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On this page are computer-accessible forms for the graph C4[ 180, 12 ] = PS(6,60;19).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 62} under the group generated by the following permutations:

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

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

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