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On this page are computer-accessible forms for the graph C4[ 180, 9 ] = PS(36,5;2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {9, 11} under the group generated by the following permutations:

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

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

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