Graph forms
for C4 [ 180, 53 ] = SS[180,10]
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On this page are computer-accessible forms for the graph C4[ 180, 53 ] =
SS[180,10].
(I) Following is a form readable by MAGMA:
g:=Graph<180|{ {1, 3}, {1, 2}, {68, 71}, {1, 5}, {17, 21}, {16, 20}, {1, 4},
{19, 22}, {18, 23}, {128, 137}, {130, 139}, {69, 79}, {67, 72}, {162, 169},
{161, 170}, {160, 171}, {129, 138}, {69, 78}, {70, 77}, {20, 24}, {21, 24},
{128, 141}, {16, 30}, {22, 24}, {19, 29}, {17, 31}, {23, 24}, {164, 171}, {163,
172}, {129, 142}, {67, 76}, {68, 75}, {69, 74}, {70, 73}, {14, 28}, {132, 150},
{130, 144}, {67, 80}, {167, 180}, {132, 151}, {15, 27}, {166, 178}, {165, 177},
{64, 84}, {65, 85}, {66, 86}, {12, 25}, {68, 82}, {131, 149}, {13, 26}, {70,
81}, {12, 20}, {15, 22}, {64, 89}, {13, 23}, {66, 88}, {14, 21}, {168, 179},
{131, 152}, {65, 90}, {6, 38}, {131, 163}, {6, 39}, {128, 161}, {8, 41}, {7,
37}, {18, 48}, {9, 43}, {8, 42}, {129, 162}, {144, 179}, {140, 175}, {10, 46},
{138, 174}, {137, 173}, {11, 47}, {9, 44}, {132, 161}, {11, 45}, {150, 176},
{132, 162}, {130, 164}, {131, 164}, {13, 36}, {155, 176}, {12, 33}, {15, 34},
{14, 35}, {7, 40}, {10, 59}, {18, 32}, {12, 63}, {159, 172}, {156, 175}, {135,
180}, {10, 62}, {158, 170}, {157, 169}, {154, 174}, {153, 173}, {134, 178},
{133, 177}, {11, 61}, {152, 174}, {11, 60}, {148, 172}, {151, 175}, {149, 173},
{6, 63}, {146, 171}, {10, 48}, {147, 169}, {16, 43}, {145, 170}, {143, 180},
{139, 176}, {136, 179}, {18, 41}, {17, 42}, {141, 177}, {142, 178}, {16, 46},
{19, 45}, {17, 47}, {19, 44}, {38, 103}, {32, 98}, {51, 112}, {6, 66}, {55,
115}, {52, 112}, {34, 102}, {27, 95}, {32, 101}, {33, 100}, {7, 65}, {55, 113},
{35, 101}, {25, 95}, {7, 64}, {36, 99}, {57, 113}, {58, 114}, {48, 122}, {56,
114}, {8, 67}, {56, 115}, {8, 68}, {9, 69}, {37, 104}, {50, 127}, {57, 116},
{14, 64}, {15, 65}, {58, 116}, {9, 70}, {40, 103}, {39, 104}, {13, 66}, {25,
73}, {27, 74}, {59, 106}, {26, 72}, {42, 120}, {36, 119}, {40, 123}, {45, 121},
{61, 105}, {31, 74}, {47, 122}, {35, 118}, {30, 72}, {60, 106}, {34, 117}, {46,
121}, {62, 105}, {38, 126}, {33, 120}, {54, 111}, {52, 109}, {37, 124}, {29,
71}, {53, 111}, {39, 125}, {28, 71}, {53, 110}, {44, 119}, {41, 117}, {43, 118},
{54, 107}, {51, 108}, {58, 91}, {52, 86}, {54, 85}, {40, 76}, {57, 92}, {49,
87}, {56, 94}, {53, 83}, {51, 84}, {55, 80}, {20, 124}, {50, 90}, {49, 89}, {37,
77}, {60, 84}, {61, 85}, {63, 87}, {32, 73}, {56, 81}, {53, 92}, {48, 89}, {39,
78}, {50, 88}, {55, 93}, {21, 126}, {54, 93}, {22, 125}, {57, 82}, {23, 123},
{63, 83}, {38, 75}, {51, 94}, {59, 86}, {62, 83}, {33, 79}, {52, 91}, {28, 109},
{44, 93}, {25, 107}, {41, 91}, {34, 81}, {35, 80}, {61, 78}, {62, 77}, {42, 94},
{46, 90}, {27, 110}, {58, 79}, {26, 108}, {36, 82}, {43, 92}, {47, 88}, {59,
76}, {60, 75}, {30, 102}, {29, 100}, {26, 96}, {45, 87}, {28, 96}, {31, 99},
{29, 97}, {31, 98}, {30, 97}, {4, 172}, {3, 170}, {5, 175}, {2, 169}, {3, 174},
{5, 171}, {2, 173}, {3, 179}, {49, 129}, {50, 128}, {49, 130}, {4, 176}, {5,
177}, {2, 180}, {4, 178}, {90, 155}, {102, 167}, {88, 154}, {100, 166}, {92,
152}, {89, 156}, {99, 165}, {102, 160}, {111, 168}, {94, 150}, {84, 157}, {86,
159}, {95, 150}, {93, 151}, {111, 165}, {95, 149}, {85, 158}, {101, 168}, {87,
153}, {91, 149}, {71, 146}, {112, 166}, {112, 167}, {119, 160}, {72, 145}, {73,
147}, {127, 163}, {74, 148}, {106, 139}, {125, 156}, {123, 153}, {75, 168},
{105, 138}, {106, 137}, {116, 144}, {105, 140}, {126, 155}, {109, 136}, {124,
154}, {120, 159}, {113, 153}, {118, 158}, {117, 157}, {114, 154}, {76, 165},
{110, 135}, {78, 167}, {108, 133}, {113, 155}, {77, 166}, {97, 141}, {98, 142},
{79, 162}, {98, 143}, {107, 134}, {114, 156}, {127, 143}, {97, 144}, {81, 163},
{122, 136}, {82, 161}, {127, 140}, {118, 133}, {117, 134}, {83, 160}, {103,
148}, {80, 164}, {126, 138}, {125, 137}, {103, 147}, {96, 151}, {124, 139},
{123, 140}, {96, 152}, {108, 148}, {104, 145}, {107, 146}, {100, 158}, {101,
159}, {104, 146}, {116, 143}, {115, 142}, {99, 157}, {121, 135}, {115, 141},
{109, 147}, {110, 145}, {122, 133}, {121, 134}, {120, 135}, {119, 136} }>;
(II) A more general form is to represent the graph as the orbit of {1, 3}
under the group generated by the following permutations:
a: (1, 8)(2, 68)(3, 41)(4, 67)(5, 42)(6, 87)(7, 90)(10, 124)(11, 125)(12,
83)(13, 129)(14, 127)(15, 85)(16, 77)(17, 175)(18, 174)(19, 78)(20, 62)(21,
140)(22, 61)(23, 138)(24, 105)(25, 53)(26, 142)(27, 54)(28, 143)(29, 167)(30,
166)(31, 151)(32, 152)(33, 160)(34, 158)(35, 163)(36, 162)(37, 46)(38, 153)(39,
45)(40, 155)(43, 70)(44, 69)(47, 156)(48, 154)(49, 66)(50, 64)(51, 141)(52,
144)(55, 148)(56, 133)(57, 147)(58, 136)(59, 139)(60, 137)(71, 180)(72, 178)(73,
92)(74, 93)(75, 173)(76, 176)(79, 119)(80, 172)(81, 118)(82, 169)(84, 128)(86,
130)(88, 89)(91, 179)(94, 177)(95, 111)(96, 98)(97, 112)(99, 132)(100, 102)(101,
131)(103, 113)(104, 121)(107, 110)(108, 115)(109, 116)(114, 122)(117, 170)(120,
171)(123, 126)(134, 145)(135, 146)(149, 168)(150, 165)(157, 161)(159, 164) (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.
**************
&Graph **************
b: (2, 5)(3, 4)(6, 7)(8, 9)(10, 11)(12, 14)(13, 15)(16, 17)(18, 19)(20, 21)(22,
23)(25, 28)(26, 27)(29, 32)(30, 31)(33, 35)(34, 36)(37, 38)(39, 40)(41, 44)(42,
43)(45, 48)(46, 47)(51, 53)(52, 54)(55, 58)(56, 57)(59, 61)(60, 62)(63, 64)(65,
66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 80)(81, 82)(83, 84)(85,
86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 96)(97, 98)(99, 102)(100, 101)(103,
104)(105, 106)(107, 109)(108, 110)(111, 112)(113, 114)(115, 116)(117, 119)(118,
120)(121, 122)(123, 125)(124, 126)(127, 128)(129, 130)(131, 132)(133, 135)(134,
136)(137, 140)(138, 139)(141, 143)(142, 144)(145, 148)(146, 147)(149, 151)(150,
152)(153, 156)(154, 155)(157, 160)(158, 159)(161, 163)(162, 164)(165, 167)(166,
168)(169, 171)(170, 172)(173, 175)(174, 176)(177, 180)(178, 179)
c: (2, 3)(4, 5)(8, 9)(12, 13)(14, 15)(16, 18)(17, 19)(20, 23)(21, 22)(25,
26)(27, 28)(29, 31)(30, 32)(33, 36)(34, 35)(37, 40)(38, 39)(41, 43)(42, 44)(45,
47)(46, 48)(49, 50)(51, 54)(52, 53)(55, 56)(57, 58)(59, 62)(60, 61)(63, 66)(64,
65)(67, 70)(68, 69)(71, 74)(72, 73)(75, 78)(76, 77)(79, 82)(80, 81)(83, 86)(84,
85)(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)(117, 118)(119, 120)(121,
122)(123, 124)(125, 126)(127, 130)(128, 129)(133, 134)(135, 136)(137, 138)(139,
140)(141, 142)(143, 144)(145, 147)(146, 148)(149, 152)(150, 151)(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)
d: (1, 6, 132, 11)(2, 39, 161, 60)(3, 38, 162, 61)(4, 63, 151, 47)(5, 66, 150,
45)(7, 116)(8, 117, 102, 72)(9, 118, 101, 73)(10, 131, 24, 115)(12, 93, 122,
172)(13, 94, 121, 171)(14, 98, 77, 92)(15, 97, 76, 91)(16, 80, 18, 81)(17, 178,
83, 96)(19, 177, 86, 95)(20, 55, 48, 163)(21, 142, 62, 152)(22, 141, 59,
149)(23, 56, 46, 164)(25, 44, 133, 159)(26, 42, 134, 160)(27, 29, 165, 52)(28,
31, 166, 53)(30, 67, 41, 34)(32, 70, 43, 35)(33, 54, 136, 148)(36, 51, 135,
146)(37, 57, 64, 143)(40, 58, 65, 144)(49, 140, 154, 155)(50, 139, 153, 156)(68,
157, 167, 145)(69, 158, 168, 147)(71, 99, 112, 110)(74, 100, 111, 109)(75, 169,
78, 170)(79, 85, 179, 103)(82, 84, 180, 104)(87, 175, 88, 176)(89, 127, 124,
113)(90, 130, 123, 114)(105, 174, 126, 129)(106, 173, 125, 128)(107, 119, 108,
120)
C4[ 180, 53 ]
180
-1 2 3 4 5
-2 1 169 180 173
-3 1 179 170 174
-4 176 1 178 172
-5 1 177 171 175
-6 66 38 39 63
-7 37 40 64 65
-8 67 68 41 42
-9 44 69 70 43
-10 46 48 59 62
-11 45 47 60 61
-12 33 25 63 20
-13 66 23 36 26
-14 35 28 64 21
-15 22 34 27 65
-16 46 30 20 43
-17 47 31 42 21
-18 23 48 41 32
-19 22 44 45 29
-20 12 24 124 16
-21 24 14 126 17
-22 24 15 125 19
-23 13 24 123 18
-24 22 23 20 21
-25 12 73 95 107
-26 13 72 96 108
-27 110 15 95 74
-28 14 71 96 109
-29 100 71 19 97
-30 102 16 72 97
-31 99 17 74 98
-32 101 18 73 98
-33 12 100 79 120
-34 102 15 81 117
-35 101 14 80 118
-36 99 13 82 119
-37 77 124 104 7
-38 103 126 6 75
-39 78 125 104 6
-40 123 103 7 76
-41 91 18 117 8
-42 17 94 8 120
-43 92 16 118 9
-44 93 19 9 119
-45 11 121 19 87
-46 121 90 16 10
-47 11 88 122 17
-48 89 122 18 10
-49 89 129 130 87
-50 88 90 127 128
-51 112 94 84 108
-52 112 91 86 109
-53 110 111 92 83
-54 111 93 85 107
-55 80 113 93 115
-56 81 114 115 94
-57 113 92 82 116
-58 79 91 114 116
-59 106 86 10 76
-60 11 84 106 75
-61 11 78 105 85
-62 77 83 105 10
-63 12 6 83 87
-64 89 14 7 84
-65 90 15 7 85
-66 88 13 6 86
-67 80 72 8 76
-68 71 82 8 75
-69 78 79 74 9
-70 77 81 73 9
-71 68 146 28 29
-72 67 145 26 30
-73 25 70 147 32
-74 69 27 148 31
-75 68 168 38 60
-76 165 67 59 40
-77 166 37 70 62
-78 167 69 39 61
-79 33 58 69 162
-80 55 67 35 164
-81 34 56 70 163
-82 57 68 36 161
-83 160 62 63 53
-84 157 60 51 64
-85 158 61 54 65
-86 66 59 159 52
-87 45 49 63 153
-88 66 154 47 50
-89 156 48 49 64
-90 155 46 50 65
-91 58 149 41 52
-92 57 53 152 43
-93 44 55 151 54
-94 56 51 150 42
-95 25 27 149 150
-96 26 28 151 152
-97 144 29 30 141
-98 143 31 32 142
-99 165 36 157 31
-100 33 166 158 29
-101 35 168 159 32
-102 34 167 160 30
-103 147 38 148 40
-104 145 146 37 39
-105 61 138 62 140
-106 59 60 137 139
-107 134 25 146 54
-108 133 26 148 51
-109 136 147 28 52
-110 145 135 27 53
-111 165 168 53 54
-112 166 167 51 52
-113 55 155 57 153
-114 154 56 156 58
-115 55 56 141 142
-116 143 144 57 58
-117 34 134 157 41
-118 133 35 158 43
-119 44 36 136 160
-120 33 135 159 42
-121 45 46 134 135
-122 133 47 48 136
-123 23 40 140 153
-124 154 37 139 20
-125 22 156 137 39
-126 155 38 138 21
-127 143 50 140 163
-128 137 50 161 141
-129 49 138 162 142
-130 144 49 139 164
-131 149 152 163 164
-132 150 161 151 162
-133 122 177 118 108
-134 121 178 117 107
-135 110 121 180 120
-136 122 179 119 109
-137 125 106 128 173
-138 126 105 129 174
-139 176 124 106 130
-140 123 105 127 175
-141 177 115 128 97
-142 178 115 129 98
-143 180 116 127 98
-144 179 116 97 130
-145 110 104 170 72
-146 71 104 171 107
-147 103 169 73 109
-148 103 172 74 108
-149 91 95 173 131
-150 132 176 94 95
-151 132 93 96 175
-152 92 96 174 131
-153 123 113 173 87
-154 88 124 114 174
-155 176 90 113 126
-156 89 114 125 175
-157 99 169 84 117
-158 100 170 85 118
-159 101 172 86 120
-160 102 83 171 119
-161 132 82 170 128
-162 132 79 169 129
-163 81 127 172 131
-164 80 171 130 131
-165 99 111 177 76
-166 77 100 112 178
-167 78 112 102 180
-168 111 101 179 75
-169 2 157 147 162
-170 145 3 158 161
-171 146 5 160 164
-172 4 148 159 163
-173 2 137 149 153
-174 154 3 138 152
-175 156 5 140 151
-176 155 4 139 150
-177 165 133 5 141
-178 166 134 4 142
-179 144 3 168 136
-180 143 2 167 135
0