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