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