Graph forms
for C4 [ 216, 85 ] =
PL(CS(AMC(3,3,[0.1:2.2])[6^9],1))
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On this page are computer-accessible forms for the graph C4[ 216, 85 ] =
PL(CS(AMC(3,3,[0.1:2.2])[6^9],1)).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {108, 109}, {107, 109}, {107, 120}, {108, 120}, {96, 117}, {96,
118}, {106, 114}, {101, 124}, {106, 115}, {102, 124}, {105, 115}, {105, 114},
{102, 123}, {101, 123}, {91, 121}, {90, 126}, {90, 127}, {92, 121}, {89, 127},
{89, 126}, {95, 118}, {95, 117}, {93, 112}, {94, 112}, {65, 113}, {66, 114},
{94, 111}, {93, 111}, {65, 114}, {66, 113}, {68, 119}, {67, 119}, {67, 120},
{68, 120}, {52, 116}, {52, 117}, {57, 125}, {58, 126}, {62, 122}, {62, 123},
{51, 117}, {61, 123}, {51, 116}, {57, 126}, {58, 125}, {61, 122}, {50, 110},
{50, 111}, {49, 111}, {49, 110}, {1, 109}, {2, 110}, {1, 110}, {2, 109}, {3,
115}, {7, 119}, {4, 116}, {7, 118}, {5, 113}, {9, 125}, {5, 112}, {9, 124}, {6,
112}, {10, 124}, {3, 116}, {10, 125}, {6, 113}, {4, 115}, {2, 122}, {3, 122},
{3, 121}, {2, 121}, {4, 127}, {1, 127}, {8, 118}, {8, 119}, {6, 134}, {88, 216},
{46, 174}, {45, 173}, {21, 149}, {1, 128}, {77, 204}, {21, 148}, {7, 134}, {7,
133}, {24, 154}, {22, 148}, {12, 142}, {11, 137}, {10, 136}, {6, 133}, {48,
179}, {46, 173}, {45, 174}, {43, 168}, {24, 155}, {22, 149}, {12, 143}, {11,
136}, {10, 137}, {8, 139}, {4, 128}, {87, 211}, {86, 210}, {48, 180}, {44, 168},
{8, 140}, {75, 207}, {74, 207}, {87, 210}, {86, 211}, {9, 143}, {9, 142}, {16,
151}, {56, 191}, {11, 131}, {79, 199}, {78, 198}, {42, 162}, {41, 161}, {16,
152}, {5, 140}, {79, 198}, {78, 199}, {11, 130}, {53, 191}, {41, 162}, {44,
167}, {42, 161}, {23, 155}, {77, 193}, {43, 167}, {54, 186}, {23, 154}, {85,
216}, {55, 186}, {5, 139}, {12, 130}, {55, 185}, {12, 131}, {54, 185}, {14,
158}, {89, 201}, {39, 183}, {38, 182}, {15, 158}, {80, 193}, {39, 182}, {38,
183}, {15, 157}, {14, 157}, {89, 202}, {40, 188}, {40, 189}, {92, 201}, {88,
205}, {92, 202}, {15, 152}, {15, 151}, {91, 195}, {85, 205}, {37, 189}, {61,
165}, {37, 188}, {90, 195}, {61, 164}, {76, 213}, {74, 208}, {76, 214}, {47,
180}, {75, 208}, {13, 145}, {80, 204}, {47, 179}, {14, 146}, {73, 213}, {93,
192}, {32, 190}, {90, 196}, {13, 146}, {91, 196}, {32, 191}, {14, 145}, {73,
214}, {27, 187}, {96, 192}, {31, 191}, {28, 188}, {62, 158}, {63, 159}, {17,
176}, {31, 190}, {62, 159}, {63, 158}, {20, 176}, {29, 185}, {29, 184}, {21,
179}, {30, 184}, {21, 178}, {30, 185}, {28, 187}, {27, 188}, {13, 164}, {24,
178}, {24, 179}, {25, 181}, {26, 182}, {13, 163}, {25, 182}, {26, 181}, {17,
161}, {40, 152}, {54, 134}, {17, 160}, {40, 153}, {54, 135}, {18, 160}, {20,
166}, {53, 135}, {16, 163}, {20, 167}, {18, 161}, {53, 134}, {16, 164}, {38,
146}, {19, 167}, {56, 140}, {19, 166}, {38, 147}, {56, 141}, {37, 147}, {37,
146}, {18, 170}, {59, 131}, {60, 132}, {19, 170}, {19, 169}, {23, 173}, {22,
172}, {55, 141}, {18, 169}, {23, 172}, {22, 173}, {20, 175}, {55, 140}, {17,
175}, {39, 153}, {63, 129}, {39, 152}, {59, 132}, {60, 131}, {63, 128}, {64,
128}, {64, 129}, {72, 143}, {71, 143}, {99, 171}, {29, 212}, {108, 165}, {98,
171}, {84, 157}, {80, 153}, {80, 154}, {108, 166}, {106, 160}, {107, 160}, {69,
137}, {105, 165}, {70, 138}, {29, 211}, {98, 172}, {83, 157}, {69, 138}, {105,
166}, {99, 172}, {70, 137}, {30, 206}, {97, 177}, {70, 150}, {25, 200}, {86,
135}, {31, 206}, {71, 150}, {31, 205}, {85, 135}, {71, 149}, {30, 205}, {97,
178}, {70, 149}, {72, 155}, {28, 200}, {72, 156}, {79, 154}, {100, 177}, {96,
181}, {88, 141}, {79, 153}, {100, 178}, {88, 142}, {71, 144}, {26, 194}, {92,
132}, {72, 144}, {27, 194}, {87, 142}, {77, 148}, {69, 156}, {27, 193}, {87,
141}, {78, 148}, {26, 193}, {28, 199}, {78, 147}, {85, 136}, {25, 199}, {86,
136}, {69, 155}, {77, 147}, {91, 132}, {45, 204}, {100, 133}, {57, 216}, {75,
169}, {33, 197}, {95, 187}, {94, 186}, {83, 183}, {43, 207}, {42, 206}, {60,
216}, {64, 164}, {74, 174}, {33, 196}, {103, 130}, {95, 186}, {94, 187}, {82,
183}, {43, 206}, {42, 207}, {64, 165}, {74, 175}, {76, 169}, {34, 196}, {103,
129}, {99, 133}, {45, 203}, {73, 175}, {34, 197}, {73, 174}, {35, 203}, {98,
138}, {93, 181}, {46, 198}, {58, 210}, {66, 170}, {67, 171}, {35, 202}, {104,
129}, {98, 139}, {84, 189}, {47, 198}, {59, 210}, {66, 171}, {67, 170}, {47,
197}, {104, 130}, {97, 139}, {84, 190}, {82, 184}, {59, 209}, {46, 197}, {97,
138}, {83, 184}, {58, 209}, {60, 215}, {81, 189}, {36, 202}, {57, 215}, {36,
203}, {81, 190}, {50, 194}, {103, 151}, {102, 150}, {82, 162}, {51, 195}, {65,
177}, {50, 195}, {103, 150}, {102, 151}, {82, 163}, {51, 194}, {65, 176}, {34,
208}, {81, 163}, {36, 214}, {35, 209}, {32, 211}, {99, 144}, {81, 162}, {36,
215}, {35, 208}, {34, 209}, {32, 212}, {107, 159}, {104, 156}, {101, 145}, {100,
144}, {68, 176}, {53, 192}, {106, 159}, {68, 177}, {33, 215}, {33, 214}, {44,
212}, {49, 201}, {56, 192}, {76, 180}, {44, 213}, {104, 145}, {101, 156}, {49,
200}, {48, 203}, {83, 168}, {41, 213}, {84, 168}, {52, 200}, {48, 204}, {41,
212}, {52, 201}, {75, 180} }>;
(II) A more general form is to represent the graph as the orbit of {108, 109}
under the group generated by the following permutations:
a: (1, 37, 4, 38)(2, 40, 3, 39)(5, 54, 8, 53)(6, 55, 7, 56)(9, 71)(10, 70)(11,
69)(12, 72)(13, 63)(14, 64)(15, 61)(16, 62)(17, 41, 18, 42)(19, 43, 20, 44)(21,
58, 22, 57)(23, 60, 24, 59)(25, 50, 28, 51)(26, 49, 27, 52)(29, 67, 31, 65)(30,
68, 32, 66)(33, 47, 34, 46)(35, 45, 36, 48)(73, 76, 75, 74)(77, 89)(78, 90)(79,
91)(80, 92)(81, 106, 82, 107)(83, 108, 84, 105)(85, 97, 86, 98)(87, 99, 88,
100)(93, 94, 95, 96)(101, 103)(109, 189, 115, 183)(110, 188, 116, 182)(111, 187,
117, 181)(112, 186, 118, 192)(113, 185, 119, 191)(114, 184, 120, 190)(121,
153)(122, 152)(123, 151)(124, 150)(125, 149)(126, 148)(127, 147)(128, 146)(129,
145)(130, 156)(131, 155)(132, 154)(133, 141)(134, 140)(135, 139)(136, 138)(142,
144)(157, 165)(158, 164)(159, 163)(160, 162)(166, 168)(169, 207, 175, 213)(170,
206, 176, 212)(171, 205, 177, 211)(172, 216, 178, 210)(173, 215, 179, 209)(174,
214, 180, 208)(193, 201)(194, 200)(195, 199)(196, 198)(202, 204) (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: (25, 26)(27, 28)(33, 36)(34, 35)(45, 46)(47, 48)(49, 50)(51, 52)(77, 78)(79,
80)(89, 90)(91, 92)(193, 199)(194, 200)(195, 201)(196, 202)(197, 203)(198,
204)
c: (13, 16)(14, 15)(21, 24)(22, 23)(37, 40)(38, 39)(69, 70)(71, 72)(77, 80)(78,
79)(101, 102)(103, 104)(145, 151)(146, 152)(147, 153)(148, 154)(149, 155)(150,
156)
d: (1, 5, 12, 3, 7, 10)(2, 8, 11, 4, 6, 9)(13, 20, 24)(14, 19, 21)(15, 18,
22)(16, 17, 23)(25, 30, 35, 27, 32, 33)(26, 31, 36, 28, 29, 34)(37, 44, 47, 38,
43, 48)(39, 42, 45, 40, 41, 46)(49, 55, 59, 51, 53, 57)(50, 56, 60, 52, 54,
58)(61, 68, 69, 64, 65, 72)(62, 67, 70, 63, 66, 71)(73, 79, 82, 74, 80, 81)(75,
77, 84, 76, 78, 83)(85, 89, 94, 87, 91, 96)(86, 90, 93, 88, 92, 95)(97, 104,
105, 100, 101, 108)(98, 103, 106, 99, 102, 107)(109, 139, 130, 115, 133,
124)(110, 140, 131, 116, 134, 125)(111, 141, 132, 117, 135, 126)(112, 142, 121,
118, 136, 127)(113, 143, 122, 119, 137, 128)(114, 144, 123, 120, 138, 129)(145,
166, 178)(146, 167, 179)(147, 168, 180)(148, 157, 169)(149, 158, 170)(150, 159,
171)(151, 160, 172)(152, 161, 173)(153, 162, 174)(154, 163, 175)(155, 164,
176)(156, 165, 177)(181, 205, 202, 187, 211, 196)(182, 206, 203, 188, 212,
197)(183, 207, 204, 189, 213, 198)(184, 208, 193, 190, 214, 199)(185, 209, 194,
191, 215, 200)(186, 210, 195, 192, 216, 201)
e: (1, 13)(2, 14)(3, 15)(4, 16)(5, 21, 6, 22)(7, 23, 8, 24)(9, 18, 10, 17)(11,
20, 12, 19)(25, 27)(29, 34, 30, 33)(31, 36, 32, 35)(37, 49)(38, 50)(39, 51)(40,
52)(41, 58, 42, 57)(43, 60, 44, 59)(45, 56, 48, 53)(46, 55, 47, 54)(61, 63)(65,
71, 66, 70)(67, 69, 68, 72)(73, 87, 75, 85)(74, 88, 76, 86)(77, 93)(78, 94)(79,
95)(80, 96)(81, 89)(82, 90)(83, 91)(84, 92)(97, 100, 99, 98)(101, 107)(102,
106)(103, 105)(104, 108)(109, 145)(110, 146)(111, 147)(112, 148)(113, 149)(114,
150)(115, 151)(116, 152)(117, 153)(118, 154)(119, 155)(120, 156)(121, 157)(122,
158)(123, 159)(124, 160)(125, 161)(126, 162)(127, 163)(128, 164)(129, 165)(130,
166)(131, 167)(132, 168)(133, 172, 139, 178)(134, 173, 140, 179)(135, 174, 141,
180)(136, 175, 142, 169)(137, 176, 143, 170)(138, 177, 144, 171)(181, 193)(182,
194)(183, 195)(184, 196)(185, 197)(186, 198)(187, 199)(188, 200)(189, 201)(190,
202)(191, 203)(192, 204)(205, 214, 211, 208)(206, 215, 212, 209)(207, 216, 213,
210)
f: (25, 28)(26, 27)(29, 32)(30, 31)(37, 38)(39, 40)(53, 54)(55, 56)(81, 82)(83,
84)(93, 94)(95, 96)(181, 187)(182, 188)(183, 189)(184, 190)(185, 191)(186,
192)
g: (17, 18)(19, 20)(21, 22)(23, 24)(45, 48)(46, 47)(65, 66)(67, 68)(73, 76)(74,
75)(97, 98)(99, 100)(169, 175)(170, 176)(171, 177)(172, 178)(173, 179)(174,
180)
h: (5, 6)(7, 8)(9, 10)(11, 12)(25, 28)(26, 27)(29, 32)(30, 31)(37, 38)(39,
40)(53, 55)(54, 56)(69, 72)(70, 71)(81, 82)(83, 84)(85, 88)(86, 87)(93, 94)(95,
96)(97, 100)(98, 99)(133, 139)(134, 140)(135, 141)(136, 142)(137, 143)(138,
144)(181, 187)(182, 188)(183, 189)(184, 190)(185, 191)(186, 192)
m: (13, 14)(15, 16)(17, 20)(18, 19)(41, 44)(42, 43)(61, 62)(63, 64)(81, 84)(82,
83)(105, 106)(107, 108)(157, 163)(158, 164)(159, 165)(160, 166)(161, 167)(162,
168)
n1: (1, 2)(3, 4)(9, 12)(10, 11)(57, 60)(58, 59)(61, 64)(62, 63)(89, 92)(90,
91)(101, 104)(102, 103)(121, 127)(122, 128)(123, 129)(124, 130)(125, 131)(126,
132)
a1: (2, 4)(5, 12, 6, 11)(7, 10, 8, 9)(13, 25)(14, 26)(15, 27)(16, 28)(17,
33)(18, 34)(19, 35)(20, 36)(21, 30)(22, 29)(23, 32)(24, 31)(37, 39)(41, 46)(42,
47)(43, 48)(44, 45)(49, 64)(50, 63)(51, 62)(52, 61)(53, 69, 56, 72)(54, 70, 55,
71)(57, 68)(58, 67)(59, 66)(60, 65)(74, 76)(77, 83)(78, 82)(79, 81)(80, 84)(85,
97, 88, 100)(86, 98, 87, 99)(89, 108)(90, 107)(91, 106)(92, 105)(93, 104)(94,
103)(95, 102)(96, 101)(109, 127)(110, 128)(111, 129)(112, 130)(113, 131)(114,
132)(115, 121)(116, 122)(117, 123)(118, 124)(119, 125)(120, 126)(133, 136, 139,
142)(134, 137, 140, 143)(135, 138, 141, 144)(145, 181)(146, 182)(147, 183)(148,
184)(149, 185)(150, 186)(151, 187)(152, 188)(153, 189)(154, 190)(155, 191)(156,
192)(157, 193)(158, 194)(159, 195)(160, 196)(161, 197)(162, 198)(163, 199)(164,
200)(165, 201)(166, 202)(167, 203)(168, 204)(169, 208)(170, 209)(171, 210)(172,
211)(173, 212)(174, 213)(175, 214)(176, 215)(177, 216)(178, 205)(179, 206)(180,
207)
b1: (29, 30)(31, 32)(33, 34)(35, 36)(41, 42)(43, 44)(57, 58)(59, 60)(73, 74)(75,
76)(85, 86)(87, 88)(205, 211)(206, 212)(207, 213)(208, 214)(209, 215)(210,
216)
c1: (2, 4)(5, 9)(6, 10)(7, 11)(8, 12)(13, 17)(14, 20)(15, 19)(16, 18)(21,
23)(25, 33)(26, 36)(27, 35)(28, 34)(30, 32)(37, 74)(38, 73)(39, 76)(40, 75)(41,
82)(42, 81)(43, 84)(44, 83)(45, 77)(46, 78)(47, 79)(48, 80)(49, 90)(50, 89)(51,
92)(52, 91)(53, 85)(54, 86)(55, 87)(56, 88)(57, 93)(58, 94)(59, 95)(60, 96)(61,
106)(62, 105)(63, 108)(64, 107)(65, 101)(66, 102)(67, 103)(68, 104)(69, 100)(70,
99)(71, 98)(72, 97)(109, 128)(110, 127)(111, 126)(112, 125)(113, 124)(114,
123)(115, 122)(116, 121)(117, 132)(118, 131)(119, 130)(120, 129)(133, 137)(134,
136)(138, 144)(139, 143)(140, 142)(145, 176)(146, 175)(147, 174)(148, 173)(149,
172)(150, 171)(151, 170)(152, 169)(153, 180)(154, 179)(155, 178)(156, 177)(157,
167)(158, 166)(159, 165)(160, 164)(161, 163)(181, 215)(182, 214)(183, 213)(184,
212)(185, 211)(186, 210)(187, 209)(188, 208)(189, 207)(190, 206)(191, 205)(192,
216)(193, 203)(194, 202)(195, 201)(196, 200)(197, 199)
C4[ 216, 85 ]
216
-1 110 127 128 109
-2 110 121 122 109
-3 121 122 115 116
-4 115 116 127 128
-5 112 113 139 140
-6 133 112 134 113
-7 133 134 118 119
-8 139 118 140 119
-9 143 124 125 142
-10 124 125 136 137
-11 136 137 130 131
-12 143 130 131 142
-13 145 146 163 164
-14 145 146 157 158
-15 157 158 151 152
-16 151 152 163 164
-17 176 160 161 175
-18 169 170 160 161
-19 166 167 169 170
-20 176 166 167 175
-21 178 179 148 149
-22 148 149 172 173
-23 154 155 172 173
-24 154 155 178 179
-25 199 200 181 182
-26 181 182 193 194
-27 187 188 193 194
-28 187 188 199 200
-29 211 212 184 185
-30 205 184 206 185
-31 190 191 205 206
-32 211 190 212 191
-33 214 215 196 197
-34 209 196 197 208
-35 209 202 203 208
-36 202 203 214 215
-37 188 189 146 147
-38 146 147 182 183
-39 182 183 152 153
-40 188 189 152 153
-41 212 213 161 162
-42 161 162 206 207
-43 167 168 206 207
-44 167 168 212 213
-45 203 204 173 174
-46 198 173 174 197
-47 198 179 180 197
-48 179 180 203 204
-49 110 111 200 201
-50 110 111 194 195
-51 116 117 194 195
-52 200 201 116 117
-53 134 135 191 192
-54 134 135 185 186
-55 140 141 185 186
-56 191 192 140 141
-57 125 126 215 216
-58 209 210 125 126
-59 132 209 210 131
-60 132 215 216 131
-61 165 122 123 164
-62 122 123 158 159
-63 158 159 128 129
-64 165 128 129 164
-65 176 177 113 114
-66 113 114 170 171
-67 170 171 119 120
-68 176 177 119 120
-69 155 156 137 138
-70 137 138 149 150
-71 143 144 149 150
-72 143 144 155 156
-73 213 214 174 175
-74 174 207 175 208
-75 169 180 207 208
-76 169 180 213 214
-77 147 148 193 204
-78 198 199 147 148
-79 154 198 199 153
-80 154 193 204 153
-81 189 190 162 163
-82 183 162 184 163
-83 157 168 183 184
-84 189 157 168 190
-85 135 136 205 216
-86 210 211 135 136
-87 210 211 141 142
-88 205 216 141 142
-89 201 202 126 127
-90 126 127 195 196
-91 121 132 195 196
-92 121 132 201 202
-93 111 112 181 192
-94 187 111 112 186
-95 187 117 118 186
-96 181 192 117 118
-97 177 178 138 139
-98 138 171 139 172
-99 133 144 171 172
-100 133 144 177 178
-101 123 145 156 124
-102 123 124 150 151
-103 150 129 151 130
-104 145 156 129 130
-105 165 166 114 115
-106 114 115 159 160
-107 159 160 109 120
-108 165 166 109 120
-109 1 2 107 108
-110 1 2 49 50
-111 49 93 50 94
-112 5 93 6 94
-113 66 5 6 65
-114 66 105 106 65
-115 3 4 105 106
-116 3 4 51 52
-117 51 95 52 96
-118 7 95 8 96
-119 67 68 7 8
-120 67 68 107 108
-121 2 3 91 92
-122 2 3 61 62
-123 101 102 61 62
-124 101 102 9 10
-125 57 58 9 10
-126 89 57 90 58
-127 1 89 90 4
-128 1 4 63 64
-129 103 104 63 64
-130 11 12 103 104
-131 11 12 59 60
-132 91 59 92 60
-133 99 100 6 7
-134 6 7 53 54
-135 85 53 86 54
-136 11 85 86 10
-137 11 69 70 10
-138 69 70 97 98
-139 5 8 97 98
-140 55 56 5 8
-141 55 88 56 87
-142 88 12 9 87
-143 12 71 72 9
-144 99 100 71 72
-145 13 101 14 104
-146 13 14 37 38
-147 77 78 37 38
-148 22 77 78 21
-149 22 70 71 21
-150 102 70 103 71
-151 102 15 103 16
-152 15 16 39 40
-153 79 80 39 40
-154 23 24 79 80
-155 23 24 69 72
-156 101 69 104 72
-157 14 15 83 84
-158 14 15 62 63
-159 62 106 63 107
-160 17 18 106 107
-161 17 18 41 42
-162 81 82 41 42
-163 13 81 16 82
-164 13 16 61 64
-165 61 105 64 108
-166 105 19 20 108
-167 44 19 20 43
-168 44 83 84 43
-169 18 19 75 76
-170 66 67 18 19
-171 66 99 67 98
-172 22 99 23 98
-173 22 23 45 46
-174 45 46 73 74
-175 17 73 74 20
-176 68 17 20 65
-177 100 68 97 65
-178 100 24 97 21
-179 24 47 48 21
-180 47 48 75 76
-181 25 26 93 96
-182 25 26 38 39
-183 38 82 39 83
-184 82 83 29 30
-185 55 29 30 54
-186 55 94 95 54
-187 27 28 94 95
-188 37 27 28 40
-189 37 81 40 84
-190 81 84 31 32
-191 56 31 53 32
-192 56 93 96 53
-193 77 80 26 27
-194 26 27 50 51
-195 90 91 50 51
-196 33 34 90 91
-197 33 34 46 47
-198 78 46 79 47
-199 78 79 25 28
-200 25 49 28 52
-201 89 92 49 52
-202 89 35 36 92
-203 45 35 36 48
-204 77 45 80 48
-205 88 30 85 31
-206 30 31 42 43
-207 74 42 75 43
-208 34 35 74 75
-209 34 35 58 59
-210 58 59 86 87
-211 29 86 32 87
-212 44 29 41 32
-213 44 73 41 76
-214 33 36 73 76
-215 33 57 36 60
-216 88 57 60 85
0