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