Graph forms
for C4 [ 216, 25 ] =
PL(WH_36(9,1,6,19),[4^27,18^6])
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On this page are computer-accessible forms for the graph C4[ 216, 25 ] =
PL(WH_36(9,1,6,19),[4^27,18^6]).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {107, 109}, {98, 109}, {108, 126}, {103, 114}, {105, 126}, {95,
126}, {83, 113}, {89, 127}, {80, 119}, {81, 121}, {85, 127}, {66, 111}, {93,
114}, {68, 116}, {69, 117}, {71, 118}, {91, 111}, {86, 111}, {87, 109}, {48,
112}, {63, 127}, {53, 119}, {61, 121}, {63, 119}, {57, 112}, {52, 127}, {60,
119}, {54, 122}, {55, 123}, {35, 110}, {62, 113}, {32, 113}, {45, 124}, {33,
114}, {32, 116}, {34, 118}, {46, 123}, {41, 116}, {51, 110}, {50, 111}, {43,
118}, {28, 124}, {24, 121}, {26, 123}, {25, 122}, {11, 110}, {29, 123}, {20,
126}, {16, 124}, {28, 112}, {26, 118}, {24, 116}, {19, 125}, {21, 122}, {31,
112}, {23, 120}, {2, 115}, {12, 125}, {1, 115}, {10, 120}, {8, 122}, {4, 113},
{9, 124}, {6, 115}, {4, 115}, {1, 121}, {5, 125}, {15, 117}, {3, 120}, {18,
110}, {8, 117}, {3, 125}, {12, 114}, {11, 117}, {7, 120}, {18, 109}, {19, 147},
{49, 177}, {28, 156}, {47, 174}, {67, 194}, {68, 197}, {78, 207}, {42, 168},
{76, 206}, {18, 145}, {65, 194}, {9, 141}, {38, 162}, {37, 161}, {22, 147}, {42,
175}, {62, 187}, {13, 139}, {82, 212}, {52, 178}, {14, 137}, {32, 167}, {27,
156}, {69, 194}, {71, 192}, {73, 206}, {31, 151}, {92, 212}, {89, 209}, {72,
192}, {55, 190}, {59, 178}, {57, 179}, {58, 176}, {51, 184}, {50, 190}, {77,
193}, {16, 157}, {88, 213}, {48, 189}, {36, 169}, {26, 151}, {24, 149}, {20,
153}, {7, 137}, {95, 209}, {35, 173}, {15, 129}, {54, 185}, {1, 145}, {39, 183},
{33, 177}, {12, 157}, {22, 135}, {61, 172}, {66, 211}, {70, 215}, {73, 216},
{80, 193}, {17, 131}, {2, 145}, {87, 196}, {30, 141}, {6, 146}, {44, 184}, {27,
143}, {13, 153}, {9, 157}, {62, 170}, {7, 146}, {93, 200}, {87, 194}, {51, 166},
{67, 214}, {56, 174}, {51, 164}, {92, 203}, {70, 209}, {37, 189}, {47, 183},
{74, 210}, {15, 150}, {81, 200}, {4, 158}, {11, 145}, {5, 158}, {85, 206}, {35,
184}, {22, 141}, {72, 211}, {75, 208}, {14, 146}, {41, 181}, {40, 180}, {58,
166}, {3, 158}, {88, 197}, {52, 169}, {46, 179}, {79, 210}, {81, 204}, {8, 150},
{40, 182}, {55, 169}, {27, 132}, {20, 180}, {39, 135}, {10, 171}, {9, 171},
{105, 203}, {49, 147}, {31, 189}, {23, 180}, {99, 192}, {47, 140}, {55, 148},
{48, 148}, {50, 150}, {21, 176}, {96, 197}, {57, 156}, {16, 183}, {108, 203},
{97, 198}, {38, 129}, {17, 182}, {56, 159}, {63, 152}, {33, 137}, {44, 132},
{97, 200}, {101, 204}, {7, 172}, {43, 128}, {42, 129}, {40, 131}, {20, 191},
{60, 151}, {53, 153}, {106, 198}, {29, 176}, {102, 203}, {53, 152}, {1, 175},
{36, 138}, {11, 165}, {3, 172}, {37, 138}, {30, 174}, {44, 156}, {13, 191}, {45,
159}, {5, 182}, {48, 131}, {26, 169}, {34, 150}, {39, 147}, {27, 174}, {25,
175}, {98, 212}, {59, 141}, {2, 181}, {24, 175}, {21, 162}, {56, 143}, {8, 176},
{49, 137}, {14, 182}, {6, 191}, {17, 171}, {58, 128}, {4, 191}, {33, 157}, {43,
151}, {41, 149}, {37, 153}, {22, 171}, {56, 133}, {32, 158}, {57, 135}, {53,
138}, {10, 202}, {100, 164}, {91, 155}, {15, 207}, {14, 204}, {87, 149}, {6,
197}, {105, 170}, {102, 165}, {99, 160}, {96, 163}, {73, 138}, {79, 140}, {80,
148}, {100, 160}, {94, 154}, {93, 152}, {17, 215}, {103, 161}, {30, 216}, {66,
132}, {64, 136}, {96, 168}, {5, 204}, {25, 211}, {75, 129}, {77, 135}, {12,
199}, {106, 161}, {104, 163}, {29, 214}, {71, 140}, {25, 213}, {67, 143}, {72,
132}, {76, 128}, {70, 139}, {64, 142}, {94, 144}, {65, 143}, {78, 128}, {74,
133}, {108, 163}, {84, 155}, {69, 149}, {108, 188}, {101, 181}, {82, 130}, {21,
196}, {107, 186}, {2, 208}, {77, 159}, {80, 131}, {19, 199}, {104, 188}, {92,
136}, {90, 142}, {29, 201}, {19, 198}, {94, 139}, {31, 202}, {28, 201}, {74,
159}, {18, 196}, {88, 142}, {68, 146}, {76, 148}, {66, 155}, {13, 215}, {99,
185}, {86, 140}, {23, 205}, {64, 155}, {103, 188}, {84, 136}, {102, 186}, {90,
134}, {10, 215}, {30, 195}, {23, 202}, {16, 205}, {91, 133}, {100, 187}, {101,
186}, {69, 165}, {102, 134}, {34, 195}, {93, 188}, {46, 207}, {70, 167}, {34,
192}, {100, 134}, {91, 185}, {38, 196}, {36, 199}, {104, 139}, {54, 213}, {68,
167}, {75, 168}, {45, 201}, {89, 189}, {85, 177}, {40, 205}, {103, 130}, {43,
206}, {65, 164}, {71, 162}, {54, 208}, {99, 133}, {65, 166}, {101, 130}, {85,
178}, {82, 181}, {72, 160}, {106, 130}, {86, 190}, {83, 187}, {78, 166}, {38,
207}, {59, 210}, {61, 212}, {39, 205}, {98, 136}, {62, 213}, {95, 180}, {81,
186}, {45, 193}, {64, 173}, {107, 134}, {63, 209}, {96, 142}, {67, 173}, {84,
187}, {83, 163}, {84, 164}, {50, 195}, {107, 154}, {97, 144}, {74, 184}, {104,
154}, {88, 170}, {75, 185}, {76, 190}, {52, 199}, {58, 201}, {86, 162}, {94,
170}, {35, 214}, {61, 200}, {60, 202}, {47, 216}, {90, 173}, {49, 198}, {46,
214}, {98, 154}, {95, 167}, {89, 161}, {59, 195}, {73, 177}, {79, 183}, {41,
208}, {105, 144}, {97, 152}, {92, 165}, {42, 211}, {90, 160}, {106, 144}, {83,
168}, {36, 216}, {60, 193}, {78, 179}, {79, 178}, {44, 210}, {82, 172}, {77,
179} }>;
(II) A more general form is to represent the graph as the orbit of {107, 109}
under the group generated by the following permutations:
a: (1, 3, 24, 5)(2, 7, 41, 14)(4, 61, 32, 81)(6, 82, 68, 101)(8, 9)(10, 69, 17,
11)(12, 25)(13, 92, 70, 102)(15, 22)(16, 21)(18, 23, 87, 40)(19, 42)(20, 98, 95,
107)(26, 27, 55, 44)(28, 29)(30, 50, 59, 34)(31, 67, 48, 35)(33, 54)(36, 66, 52,
72)(37, 64, 89, 90)(38, 39)(43, 56, 76, 74)(45, 58)(46, 57)(47, 86, 79, 71)(49,
75)(51, 60, 65, 80)(53, 84, 63, 100)(62, 93)(73, 91, 85, 99)(77, 78)(83, 97)(88,
103)(94, 108)(96, 106)(104, 105)(109, 180)(110, 202, 194, 131)(111, 178, 192,
216)(112, 214)(113, 200)(114, 213)(115, 172, 116, 204)(117, 171)(118, 174, 190,
210)(119, 164)(120, 149, 182, 145)(121, 158)(122, 157)(123, 156)(124, 176)(125,
175)(126, 154)(127, 160, 138, 155)(128, 159)(129, 147)(130, 197)(132, 169)(133,
206)(134, 153, 136, 209)(135, 207)(137, 208)(139, 203)(141, 150)(142, 161)(143,
148, 184, 151)(144, 163)(146, 181)(152, 187)(162, 183)(165, 215)(166, 193)(167,
186, 191, 212)(168, 198)(170, 188)(173, 189)(177, 185)(196, 205)(199, 211) (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: (8, 21)(9, 16)(10, 23)(11, 18)(13, 20)(15, 38)(17, 40)(22, 39)(30, 47)(34,
71)(50, 86)(59, 79)(69, 87)(70, 95)(92, 98)(94, 105)(102, 107)(104, 108)(109,
165)(117, 196)(126, 139)(140, 195)(141, 183)(150, 162)(154, 203)(171, 205)(180,
215)
c: (2, 24)(3, 8)(4, 25)(5, 21)(6, 42)(7, 15)(9, 26)(10, 34)(11, 61)(12, 29)(13,
72)(14, 38)(16, 55)(17, 71)(18, 81)(19, 58)(20, 66)(22, 43)(23, 50)(27, 37)(28,
36)(30, 31)(32, 54)(33, 46)(35, 93)(39, 76)(40, 86)(44, 53)(45, 52)(47, 48)(49,
78)(51, 97)(56, 89)(57, 73)(59, 60)(63, 74)(64, 108)(65, 106)(67, 103)(68,
75)(69, 82)(70, 99)(77, 85)(79, 80)(83, 88)(84, 105)(87, 101)(90, 104)(91,
95)(94, 100)(98, 102)(109, 186)(110, 200)(111, 180)(112, 216)(113, 213)(114,
214)(115, 175)(116, 208)(117, 172)(118, 171)(119, 210)(120, 150)(121, 145)(122,
158)(123, 157)(124, 169)(125, 176)(126, 155)(127, 159)(128, 147)(129, 146)(130,
194)(131, 140)(132, 153)(133, 209)(134, 154)(135, 206)(136, 203)(137, 207)(138,
156)(139, 160)(141, 151)(142, 163)(143, 161)(144, 164)(148, 183)(149, 181)(152,
184)(162, 182)(165, 212)(166, 198)(167, 185)(168, 197)(170, 187)(173, 188)(174,
189)(177, 179)(178, 193)(190, 205)(191, 211)(192, 215)(195, 202)(196, 204)(199,
201)
d: (3, 7)(4, 6)(5, 14)(12, 33)(19, 49)(26, 43)(29, 58)(32, 68)(35, 51)(36,
73)(46, 78)(52, 85)(55, 76)(62, 88)(64, 84)(65, 67)(83, 96)(90, 100)(113,
197)(123, 128)(125, 137)(142, 187)(146, 158)(164, 173)(166, 214)(169, 206)(177,
199)
e: (1, 4)(2, 6)(3, 25)(5, 42)(7, 54)(8, 10)(9, 34)(11, 13)(12, 72)(14, 75)(15,
17)(16, 71)(18, 20)(19, 66)(21, 23)(22, 50)(24, 32)(26, 28)(27, 52)(29, 31)(30,
59)(33, 99)(35, 37)(36, 44)(38, 40)(39, 86)(41, 68)(43, 45)(46, 48)(47, 79)(49,
91)(51, 53)(55, 57)(56, 85)(58, 60)(61, 62)(63, 65)(64, 106)(67, 89)(69, 70)(73,
74)(76, 77)(78, 80)(81, 83)(82, 88)(84, 97)(87, 95)(90, 103)(92, 94)(93,
100)(96, 101)(98, 105)(102, 104)(107, 108)(109, 126)(110, 153)(111, 147)(112,
123)(113, 121)(114, 160)(117, 215)(118, 124)(119, 166)(120, 122)(125, 211)(127,
143)(128, 193)(129, 182)(130, 142)(131, 207)(132, 199)(133, 177)(134, 188)(135,
190)(136, 144)(137, 185)(138, 184)(139, 165)(140, 183)(141, 195)(145, 191)(146,
208)(148, 179)(149, 167)(150, 171)(151, 201)(152, 164)(154, 203)(155, 198)(156,
169)(157, 192)(158, 175)(159, 206)(161, 173)(162, 205)(163, 186)(168, 204)(170,
212)(172, 213)(174, 178)(176, 202)(180, 196)(181, 197)(187, 200)(189, 214)(194,
209)(210, 216)
f: (3, 5)(7, 14)(10, 17)(23, 40)(26, 55)(31, 48)(34, 50)(43, 76)(60, 80)(61,
81)(64, 90)(66, 72)(71, 86)(82, 101)(84, 100)(91, 99)(92, 102)(98, 107)(111,
192)(118, 190)(120, 182)(131, 202)(134, 136)(148, 151)(155, 160)(172, 204)(186,
212)
g: (2, 24)(4, 61)(5, 7)(6, 81)(8, 15, 38, 21)(9, 22, 39, 16)(10, 19, 23, 12)(11,
42, 18, 25)(13, 97, 20, 93)(17, 49, 40, 33)(27, 74)(28, 59, 57, 79)(29, 34, 46,
71)(30, 77, 47, 45)(31, 52)(32, 82)(35, 72)(36, 60)(37, 63)(43, 55)(48, 85)(50,
78, 86, 58)(51, 66)(54, 69, 75, 87)(62, 92, 83, 98)(64, 100)(65, 91)(67, 99)(68,
101)(70, 106, 95, 103)(73, 80)(88, 102, 96, 107)(94, 105, 108, 104)(109, 213,
165, 168)(110, 211)(111, 166)(112, 178)(113, 212)(114, 215, 198, 180)(115,
121)(116, 181)(117, 129, 196, 122)(118, 123)(119, 138)(120, 125)(124, 141, 135,
183)(126, 188, 139, 144)(127, 189)(128, 190)(130, 167)(131, 177)(132, 184)(133,
143)(134, 142)(136, 187)(137, 182)(140, 201, 195, 179)(145, 175)(146, 204)(147,
205, 157, 171)(148, 206)(149, 208)(150, 207, 162, 176)(151, 169)(152, 153)(154,
170, 203, 163)(155, 164)(156, 210)(158, 172)(159, 174)(160, 173)(161, 209)(185,
194)(186, 197)(191, 200)(192, 214)(193, 216)(199, 202)
h: (1, 2)(3, 8)(4, 11)(5, 15)(6, 18)(7, 21)(9, 26)(10, 29)(12, 34)(13, 35)(14,
38)(16, 43)(17, 46)(19, 50)(20, 51)(22, 55)(23, 58)(24, 41)(25, 82)(27, 89)(28,
31)(30, 52)(32, 69)(33, 71)(36, 59)(37, 44)(39, 76)(40, 78)(42, 101)(45, 60)(47,
85)(48, 57)(49, 86)(53, 74)(54, 61)(56, 63)(62, 92)(64, 94)(65, 95)(66, 106)(67,
70)(68, 87)(72, 103)(73, 79)(75, 81)(77, 80)(83, 102)(84, 105)(88, 98)(90,
104)(91, 97)(93, 99)(96, 107)(100, 108)(109, 197)(110, 191)(111, 198)(113,
165)(114, 192)(115, 145)(116, 149)(117, 158)(118, 157)(119, 159)(120, 176)(121,
208)(122, 172)(123, 171)(124, 151)(125, 150)(126, 164)(127, 174)(128, 205)(129,
204)(130, 211)(131, 179)(132, 161)(133, 152)(134, 163)(135, 148)(136, 170)(137,
162)(138, 210)(139, 173)(140, 177)(141, 169)(142, 154)(143, 209)(144, 155)(146,
196)(147, 190)(153, 184)(156, 189)(160, 188)(166, 180)(167, 194)(168, 186)(175,
181)(178, 216)(182, 207)(183, 206)(185, 200)(187, 203)(195, 199)(201, 202)(212,
213)(214, 215)
C4[ 216, 25 ]
216
-1 121 145 115 175
-2 145 115 181 208
-3 125 158 172 120
-4 113 158 191 115
-5 125 158 182 204
-6 146 191 115 197
-7 146 137 172 120
-8 176 122 117 150
-9 124 157 171 141
-10 202 171 215 120
-11 110 165 145 117
-12 199 157 114 125
-13 191 215 139 153
-14 146 137 182 204
-15 117 150 129 207
-16 124 157 183 205
-17 171 182 215 131
-18 110 145 196 109
-19 198 199 125 147
-20 180 191 126 153
-21 176 122 162 196
-22 135 147 171 141
-23 180 202 205 120
-24 121 116 149 175
-25 122 211 213 175
-26 123 169 118 151
-27 132 143 156 174
-28 112 156 124 201
-29 176 123 201 214
-30 216 195 141 174
-31 112 189 202 151
-32 167 113 158 116
-33 177 157 114 137
-34 192 150 118 195
-35 110 214 173 184
-36 199 169 138 216
-37 189 138 161 153
-38 129 162 196 207
-39 135 147 183 205
-40 180 182 205 131
-41 181 116 149 208
-42 211 168 129 175
-43 128 118 151 206
-44 132 210 156 184
-45 124 201 159 193
-46 123 179 214 207
-47 183 216 140 174
-48 112 189 148 131
-49 198 177 147 137
-50 111 190 150 195
-51 110 166 184 164
-52 199 178 169 127
-53 138 119 152 153
-54 122 213 185 208
-55 123 190 169 148
-56 143 133 159 174
-57 112 156 135 179
-58 176 166 201 128
-59 210 178 195 141
-60 202 193 151 119
-61 121 200 212 172
-62 187 113 213 170
-63 209 127 119 152
-64 155 136 173 142
-65 143 166 194 164
-66 132 111 155 211
-67 143 214 194 173
-68 167 146 116 197
-69 165 149 117 194
-70 209 167 215 139
-71 192 118 140 162
-72 132 211 192 160
-73 177 138 216 206
-74 133 210 159 184
-75 168 129 185 208
-76 190 148 128 206
-77 135 179 159 193
-78 166 179 128 207
-79 210 178 183 140
-80 148 193 119 131
-81 121 200 204 186
-82 212 181 172 130
-83 187 113 168 163
-84 187 155 136 164
-85 177 178 127 206
-86 111 190 140 162
-87 149 194 196 109
-88 213 170 142 197
-89 209 189 127 161
-90 134 160 173 142
-91 111 133 155 185
-92 165 212 136 203
-93 188 200 114 152
-94 154 144 170 139
-95 209 167 180 126
-96 168 163 142 197
-97 198 144 200 152
-98 154 212 136 109
-99 133 192 160 185
-100 187 134 160 164
-101 181 204 130 186
-102 165 134 203 186
-103 188 114 161 130
-104 154 188 139 163
-105 144 126 170 203
-106 198 144 161 130
-107 154 134 109 186
-108 188 126 203 163
-109 18 107 87 98
-110 11 35 18 51
-111 66 91 50 86
-112 57 48 28 31
-113 4 83 62 32
-114 33 12 103 93
-115 1 2 4 6
-116 24 68 41 32
-117 11 69 15 8
-118 34 26 71 43
-119 80 60 63 53
-120 23 3 7 10
-121 1 24 81 61
-122 25 8 21 54
-123 55 46 26 29
-124 45 16 28 9
-125 12 3 5 19
-126 105 95 20 108
-127 89 52 63 85
-128 78 58 43 76
-129 15 38 42 75
-130 101 103 82 106
-131 80 48 17 40
-132 44 66 27 72
-133 99 56 91 74
-134 100 90 102 107
-135 22 77 57 39
-136 92 84 64 98
-137 33 14 49 7
-138 36 37 73 53
-139 13 70 104 94
-140 79 47 71 86
-141 22 59 30 9
-142 88 90 96 64
-143 56 67 27 65
-144 94 105 106 97
-145 11 1 2 18
-146 68 14 6 7
-147 22 49 39 19
-148 55 80 48 76
-149 24 69 41 87
-150 34 15 50 8
-151 26 60 31 43
-152 93 63 53 97
-153 13 37 20 53
-154 104 94 107 98
-155 66 91 84 64
-156 44 57 27 28
-157 33 12 16 9
-158 3 4 5 32
-159 77 45 56 74
-160 99 100 90 72
-161 89 37 103 106
-162 38 71 86 21
-163 104 83 96 108
-164 100 51 84 65
-165 11 69 102 92
-166 78 58 51 65
-167 68 70 95 32
-168 83 96 42 75
-169 55 36 26 52
-170 88 94 105 62
-171 22 17 9 10
-172 3 82 61 7
-173 67 35 90 64
-174 56 47 27 30
-175 1 24 25 42
-176 58 29 8 21
-177 33 49 73 85
-178 79 59 52 85
-179 77 78 46 57
-180 23 40 95 20
-181 2 101 82 41
-182 14 5 17 40
-183 79 47 16 39
-184 44 35 51 74
-185 99 91 75 54
-186 101 102 81 107
-187 100 83 62 84
-188 103 93 104 108
-189 89 37 48 31
-190 55 50 86 76
-191 13 4 6 20
-192 99 34 71 72
-193 77 45 80 60
-194 67 69 65 87
-195 34 59 50 30
-196 38 18 21 87
-197 88 68 6 96
-198 49 106 19 97
-199 12 36 19 52
-200 81 93 61 97
-201 45 58 28 29
-202 23 60 31 10
-203 102 92 105 108
-204 101 14 81 5
-205 23 16 39 40
-206 73 85 43 76
-207 78 46 15 38
-208 2 41 75 54
-209 89 70 95 63
-210 44 79 59 74
-211 66 25 72 42
-212 92 82 61 98
-213 88 25 62 54
-214 67 35 46 29
-215 13 70 17 10
-216 36 47 73 30
0