, 21}, {10, 24}, {11, 25}, {14, 28}, {15, 29}, {34, 48}, {35, 49}, {38, 52}, {98, 112}, {99, 113}, {102, 116}, {103, 117}, {130, 144}, {131, 145}, {134, 148}, {135, 149}, {76, 95}, {140, 159}, {108, 127}, {136, 155}, {107, 126}, {143, 154}, {141, 152}, {139, 158}, {137, 156}, {111, 122}, {4, 18}, {165, 179}, {164, 178}, {69, 83}, {68, 82}, {45, 59}, {44, 58}, {5, 19}, {12, 26}, {13, 27}, {36, 50}, {37, 51}, {100, 114}, {101, 115}, {132, 146}, {133, 147}, {106, 125}, {142, 153}, {138, 157}, {110, 121}, {140, 151}, {8, 22}, {73, 87}, {72, 86}, {41, 55}, {40, 54}, {9, 23}, {104, 118}, {105, 119}, {1, 30}, {15, 16}, {31, 60}, {151, 180}, {91, 120}, {78, 104}, {79, 105}, {76, 102}, {137, 163}, {136, 162}, {77, 103}, {77, 96}, {143, 162}, {141, 160}, {79, 98}, {138, 164}, {139, 165}, {78, 97}, {142, 161}, {31, 47}, {159, 175}, {158, 174}, {157, 173}, {156, 172}, {155, 171}, {154, 170}, {153, 169}, {152, 168}, {151, 167}, {91, 107}, {92, 108}, {93, 109}, {94, 110}, {95, 111}, {94, 108}, {159, 173}, {158, 172}, {155, 169}, {154, 168}, {95, 109}, {16, 35}, {144, 163}, {20, 39}, {24, 43}, {80, 99}, {84, 103}, {17, 36}, {149, 160}, {145, 164}, {19, 38}, {21, 32}, {23, 34}, {25, 44}, {29, 40}, {81, 100}, {83, 102}, {85, 96}, {87, 98}, {92, 106}, {157, 171}, {156, 170}, {93, 107}, {18, 37}, {150, 161}, {146, 165}, {22, 33}, {26, 45}, {30, 41}, {82, 101}, {86, 97}, {16, 42}, {17, 43}, {24, 35}, {28, 39}, {88, 99}, {28, 32}, {29, 33}, {30, 34}, {21, 40}, {23, 42}, {25, 36}, {27, 38}, {85, 104}, {89, 100}, {18, 44}, {153, 167}, {152, 166}, {19, 45}, {22, 41}, {26, 37}, {86, 105}, {90, 101}, {46, 72}, {47, 73}, {61, 90}, {47, 66}, {46, 65}, {61, 77}, {63, 79}, {62, 78}, {62, 76}, {63, 77}, {48, 67}, {56, 75}, {52, 71}, {49, 68}, {55, 66}, {53, 64}, {51, 70}, {50, 69}, {54, 65}, {48, 74}, {49, 75}, {56, 67}, {60, 71}, {60, 64}, {53, 72}, {59, 70}, {57, 68}, {55, 74}, {54, 73}, {58, 69}, {6, 167}, {8, 169}, {10, 171}, {12, 173}, {14, 175}, {5, 166}, {9, 170}, {13, 174}, {14, 168}, {15, 169}, {11, 172}, {2, 171}, {4, 173}, {6, 175}, {12, 166}, {13, 167}, {1, 170}, {5, 174}, {3, 172}, {7, 168}, {1, 177}, {2, 178}, {3, 179}, {4, 180}, {7, 176}, {8, 177}, {10, 179}, {9, 178}, {11, 180}, {15, 176}, {108, 134}, {109, 135}, {109, 128}, {111, 130}, {106, 132}, {107, 133}, {110, 129}, {121, 150}, {121, 137}, {122, 138}, {123, 139}, {124, 140}, {125, 141}, {126, 142}, {127, 143}, {122, 136}, {123, 137}, {126, 140}, {127, 141}, {112, 131}, {116, 135}, {113, 132}, {115, 134}, {117, 128}, {119, 130}, {124, 138}, {125, 139}, {114, 133}, {118, 129}, {120, 131} }>;

(II) A more general form is to represent the graph as the orbit of {45, 46} under the group generated by the following permutations:

a: (2, 15)(3, 14)(4, 13)(5, 12)(6, 11)(7, 10)(8, 9)(17, 30)(18, 29)(19, 28)(20, 27)(21, 26)(22, 25)(23, 24)(32, 45)(33, 44)(34, 43)(35, 42)(36, 41)(37, 40)(38, 39)(47, 60)(48, 59)(49, 58)(50, 57)(51, 56)(52, 55)(53, 54)(62, 75)(63, 74)(64, 73)(65, 72)(66, 71)(67, 70)(68, 69)(77, 90)(78, 89)(79, 88)(80, 87)(81, 86)(82, 85)(83, 84)(92, 105)(93, 104)(94, 103)(95, 102)(96, 101)(97, 100)(98, 99)(107, 120)(108, 119)(109, 118)(110, 117)(111, 116)(112, 115)(113, 114)(122, 135)(123, 134)(124, 133)(125, 132)(126, 131)(127, 130)(128, 129)(137, 150)(138, 149)(139, 148)(140, 147)(141, 146)(142, 145)(143, 144)(152, 165)(153, 164)(154, 163)(155, 162)(156, 161)(157, 160)(158, 159)(167, 180)(168, 179)(169, 178)(170, 177)(171, 176)(172, 175)(173, 174)
b: (2, 12)(3, 8)(5, 15)(6, 11)(9, 14)(16, 166)(17, 177)(18, 173)(19, 169)(20, 180)(21, 176)(22, 172)(23, 168)(24, 179)(25, 175)(26, 171)(27, 167)(28, 178)(29, 174)(30, 170)(31, 151)(32, 162)(33, 158)(34, 154)(35, 165)(36, 161)(37, 157)(38, 153)(39, 164)(40, 160)(41, 156)(42, 152)(43, 163)(44, 159)(45, 155)(46, 136)(47, 147)(48, 143)(49, 139)(50, 150)(51, 146)(52, 142)(53, 138)(54, 149)(55, 145)(56, 141)(57, 137)(58, 148)(59, 144)(60, 140)(61, 121)(62, 132)(63, 128)(64, 124)(65, 135)(66, 131)(67, 127)(68, 123)(69, 134)(70, 130)(71, 126)(72, 122)(73, 133)(74, 129)(75, 125)(76, 106)(77, 117)(78, 113)(79, 109)(80, 120)(81, 116)(82, 112)(83, 108)(84, 119)(85, 115)(86, 111)(87, 107)(88, 118)(89, 114)(90, 110)(92, 102)(93, 98)(95, 105)(96, 101)(99, 104)
c: (1, 16, 31, 46, 61, 76, 91, 106, 121, 136, 151, 166)(2, 27, 32, 57, 62, 87, 92, 117, 122, 147, 152, 177)(3, 23, 33, 53, 63, 83, 93, 113, 123, 143, 153, 173)(4, 19, 34, 49, 64, 79, 94, 109, 124, 139, 154, 169)(5, 30, 35, 60, 65, 90, 95, 120, 125, 150, 155, 180)(6, 26, 36, 56, 66, 86, 96, 116, 126, 146, 156, 176)(7, 22, 37, 52, 67, 82, 97, 112, 127, 142, 157, 172)(8, 18, 38, 48, 68, 78, 98, 108, 128, 138, 158, 168)(9, 29, 39, 59, 69, 89, 99, 119, 129, 149, 159, 179)(10, 25, 40, 55, 70, 85, 100, 115, 130, 145, 160, 175)(11, 21, 41, 51, 71, 81, 101, 111, 131, 141, 161, 171)(12, 17, 42, 47, 72, 77, 102, 107, 132, 137, 162, 167)(13, 28, 43, 58, 73, 88, 103, 118, 133, 148, 163, 178)(14, 24, 44, 54, 74, 84, 104, 114, 134, 144, 164, 174)(15, 20, 45, 50, 75, 80, 105, 110, 135, 140, 165, 170)
d: (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)(121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135)(136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150)(151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165)(166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180)

(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[ 180, 11 ]
180
-1 177 170 17 30
-2 178 16 171 18
-3 179 17 172 19
-4 180 18 173 20
-5 166 19 174 21
-6 22 167 20 175
-7 176 23 168 21
-8 22 177 24 169
-9 23 178 25 170
-10 24 179 26 171
-11 25 180 27 172
-12 166 26 28 173
-13 167 27 29 174
-14 168 28 30 175
-15 176 169 16 29
-16 2 35 15 42
-17 1 3 36 43
-18 44 2 4 37
-19 45 3 5 38
-20 4 6 39 31
-21 5 7 40 32
-22 33 6 8 41
-23 34 7 9 42
-24 35 8 10 43
-25 11 44 36 9
-26 12 45 37 10
-27 11 13 38 31
-28 12 14 39 32
-29 33 13 15 40
-30 1 34 14 41
-31 47 27 60 20
-32 46 48 28 21
-33 22 47 49 29
-34 23 48 50 30
-35 24 16 49 51
-36 25 17 50 52
-37 26 18 51 53
-38 27 19 52 54
-39 55 28 20 53
-40 56 29 21 54
-41 22 55 57 30
-42 23 56 58 16
-43 24 57 59 17
-44 25 58 60 18
-45 46 26 59 19
-46 45 72 32 65
-47 33 66 73 31
-48 34 67 74 32
-49 33 35 68 75
-50 34 36 69 61
-51 35 37 70 62
-52 36 38 71 63
-53 37 39 72 64
-54 38 40 73 65
-55 66 39 41 74
-56 67 40 42 75
-57 68 61 41 43
-58 44 69 62 42
-59 45 70 63 43
-60 44 71 31 64
-61 77 57 90 50
-62 78 58 51 76
-63 77 79 59 52
-64 78 80 60 53
-65 46 79 81 54
-66 55 47 80 82
-67 56 48 81 83
-68 57 49 82 84
-69 58 50 83 85
-70 59 51 84 86
-71 60 52 85 87
-72 88 46 53 86
-73 89 47 54 87
-74 55 88 90 48
-75 56 89 49 76
-76 102 62 95 75
-77 103 61 63 96
-78 104 62 64 97
-79 105 63 65 98
-80 66 99 91 64
-81 67 100 92 65
-82 66 68 101 93
-83 67 69 102 94
-84 68 70 103 95
-85 69 71 104 96
-86 70 72 105 97
-87 91 71 73 98
-88 99 92 72 74
-89 100 93 73 75
-90 101 61 94 74
-91 80 107 87 120
-92 88 81 106 108
-93 89 82 107 109
-94 110 90 83 108
-95 111 84 76 109
-96 77 110 112 85
-97 78 111 113 86
-98 79 112 114 87
-99 88 80 113 115
-100 89 81 114 116
-101 90 82 115 117
-102 83 116 118 76
-103 77 84 117 119
-104 78 85 118 120
-105 79 106 86 119
-106 132 92 125 105
-107 133 91 93 126
-108 134 92 94 127
-109 135 93 95 128
-110 121 94 96 129
-111 122 95 97 130
-112 123 96 98 131
-113 99 132 124 97
-114 100 133 125 98
-115 99 101 134 126
-116 100 102 135 127
-117 121 101 103 128
-118 122 102 104 129
-119 123 103 105 130
-120 91 124 104 131
-121 110 137 117 150
-122 111 136 138 118
-123 112 137 139 119
-124 113 138 140 120
-125 114 106 139 141
-126 115 107 140 142
-127 143 116 108 141
-128 144 117 109 142
-129 110 143 145 118
-130 111 144 146 119
-131 112 145 147 120
-132 113 146 148 106
-133 114 147 149 107
-134 115 148 150 108
-135 136 116 149 109
-136 122 155 135 162
-137 121 123 156 163
-138 122 124 157 164
-139 165 123 125 158
-140 124 126 159 151
-141 125 127 160 152
-142 126 128 161 153
-143 154 127 129 162
-144 155 128 130 163
-145 156 129 131 164
-146 132 165 157 130
-147 133 158 151 131
-148 132 134 159 152
-149 133 135 160 153
-150 121 154 134 161
-151 167 147 180 140
-152 166 168 148 141
-153 167 169 149 142
-154 143 168 170 150
-155 144 136 169 171
-156 145 137 170 172
-157 146 138 171 173
-158 147 139 172 174
-159 148 140 173 175
-160 176 149 141 174
-161 177 150 142 175
-162 143 176 178 136
-163 144 177 179 137
-164 145 178 180 138
-165 166 146 179 139
-166 165 12 5 152
-167 13 6 151 153
-168 154 14 7 152
-169 155 15 8 153
-170 154 1 156 9
-171 155 2 157 10
-172 11 156 3 158
-173 12 157 4 159
-174 13 158 5 160
-175 14 159 6 161
-176 15 160 7 162
-177 1 161 8 163
-178 2 162 9 164
-179 165 3 163 10
-180 11 4 151 164
0

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