Graph forms
for C4 [ 216, 84 ] =
PL(CS(AMC(3,3,[0.1:2.2])[3^18],1))
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On this page are computer-accessible forms for the graph C4[ 216, 84 ] =
PL(CS(AMC(3,3,[0.1:2.2])[3^18],1)).
(I) Following is a form readable by MAGMA:
g:=Graph<216|{ {107, 120}, {108, 120}, {107, 115}, {96, 121}, {100, 127}, {99,
127}, {106, 118}, {105, 117}, {96, 126}, {105, 118}, {108, 115}, {106, 117},
{93, 124}, {95, 126}, {94, 124}, {94, 123}, {93, 123}, {95, 121}, {89, 112},
{91, 114}, {90, 112}, {92, 114}, {92, 109}, {90, 111}, {89, 111}, {91, 109},
{64, 119}, {64, 120}, {51, 114}, {51, 113}, {52, 113}, {56, 125}, {52, 114},
{56, 126}, {63, 120}, {61, 117}, {63, 119}, {55, 126}, {61, 116}, {55, 125},
{62, 116}, {62, 117}, {54, 122}, {54, 123}, {53, 123}, {53, 122}, {50, 110},
{50, 111}, {49, 111}, {49, 110}, {1, 109}, {2, 110}, {1, 110}, {2, 109}, {3,
115}, {2, 115}, {3, 113}, {4, 118}, {3, 112}, {4, 119}, {4, 112}, {8, 124}, {4,
113}, {8, 125}, {1, 119}, {2, 116}, {1, 118}, {3, 116}, {7, 127}, {6, 127}, {7,
125}, {7, 124}, {5, 121}, {6, 122}, {5, 122}, {6, 121}, {11, 139}, {10, 139},
{89, 216}, {47, 174}, {76, 205}, {11, 137}, {47, 173}, {12, 142}, {11, 136},
{12, 143}, {12, 136}, {92, 216}, {46, 170}, {16, 148}, {73, 205}, {75, 207},
{12, 137}, {46, 171}, {16, 149}, {74, 207}, {5, 131}, {45, 171}, {10, 140}, {9,
143}, {6, 128}, {5, 130}, {45, 170}, {11, 140}, {9, 142}, {7, 128}, {43, 162},
{8, 130}, {89, 211}, {43, 161}, {16, 154}, {8, 131}, {52, 191}, {16, 155}, {9,
133}, {90, 214}, {18, 158}, {17, 157}, {10, 134}, {44, 161}, {91, 214}, {44,
162}, {91, 213}, {51, 189}, {50, 188}, {49, 191}, {9, 134}, {92, 211}, {90,
213}, {51, 188}, {50, 189}, {18, 157}, {17, 158}, {10, 133}, {38, 182}, {83,
195}, {81, 193}, {39, 183}, {38, 183}, {82, 195}, {40, 185}, {39, 182}, {40,
186}, {85, 199}, {84, 198}, {88, 204}, {84, 193}, {13, 155}, {82, 196}, {14,
152}, {13, 154}, {83, 196}, {81, 198}, {15, 152}, {15, 151}, {14, 151}, {85,
204}, {15, 149}, {74, 208}, {15, 148}, {73, 210}, {75, 208}, {13, 145}, {86,
202}, {37, 185}, {14, 146}, {48, 173}, {93, 192}, {87, 202}, {48, 174}, {87,
201}, {76, 210}, {13, 146}, {88, 199}, {86, 201}, {37, 186}, {14, 145}, {27,
187}, {96, 192}, {26, 187}, {61, 156}, {27, 185}, {28, 190}, {27, 184}, {28,
191}, {28, 184}, {28, 185}, {21, 179}, {26, 188}, {25, 191}, {22, 176}, {61,
155}, {62, 152}, {63, 153}, {21, 178}, {27, 188}, {25, 190}, {23, 176}, {62,
153}, {63, 152}, {24, 178}, {24, 179}, {25, 181}, {26, 182}, {25, 182}, {26,
181}, {19, 163}, {18, 163}, {39, 150}, {59, 138}, {19, 161}, {39, 149}, {20,
166}, {59, 137}, {19, 160}, {20, 167}, {20, 160}, {42, 158}, {38, 146}, {24,
172}, {20, 161}, {42, 159}, {38, 147}, {24, 173}, {60, 137}, {17, 167}, {41,
159}, {37, 147}, {18, 164}, {60, 138}, {17, 166}, {41, 158}, {37, 146}, {19,
164}, {23, 175}, {22, 175}, {23, 173}, {23, 172}, {21, 169}, {22, 170}, {58,
134}, {40, 149}, {58, 135}, {40, 150}, {57, 135}, {21, 170}, {22, 169}, {57,
134}, {65, 129}, {67, 131}, {68, 132}, {65, 128}, {105, 168}, {82, 147}, {66,
128}, {84, 150}, {83, 145}, {81, 147}, {66, 129}, {108, 168}, {81, 148}, {84,
145}, {83, 150}, {82, 148}, {67, 132}, {68, 131}, {72, 143}, {69, 141}, {71,
143}, {69, 140}, {70, 140}, {105, 163}, {70, 141}, {100, 175}, {106, 166}, {107,
166}, {97, 175}, {107, 165}, {106, 165}, {108, 163}, {98, 178}, {100, 180}, {76,
157}, {99, 178}, {86, 135}, {85, 135}, {99, 177}, {88, 138}, {87, 133}, {98,
177}, {74, 159}, {97, 180}, {29, 203}, {30, 200}, {73, 159}, {75, 157}, {29,
202}, {31, 200}, {71, 144}, {31, 199}, {72, 144}, {30, 199}, {31, 197}, {31,
196}, {96, 187}, {64, 155}, {29, 193}, {30, 194}, {64, 156}, {85, 136}, {88,
133}, {87, 138}, {86, 136}, {29, 194}, {30, 193}, {46, 206}, {100, 132}, {98,
130}, {97, 129}, {94, 190}, {47, 207}, {46, 207}, {95, 190}, {48, 209}, {47,
206}, {57, 216}, {77, 172}, {79, 174}, {48, 210}, {95, 189}, {78, 172}, {68,
167}, {104, 139}, {98, 129}, {97, 130}, {94, 189}, {32, 196}, {60, 216}, {32,
197}, {80, 181}, {78, 171}, {65, 167}, {93, 187}, {66, 164}, {67, 165}, {77,
171}, {79, 169}, {66, 165}, {99, 132}, {67, 164}, {42, 194}, {102, 142}, {101,
141}, {43, 195}, {42, 195}, {44, 197}, {43, 194}, {65, 168}, {73, 160}, {75,
162}, {32, 202}, {80, 186}, {44, 198}, {74, 160}, {32, 203}, {102, 141}, {101,
142}, {60, 215}, {33, 205}, {103, 139}, {41, 197}, {34, 206}, {68, 168}, {57,
215}, {58, 212}, {59, 213}, {76, 162}, {33, 206}, {41, 198}, {34, 205}, {58,
213}, {59, 212}, {35, 211}, {34, 211}, {49, 192}, {69, 180}, {35, 209}, {101,
151}, {36, 214}, {35, 208}, {36, 215}, {56, 203}, {36, 208}, {104, 156}, {52,
192}, {56, 204}, {36, 209}, {33, 215}, {34, 212}, {69, 179}, {70, 176}, {71,
177}, {78, 184}, {33, 214}, {103, 144}, {79, 184}, {35, 212}, {70, 177}, {71,
176}, {77, 186}, {77, 181}, {104, 144}, {79, 183}, {53, 204}, {101, 156}, {80,
169}, {78, 183}, {72, 179}, {45, 209}, {102, 154}, {72, 180}, {103, 154}, {53,
203}, {103, 153}, {80, 174}, {54, 200}, {55, 201}, {45, 210}, {104, 151}, {102,
153}, {54, 201}, {55, 200} }>;
(II) A more general form is to represent the graph as the orbit of {107, 120}
under the group generated by the following permutations:
a: (1, 5, 3, 7)(2, 8, 4, 6)(10, 12)(13, 32)(14, 31)(15, 30)(16, 29)(17, 28)(18,
27)(19, 26)(20, 25)(21, 33)(22, 34)(23, 35)(24, 36)(37, 41)(38, 44)(39, 43)(40,
42)(45, 47)(49, 68, 52, 65)(50, 67, 51, 66)(53, 61, 56, 64)(54, 62, 55, 63)(57,
72)(58, 71)(59, 70)(60, 69)(73, 80)(74, 77)(75, 78)(76, 79)(82, 84)(85, 104)(86,
103)(87, 102)(88, 101)(89, 100, 92, 97)(90, 99, 91, 98)(93, 105, 96, 108)(94,
106, 95, 107)(109, 130, 112, 127)(110, 131, 113, 128)(111, 132, 114, 129)(115,
124, 118, 121)(116, 125, 119, 122)(117, 126, 120, 123)(133, 142)(134, 143)(135,
144)(136, 139)(137, 140)(138, 141)(145, 196)(146, 197)(147, 198)(148, 193)(149,
194)(150, 195)(151, 199)(152, 200)(153, 201)(154, 202)(155, 203)(156, 204)(157,
184)(158, 185)(159, 186)(160, 181)(161, 182)(162, 183)(163, 187)(164, 188)(165,
189)(166, 190)(167, 191)(168, 192)(169, 205)(170, 206)(171, 207)(172, 208)(173,
209)(174, 210)(175, 211)(176, 212)(177, 213)(178, 214)(179, 215)(180, 216) (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: (13, 14)(15, 16)(61, 62)(63, 64)(101, 102)(103, 104)(151, 154)(152, 155)(153,
156)
c: (21, 23)(22, 24)(45, 48)(46, 47)(69, 70)(71, 72)(77, 80)(78, 79)(97, 98)(99,
100)(169, 172)(170, 173)(171, 174)(175, 178)(176, 179)(177, 180)
d: (21, 22)(23, 24)(69, 70)(71, 72)(97, 98)(99, 100)(175, 178)(176, 179)(177,
180)
e: (5, 6)(7, 8)(65, 68)(66, 67)(97, 100)(98, 99)(127, 130)(128, 131)(129,
132)
f: (2, 4)(5, 37, 9, 73)(6, 38, 10, 74)(7, 39, 11, 75)(8, 40, 12, 76)(13, 57, 20,
95)(14, 58, 19, 96)(15, 59, 18, 93)(16, 60, 17, 94)(22, 24)(25, 103, 36, 65)(26,
104, 35, 66)(27, 101, 34, 67)(28, 102, 33, 68)(29, 30, 31, 32)(41, 53, 81,
88)(42, 54, 82, 87)(43, 55, 83, 86)(44, 56, 84, 85)(45, 98, 80, 72)(46, 99, 79,
69)(47, 100, 78, 70)(48, 97, 77, 71)(49, 63, 91, 105)(50, 64, 92, 106)(51, 61,
89, 107)(52, 62, 90, 108)(109, 118, 110, 119)(111, 120, 114, 117)(112, 115, 113,
116)(121, 146, 134, 160)(122, 147, 133, 159)(123, 148, 138, 158)(124, 149, 137,
157)(125, 150, 136, 162)(126, 145, 135, 161)(127, 183, 140, 207)(128, 182, 139,
208)(129, 181, 144, 209)(130, 186, 143, 210)(131, 185, 142, 205)(132, 184, 141,
206)(151, 212, 164, 187)(152, 213, 163, 192)(153, 214, 168, 191)(154, 215, 167,
190)(155, 216, 166, 189)(156, 211, 165, 188)(169, 179, 170, 178)(171, 177, 174,
180)(172, 176, 173, 175)(193, 199, 197, 203)(194, 200, 196, 202)(195, 201)(198,
204)
g: (33, 34)(35, 36)(57, 58)(59, 60)(89, 90)(91, 92)(211, 214)(212, 215)(213,
216)
h: (2, 4)(5, 11, 7, 9)(6, 10, 8, 12)(13, 28)(14, 27)(15, 26)(16, 25)(17, 36, 20,
33)(18, 35, 19, 34)(21, 29, 24, 32)(22, 30, 23, 31)(38, 40)(41, 45, 43, 47)(42,
48, 44, 46)(49, 64)(50, 63)(51, 62)(52, 61)(53, 69, 56, 72)(54, 70, 55, 71)(57,
68, 60, 65)(58, 67, 59, 66)(73, 76, 75, 74)(77, 82, 80, 81)(78, 83, 79, 84)(85,
100, 88, 97)(86, 99, 87, 98)(89, 108)(90, 107)(91, 106)(92, 105)(93, 101, 96,
104)(94, 102, 95, 103)(109, 118)(110, 119)(111, 120)(112, 115)(113, 116)(114,
117)(121, 139, 124, 142)(122, 140, 125, 143)(123, 141, 126, 144)(127, 133, 130,
136)(128, 134, 131, 137)(129, 135, 132, 138)(145, 184)(146, 185)(147, 186)(148,
181)(149, 182)(150, 183)(151, 187)(152, 188)(153, 189)(154, 190)(155, 191)(156,
192)(157, 208, 160, 205)(158, 209, 161, 206)(159, 210, 162, 207)(163, 211)(164,
212)(165, 213)(166, 214)(167, 215)(168, 216)(169, 193, 172, 196)(170, 194, 173,
197)(171, 195, 174, 198)(175, 199)(176, 200)(177, 201)(178, 202)(179, 203)(180,
204)
m: (17, 18)(19, 20)(65, 66)(67, 68)(105, 106)(107, 108)(163, 166)(164, 167)(165,
168)
n1: (25, 28)(26, 27)(37, 38)(39, 40)(77, 78)(79, 80)(181, 184)(182, 185)(183,
186)
a1: (33, 36)(34, 35)(45, 46)(47, 48)(73, 74)(75, 76)(205, 208)(206, 209)(207,
210)
b1: (13, 16)(14, 15)(25, 28)(26, 27)(37, 39)(38, 40)(77, 78)(79, 80)(81, 84)(82,
83)(145, 148)(146, 149)(147, 150)(181, 184)(182, 185)(183, 186)
c1: (5, 8)(6, 7)(29, 30)(31, 32)(53, 55)(54, 56)(85, 86)(87, 88)(93, 96)(94,
95)(121, 124)(122, 125)(123, 126)(199, 202)(200, 203)(201, 204)
d1: (29, 30)(31, 32)(53, 54)(55, 56)(85, 86)(87, 88)(199, 202)(200, 203)(201,
204)
e1: (17, 20)(18, 19)(29, 32)(30, 31)(41, 43)(42, 44)(73, 76)(74, 75)(81, 82)(83,
84)(157, 160)(158, 161)(159, 162)(193, 196)(194, 197)(195, 198)
f1: (25, 26)(27, 28)(49, 50)(51, 52)(93, 94)(95, 96)(187, 190)(188, 191)(189,
192)
g1: (9, 11)(10, 12)(57, 60)(58, 59)(69, 72)(70, 71)(85, 88)(86, 87)(101,
104)(102, 103)(133, 136)(134, 137)(135, 138)(139, 142)(140, 143)(141, 144)
h1: (29, 32)(30, 31)(41, 42)(43, 44)(81, 82)(83, 84)(193, 196)(194, 197)(195,
198)
m1: (1, 2)(3, 4)(61, 64)(62, 63)(105, 108)(106, 107)(115, 118)(116, 119)(117,
120)
n2: (9, 10)(11, 12)(69, 72)(70, 71)(101, 104)(102, 103)(139, 142)(140, 143)(141,
144)
C4[ 216, 84 ]
216
-1 110 118 119 109
-2 110 115 116 109
-3 112 113 115 116
-4 112 113 118 119
-5 121 122 130 131
-6 121 122 127 128
-7 124 125 127 128
-8 124 125 130 131
-9 143 133 134 142
-10 133 134 139 140
-11 136 137 139 140
-12 143 136 137 142
-13 154 155 145 146
-14 145 146 151 152
-15 148 149 151 152
-16 154 155 148 149
-17 166 167 157 158
-18 157 158 163 164
-19 160 161 163 164
-20 166 167 160 161
-21 178 179 169 170
-22 176 169 170 175
-23 176 172 173 175
-24 178 179 172 173
-25 190 191 181 182
-26 187 188 181 182
-27 187 188 184 185
-28 190 191 184 185
-29 202 203 193 194
-30 199 200 193 194
-31 199 200 196 197
-32 202 203 196 197
-33 214 215 205 206
-34 211 212 205 206
-35 209 211 212 208
-36 209 214 215 208
-37 146 147 185 186
-38 146 147 182 183
-39 149 182 150 183
-40 149 150 185 186
-41 198 158 159 197
-42 158 159 194 195
-43 161 194 162 195
-44 198 161 162 197
-45 209 210 170 171
-46 170 171 206 207
-47 173 206 174 207
-48 209 210 173 174
-49 110 111 191 192
-50 110 111 188 189
-51 188 189 113 114
-52 113 114 191 192
-53 122 123 203 204
-54 122 123 200 201
-55 200 201 125 126
-56 125 126 203 204
-57 134 135 215 216
-58 134 135 212 213
-59 212 213 137 138
-60 137 138 215 216
-61 155 156 116 117
-62 116 117 152 153
-63 119 152 120 153
-64 155 156 119 120
-65 167 168 128 129
-66 165 128 129 164
-67 132 165 131 164
-68 132 167 168 131
-69 179 180 140 141
-70 176 177 140 141
-71 143 176 144 177
-72 143 144 179 180
-73 210 159 160 205
-74 159 160 207 208
-75 157 162 207 208
-76 210 157 205 162
-77 181 171 172 186
-78 171 172 183 184
-79 169 183 184 174
-80 169 181 174 186
-81 198 147 148 193
-82 147 148 195 196
-83 145 150 195 196
-84 198 145 193 150
-85 199 135 136 204
-86 135 201 136 202
-87 133 201 202 138
-88 133 199 138 204
-89 111 112 211 216
-90 111 112 213 214
-91 114 213 214 109
-92 211 114 216 109
-93 187 123 124 192
-94 123 189 124 190
-95 121 189 190 126
-96 121 187 126 192
-97 180 129 130 175
-98 177 178 129 130
-99 132 177 178 127
-100 132 180 127 175
-101 156 151 141 142
-102 154 141 142 153
-103 154 144 139 153
-104 144 156 139 151
-105 168 117 118 163
-106 165 166 117 118
-107 165 166 115 120
-108 168 115 163 120
-109 1 2 91 92
-110 1 2 49 50
-111 89 90 49 50
-112 89 90 3 4
-113 3 4 51 52
-114 91 92 51 52
-115 2 3 107 108
-116 2 3 61 62
-117 61 105 62 106
-118 1 4 105 106
-119 1 4 63 64
-120 63 107 64 108
-121 5 6 95 96
-122 5 6 53 54
-123 93 94 53 54
-124 93 94 7 8
-125 55 56 7 8
-126 55 56 95 96
-127 99 100 6 7
-128 66 6 7 65
-129 66 97 65 98
-130 5 8 97 98
-131 67 68 5 8
-132 99 67 100 68
-133 88 9 10 87
-134 57 58 9 10
-135 57 58 85 86
-136 11 12 85 86
-137 11 12 59 60
-138 88 59 60 87
-139 11 103 104 10
-140 11 69 70 10
-141 101 69 102 70
-142 12 101 102 9
-143 12 71 72 9
-144 103 71 104 72
-145 13 14 83 84
-146 13 14 37 38
-147 37 81 38 82
-148 15 81 16 82
-149 15 16 39 40
-150 39 83 40 84
-151 101 14 15 104
-152 14 15 62 63
-153 102 103 62 63
-154 13 102 103 16
-155 13 16 61 64
-156 101 104 61 64
-157 17 18 75 76
-158 17 18 41 42
-159 73 41 74 42
-160 73 19 74 20
-161 44 19 20 43
-162 44 75 43 76
-163 105 18 19 108
-164 66 67 18 19
-165 66 67 106 107
-166 17 106 107 20
-167 68 17 20 65
-168 68 105 108 65
-169 22 79 80 21
-170 22 45 46 21
-171 77 45 78 46
-172 77 23 78 24
-173 23 24 47 48
-174 79 47 80 48
-175 22 23 100 97
-176 22 23 70 71
-177 99 70 71 98
-178 99 24 21 98
-179 24 69 72 21
-180 100 69 72 97
-181 77 25 80 26
-182 25 26 38 39
-183 78 79 38 39
-184 78 79 27 28
-185 37 27 28 40
-186 77 80 37 40
-187 26 27 93 96
-188 26 27 50 51
-189 50 94 51 95
-190 25 28 94 95
-191 25 49 28 52
-192 49 93 52 96
-193 81 29 84 30
-194 29 30 42 43
-195 82 83 42 43
-196 82 83 31 32
-197 44 41 31 32
-198 44 81 84 41
-199 88 30 85 31
-200 55 30 31 54
-201 55 86 54 87
-202 29 86 32 87
-203 56 29 53 32
-204 88 56 85 53
-205 33 34 73 76
-206 33 34 46 47
-207 46 47 74 75
-208 35 36 74 75
-209 45 35 36 48
-210 45 48 73 76
-211 34 89 35 92
-212 34 35 58 59
-213 90 58 91 59
-214 33 90 36 91
-215 33 57 36 60
-216 89 57 92 60
0