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