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On this page are computer-accessible forms for the graph C4[ 180, 42 ] =
UG(Rmap(360,353){8,4|10}_10).
(I) Following is a form readable by MAGMA:
g:=Graph<180|{ {50, 51}, {148, 149}, {144, 145}, {104, 105}, {56, 57}, {102,
103}, {1, 3}, {177, 179}, {72, 74}, {1, 2}, {169, 170}, {1, 5}, {2, 7}, {3, 6},
{2, 4}, {168, 174}, {8, 15}, {160, 167}, {115, 116}, {3, 11}, {119, 127}, {20,
28}, {1, 8}, {18, 27}, {7, 14}, {6, 13}, {161, 173}, {163, 175}, {4, 9}, {165,
168}, {151, 154}, {150, 155}, {2, 12}, {144, 158}, {128, 142}, {17, 31}, {16,
30}, {5, 10}, {117, 122}, {113, 126}, {106, 122}, {143, 159}, {3, 18}, {41, 56},
{69, 84}, {102, 119}, {14, 28}, {161, 179}, {37, 55}, {15, 29}, {98, 112}, {42,
57}, {142, 157}, {133, 150}, {4, 16}, {160, 180}, {134, 146}, {5, 17}, {70, 83},
{43, 61}, {167, 177}, {66, 84}, {77, 91}, {97, 119}, {165, 178}, {9, 19}, {134,
156}, {130, 152}, {37, 63}, {36, 62}, {33, 59}, {32, 58}, {12, 22}, {168, 179},
{172, 176}, {68, 89}, {132, 153}, {69, 88}, {4, 26}, {35, 61}, {34, 60}, {13,
19}, {11, 21}, {10, 20}, {7, 25}, {6, 24}, {5, 27}, {8, 23}, {143, 144}, {128,
159}, {85, 117}, {146, 178}, {140, 172}, {88, 120}, {7, 38}, {6, 37}, {145,
178}, {16, 51}, {138, 174}, {139, 175}, {17, 52}, {132, 161}, {30, 56}, {143,
169}, {141, 171}, {31, 57}, {77, 107}, {75, 108}, {76, 100}, {156, 180}, {10,
35}, {134, 175}, {87, 126}, {95, 118}, {9, 34}, {12, 39}, {94, 114}, {12, 33},
{137, 164}, {65, 108}, {71, 105}, {8, 39}, {11, 36}, {64, 112}, {155, 171},
{151, 167}, {65, 113}, {67, 114}, {159, 174}, {155, 170}, {69, 116}, {18, 32},
{74, 120}, {75, 121}, {24, 43}, {154, 169}, {70, 117}, {84, 96}, {25, 44}, {29,
40}, {27, 46}, {68, 114}, {154, 172}, {76, 122}, {26, 45}, {149, 162}, {148,
163}, {147, 164}, {135, 176}, {68, 115}, {147, 171}, {142, 180}, {88, 99}, {150,
173}, {145, 170}, {89, 98}, {9, 53}, {26, 38}, {11, 55}, {10, 54}, {81, 109},
{13, 48}, {23, 42}, {21, 40}, {18, 47}, {15, 50}, {83, 110}, {70, 120}, {158,
160}, {72, 118}, {73, 119}, {14, 49}, {157, 162}, {153, 166}, {22, 41}, {82,
109}, {49, 113}, {14, 76}, {48, 114}, {15, 77}, {36, 103}, {32, 100}, {34, 102},
{33, 101}, {13, 75}, {40, 110}, {48, 120}, {30, 87}, {54, 124}, {55, 125}, {19,
95}, {53, 123}, {63, 111}, {20, 69}, {52, 101}, {42, 123}, {24, 73}, {22, 71},
{60, 109}, {21, 70}, {52, 103}, {25, 74}, {61, 110}, {63, 107}, {41, 124}, {42,
127}, {41, 127}, {19, 68}, {49, 102}, {26, 66}, {27, 67}, {58, 99}, {44, 118},
{59, 97}, {16, 78}, {17, 79}, {62, 96}, {23, 72}, {46, 78}, {28, 126}, {45, 79},
{36, 71}, {48, 85}, {50, 87}, {38, 64}, {39, 65}, {59, 93}, {49, 86}, {62, 89},
{57, 80}, {35, 73}, {58, 80}, {59, 81}, {60, 86}, {51, 88}, {52, 89}, {54, 91},
{53, 90}, {24, 108}, {55, 64}, {37, 93}, {38, 94}, {40, 81}, {54, 79}, {39, 92},
{53, 78}, {47, 84}, {43, 80}, {20, 104}, {31, 99}, {30, 98}, {29, 97}, {28, 96},
{23, 107}, {22, 106}, {21, 105}, {25, 100}, {46, 83}, {44, 81}, {45, 82}, {63,
167}, {29, 132}, {31, 133}, {32, 134}, {33, 135}, {58, 147}, {34, 136}, {35,
137}, {60, 150}, {61, 151}, {43, 128}, {50, 153}, {44, 129}, {47, 130}, {51,
131}, {47, 156}, {56, 139}, {46, 155}, {45, 154}, {62, 129}, {87, 151}, {112,
176}, {111, 175}, {100, 164}, {110, 172}, {115, 177}, {86, 146}, {91, 159}, {93,
152}, {109, 171}, {76, 132}, {107, 163}, {106, 162}, {74, 131}, {72, 130}, {73,
131}, {80, 157}, {125, 176}, {64, 142}, {75, 133}, {95, 143}, {124, 174}, {82,
129}, {92, 136}, {121, 173}, {92, 137}, {116, 161}, {90, 140}, {91, 141}, {95,
136}, {122, 173}, {125, 164}, {66, 152}, {124, 166}, {67, 153}, {78, 148}, {79,
149}, {86, 139}, {90, 135}, {77, 147}, {126, 160}, {123, 165}, {85, 138}, {101,
133}, {71, 166}, {127, 158}, {104, 137}, {103, 131}, {113, 149}, {111, 138},
{121, 156}, {121, 158}, {90, 178}, {117, 157}, {65, 168}, {67, 170}, {94, 180},
{96, 138}, {66, 169}, {93, 177}, {106, 135}, {111, 129}, {92, 179}, {98, 141},
{99, 140}, {82, 162}, {83, 163}, {85, 165}, {97, 144}, {125, 136}, {118, 128},
{94, 166}, {116, 140}, {108, 148}, {104, 145}, {123, 130}, {105, 146}, {112,
139}, {101, 152}, {115, 141} }>;
(II) A more general form is to represent the graph as the orbit of {50, 51}
under the group generated by the following permutations:
a: (3, 5)(4, 7)(6, 10)(9, 14)(11, 17)(13, 20)(15, 23)(16, 25)(18, 27)(19,
28)(21, 31)(22, 33)(24, 35)(26, 38)(29, 42)(30, 44)(32, 46)(34, 49)(36, 52)(37,
54)(40, 57)(41, 59)(43, 61)(45, 64)(47, 67)(48, 69)(50, 72)(51, 74)(53, 76)(55,
79)(56, 81)(58, 83)(60, 86)(62, 89)(63, 91)(65, 92)(66, 94)(68, 96)(70, 99)(71,
101)(75, 104)(77, 107)(78, 100)(80, 110)(82, 112)(84, 114)(85, 116)(87, 118)(88,
120)(90, 122)(93, 124)(95, 126)(97, 127)(98, 129)(105, 133)(106, 135)(108,
137)(109, 139)(111, 141)(113, 136)(115, 138)(117, 140)(121, 145)(123, 132)(125,
149)(128, 151)(130, 153)(134, 155)(142, 154)(143, 160)(144, 158)(146, 150)(147,
163)(148, 164)(152, 166)(156, 170)(157, 172)(159, 167)(161, 165)(162, 176)(168,
179)(169, 180)(171, 175)(173, 178)(174, 177) (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, 3)(4, 6)(5, 8)(7, 11)(9, 13)(10, 15)(12, 18)(14, 21)(16, 24)(17, 23)(20,
29)(22, 32)(25, 36)(26, 37)(27, 39)(28, 40)(30, 43)(31, 42)(33, 47)(34, 48)(35,
50)(38, 55)(41, 58)(44, 62)(45, 63)(46, 65)(49, 70)(51, 73)(52, 72)(53, 75)(54,
77)(56, 80)(59, 84)(60, 85)(61, 87)(66, 93)(67, 92)(68, 95)(69, 97)(71, 100)(74,
103)(76, 105)(78, 108)(79, 107)(81, 96)(82, 111)(83, 113)(86, 117)(88, 119)(89,
118)(90, 121)(94, 125)(98, 128)(99, 127)(101, 130)(102, 120)(104, 132)(106,
134)(109, 138)(110, 126)(112, 142)(114, 136)(115, 143)(116, 144)(122, 146)(123,
133)(124, 147)(135, 156)(137, 153)(139, 157)(140, 158)(141, 159)(145, 161)(149,
163)(150, 165)(154, 167)(155, 168)(160, 172)(162, 175)(164, 166)(169, 177)(170,
179)(171, 174)(173, 178)(176, 180)
c: (1, 2)(3, 4)(5, 7)(6, 9)(8, 12)(10, 14)(11, 16)(13, 19)(15, 22)(17, 25)(18,
26)(20, 28)(21, 30)(23, 33)(24, 34)(27, 38)(29, 41)(31, 44)(32, 45)(35, 49)(36,
51)(37, 53)(40, 56)(42, 59)(43, 60)(46, 64)(47, 66)(48, 68)(50, 71)(52, 74)(54,
76)(55, 78)(57, 81)(58, 82)(61, 86)(62, 88)(63, 90)(65, 92)(67, 94)(69, 96)(70,
98)(72, 101)(73, 102)(75, 95)(77, 106)(79, 100)(80, 109)(83, 112)(85, 115)(87,
105)(89, 120)(91, 122)(93, 123)(97, 127)(99, 129)(103, 131)(104, 126)(107,
135)(108, 136)(110, 139)(111, 140)(113, 137)(116, 138)(117, 141)(118, 133)(121,
143)(124, 132)(125, 148)(128, 150)(130, 152)(134, 154)(142, 155)(144, 158)(145,
160)(146, 151)(147, 162)(149, 164)(153, 166)(156, 169)(157, 171)(159, 173)(161,
174)(163, 176)(165, 177)(167, 178)(168, 179)(170, 180)(172, 175)
C4[ 180, 42 ]
180
-1 2 3 5 8
-2 1 12 4 7
-3 11 1 6 18
-4 2 26 16 9
-5 1 27 17 10
-6 13 24 3 37
-7 2 14 25 38
-8 1 23 15 39
-9 34 4 19 53
-10 35 5 20 54
-11 55 3 36 21
-12 22 33 2 39
-13 48 6 19 75
-14 49 28 7 76
-15 77 50 29 8
-16 78 4 51 30
-17 79 5 52 31
-18 3 47 27 32
-19 13 68 95 9
-20 69 104 28 10
-21 11 70 105 40
-22 12 71 106 41
-23 72 8 107 42
-24 6 73 108 43
-25 44 100 7 74
-26 66 45 4 38
-27 67 46 5 18
-28 14 126 96 20
-29 132 15 40 97
-30 56 16 87 98
-31 99 133 57 17
-32 100 134 58 18
-33 12 101 135 59
-34 102 136 60 9
-35 137 61 73 10
-36 11 103 71 62
-37 55 93 6 63
-38 26 94 7 64
-39 12 92 8 65
-40 110 81 29 21
-41 22 56 124 127
-42 23 57 123 127
-43 24 80 61 128
-44 25 81 118 129
-45 154 79 26 82
-46 78 155 27 83
-47 156 18 84 130
-48 13 114 85 120
-49 14 102 113 86
-50 15 51 87 153
-51 88 16 50 131
-52 89 101 103 17
-53 78 90 123 9
-54 79 91 124 10
-55 11 37 125 64
-56 57 139 30 41
-57 56 80 31 42
-58 99 80 147 32
-59 33 81 93 97
-60 34 150 86 109
-61 110 35 151 43
-62 89 36 96 129
-63 111 167 37 107
-64 55 112 38 142
-65 113 168 39 108
-66 26 169 84 152
-67 114 27 170 153
-68 89 114 115 19
-69 88 116 84 20
-70 83 117 21 120
-71 22 166 36 105
-72 23 74 118 130
-73 24 35 119 131
-74 25 72 120 131
-75 121 133 13 108
-76 132 100 122 14
-77 91 15 147 107
-78 46 16 148 53
-79 45 17 149 54
-80 57 58 157 43
-81 44 59 40 109
-82 45 129 162 109
-83 110 46 70 163
-84 66 47 69 96
-85 165 48 138 117
-86 146 49 60 139
-87 126 50 30 151
-88 99 69 51 120
-89 68 62 52 98
-90 178 135 140 53
-91 77 159 141 54
-92 179 136 137 39
-93 177 37 59 152
-94 166 114 180 38
-95 143 136 19 118
-96 28 138 62 84
-97 144 59 29 119
-98 89 112 30 141
-99 88 58 140 31
-100 25 32 76 164
-101 33 133 52 152
-102 34 103 49 119
-103 36 102 52 131
-104 145 137 105 20
-105 146 71 104 21
-106 22 122 135 162
-107 77 23 63 163
-108 24 148 75 65
-109 81 60 82 171
-110 61 83 40 172
-111 138 63 129 175
-112 176 139 64 98
-113 49 126 149 65
-114 67 68 48 94
-115 177 68 116 141
-116 69 115 161 140
-117 122 157 70 85
-118 44 72 95 128
-119 102 127 73 97
-120 88 48 70 74
-121 156 158 173 75
-122 106 117 173 76
-123 165 42 53 130
-124 166 41 174 54
-125 55 176 136 164
-126 113 28 160 87
-127 158 41 42 119
-128 159 118 43 142
-129 44 111 82 62
-130 123 47 72 152
-131 103 51 73 74
-132 29 161 76 153
-133 101 150 31 75
-134 156 146 32 175
-135 33 176 90 106
-136 34 92 125 95
-137 35 92 104 164
-138 111 85 96 174
-139 56 112 86 175
-140 99 90 116 172
-141 91 115 171 98
-142 157 180 128 64
-143 144 169 159 95
-144 143 145 158 97
-145 144 178 104 170
-146 134 178 105 86
-147 77 58 171 164
-148 78 149 108 163
-149 79 113 148 162
-150 133 155 60 173
-151 154 167 61 87
-152 66 101 93 130
-153 132 67 166 50
-154 45 169 172 151
-155 46 170 171 150
-156 121 134 47 180
-157 80 117 162 142
-158 121 144 127 160
-159 143 91 128 174
-160 167 158 180 126
-161 132 179 116 173
-162 157 82 149 106
-163 148 83 107 175
-164 100 125 147 137
-165 123 178 168 85
-166 124 71 94 153
-167 177 160 63 151
-168 165 179 174 65
-169 66 143 154 170
-170 67 155 145 169
-171 155 147 141 109
-172 110 154 176 140
-173 121 122 150 161
-174 124 168 159 138
-175 111 134 139 163
-176 112 135 125 172
-177 167 179 93 115
-178 165 90 145 146
-179 177 168 92 161
-180 156 94 160 142
0