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On this page are computer-accessible forms for the graph C4[ 168, 66 ] = BGCG(UG(Rmap(168,16){8,4|6}_14);K1;{3,4}).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {84, 86}, {83, 86}, {84, 95}, {68, 86}, {77, 94}, {74, 95}, {65, 87}, {64, 87}, {66, 91}, {69, 95}, {71, 92}, {67, 95}, {68, 90}, {73, 87}, {73, 86}, {74, 106}, {75, 107}, {78, 111}, {82, 115}, {69, 102}, {80, 115}, {71, 99}, {72, 109}, {67, 105}, {81, 123}, {83, 120}, {65, 108}, {78, 127}, {73, 122}, {65, 117}, {66, 116}, {66, 117}, {75, 124}, {69, 125}, {70, 126}, {67, 122}, {64, 123}, {82, 105}, {75, 112}, {82, 111}, {80, 110}, {71, 120}, {37, 101}, {48, 112}, {28, 93}, {45, 108}, {40, 106}, {42, 104}, {60, 126}, {55, 116}, {36, 96}, {50, 118}, {57, 125}, {16, 85}, {52, 114}, {43, 108}, {45, 106}, {62, 118}, {34, 107}, {40, 97}, {44, 102}, {51, 121}, {53, 127}, {18, 89}, {41, 98}, {56, 115}, {60, 119}, {44, 96}, {33, 111}, {33, 110}, {46, 97}, {40, 120}, {46, 126}, {56, 104}, {59, 107}, {34, 115}, {49, 99}, {63, 109}, {50, 96}, {54, 100}, {47, 124}, {48, 99}, {32, 116}, {11, 94}, {55, 98}, {12, 90}, {32, 118}, {13, 91}, {11, 92}, {34, 117}, {14, 89}, {43, 124}, {47, 120}, {57, 110}, {2, 90}, {35, 123}, {2, 88}, {61, 103}, {42, 112}, {39, 125}, {14, 85}, {37, 126}, {38, 122}, {44, 112}, {3, 94}, {44, 113}, {7, 89}, {36, 122}, {54, 104}, {7, 88}, {61, 98}, {59, 91}, {61, 92}, {5, 103}, {63, 93}, {21, 119}, {14, 108}, {9, 107}, {5, 102}, {62, 93}, {6, 101}, {59, 88}, {19, 118}, {48, 85}, {18, 116}, {20, 114}, {26, 125}, {30, 121}, {50, 85}, {58, 93}, {1, 105}, {29, 117}, {25, 113}, {20, 124}, {49, 88}, {53, 92}, {3, 105}, {6, 109}, {14, 101}, {15, 99}, {9, 100}, {22, 123}, {10, 103}, {17, 97}, {26, 106}, {43, 90}, {28, 110}, {37, 87}, {4, 119}, {24, 109}, {19, 100}, {46, 89}, {10, 114}, {35, 91}, {23, 111}, {8, 113}, {28, 101}, {3, 121}, {18, 104}, {4, 127}, {25, 98}, {9, 114}, {29, 97}, {2, 127}, {27, 102}, {26, 103}, {9, 119}, {15, 113}, {6, 121}, {33, 94}, {31, 96}, {27, 100}, {7, 135}, {38, 166}, {24, 152}, {23, 151}, {21, 149}, {30, 159}, {4, 134}, {39, 165}, {17, 146}, {36, 167}, {20, 151}, {7, 131}, {35, 167}, {5, 128}, {13, 136}, {15, 137}, {15, 136}, {13, 132}, {4, 142}, {27, 145}, {23, 157}, {5, 143}, {31, 148}, {1, 140}, {12, 129}, {1, 143}, {2, 140}, {10, 133}, {41, 166}, {25, 150}, {21, 154}, {13, 156}, {17, 128}, {27, 137}, {52, 166}, {54, 165}, {59, 168}, {29, 137}, {48, 164}, {8, 157}, {30, 139}, {12, 154}, {29, 139}, {8, 159}, {24, 128}, {31, 135}, {58, 162}, {23, 142}, {6, 156}, {25, 131}, {16, 138}, {16, 139}, {19, 136}, {26, 134}, {11, 149}, {22, 136}, {16, 142}, {63, 160}, {33, 129}, {36, 132}, {34, 131}, {38, 135}, {49, 144}, {51, 146}, {1, 162}, {61, 158}, {50, 145}, {46, 138}, {52, 144}, {53, 145}, {32, 133}, {60, 155}, {62, 153}, {51, 155}, {62, 150}, {55, 159}, {45, 132}, {8, 162}, {52, 158}, {60, 150}, {3, 168}, {63, 148}, {43, 128}, {47, 132}, {11, 167}, {37, 137}, {45, 129}, {54, 154}, {10, 167}, {51, 158}, {57, 148}, {55, 153}, {12, 163}, {22, 166}, {20, 165}, {41, 152}, {17, 163}, {40, 154}, {57, 139}, {49, 130}, {21, 160}, {22, 163}, {56, 141}, {19, 164}, {35, 148}, {39, 159}, {53, 141}, {24, 161}, {28, 165}, {58, 131}, {18, 168}, {38, 156}, {39, 156}, {31, 163}, {41, 149}, {32, 157}, {42, 151}, {47, 146}, {30, 160}, {42, 149}, {56, 135}, {58, 133}, {82, 146}, {80, 147}, {70, 130}, {72, 143}, {84, 147}, {77, 133}, {81, 153}, {67, 138}, {76, 134}, {71, 140}, {84, 153}, {72, 134}, {80, 158}, {79, 129}, {76, 130}, {64, 143}, {66, 141}, {65, 142}, {70, 151}, {83, 130}, {76, 157}, {74, 152}, {64, 147}, {68, 144}, {79, 155}, {68, 145}, {77, 152}, {76, 155}, {78, 150}, {81, 138}, {79, 147}, {77, 144}, {81, 140}, {83, 141}, {69, 161}, {70, 161}, {79, 168}, {73, 162}, {75, 160}, {72, 164}, {74, 164}, {78, 161} }>;

(II) A more general form is to represent the graph as the orbit of {84, 86} under the group generated by the following permutations:

a: (2, 82)(3, 71)(4, 23)(5, 58)(6, 15)(7, 17)(8, 72)(9, 20)(12, 56)(14, 29)(18, 40)(19, 39)(21, 42)(22, 38)(24, 25)(26, 32)(27, 28)(30, 48)(33, 53)(34, 43)(35, 36)(44, 63)(45, 66)(47, 59)(49, 51)(50, 57)(55, 74)(60, 70)(61, 77)(62, 69)(64, 73)(67, 81)(68, 80)(79, 83)(85, 139)(86, 147)(88, 146)(89, 97)(90, 115)(91, 132)(92, 94)(93, 102)(95, 153)(96, 148)(98, 152)(99, 121)(100, 165)(101, 137)(103, 133)(104, 154)(105, 140)(106, 116)(107, 124)(108, 117)(109, 113)(110, 145)(111, 127)(112, 160)(118, 125)(119, 151)(120, 168)(122, 123)(128, 131)(129, 141)(130, 155)(134, 157)(135, 163)(136, 156)(143, 162)(144, 158)(150, 161)(159, 164)
b: (1, 2, 12, 54, 39, 8)(3, 7, 22, 27, 26, 23)(4, 33, 18, 38, 15, 5)(6, 25, 64, 53, 45, 42)(9, 57, 32, 67, 49, 17)(10, 16, 77, 46, 52, 29)(11, 14, 41, 37, 61, 65)(13, 44, 72, 78, 79, 56)(19, 69, 76, 82, 59, 31)(20, 30, 58, 81, 68, 40)(21, 28, 55, 73, 71, 43)(24, 60, 80, 66, 36, 48)(34, 35, 50, 74, 70, 51)(47, 75, 63, 62, 84, 83)(85, 152, 126, 158, 117, 167)(86, 120, 124, 160, 93, 153)(87, 92, 108, 149, 101, 98)(88, 163, 100, 125, 157, 105)(89, 166, 137, 103, 142, 94)(90, 154, 165, 159, 162, 140)(91, 96, 164, 161, 155, 115)(95, 130, 146, 107, 148, 118)(97, 114, 139, 133, 138, 144)(99, 128, 119, 110, 116, 122)(102, 134, 111, 168, 135, 136)(104, 156, 113, 143, 127, 129)(106, 151, 121, 131, 123, 145)(109, 150, 147, 141, 132, 112)
c: (2, 8)(3, 5)(4, 23)(6, 17)(7, 15)(9, 42)(10, 11)(12, 39)(13, 31)(14, 29)(16, 65)(18, 27)(19, 56)(20, 21)(22, 38)(24, 51)(25, 49)(26, 33)(28, 40)(30, 43)(32, 53)(34, 48)(35, 36)(37, 46)(41, 52)(44, 59)(45, 57)(47, 63)(50, 66)(55, 68)(58, 71)(60, 70)(61, 77)(62, 83)(64, 67)(69, 79)(72, 82)(73, 81)(74, 80)(76, 78)(85, 117)(86, 153)(87, 138)(88, 113)(89, 137)(90, 159)(91, 96)(92, 133)(93, 120)(94, 103)(95, 147)(97, 101)(98, 144)(99, 131)(100, 104)(102, 168)(105, 143)(106, 110)(107, 112)(108, 139)(109, 146)(111, 134)(114, 149)(115, 164)(116, 145)(118, 141)(119, 151)(121, 128)(122, 123)(124, 160)(125, 129)(127, 157)(130, 150)(132, 148)(135, 136)(140, 162)(152, 158)(154, 165)(155, 161)(156, 163)
d: (2, 58)(3, 82)(4, 10)(5, 72)(6, 17)(8, 71)(11, 23)(12, 28)(13, 29)(14, 31)(16, 36)(18, 56)(19, 27)(20, 21)(22, 37)(25, 49)(30, 47)(32, 53)(34, 59)(35, 65)(38, 46)(39, 40)(41, 70)(43, 63)(44, 48)(45, 57)(52, 60)(55, 83)(61, 76)(62, 68)(69, 74)(73, 81)(77, 78)(79, 80)(85, 96)(86, 153)(87, 123)(88, 131)(89, 135)(90, 93)(91, 117)(92, 157)(94, 111)(97, 156)(98, 130)(99, 113)(101, 163)(102, 164)(103, 134)(106, 125)(108, 148)(109, 128)(110, 129)(114, 119)(115, 168)(116, 141)(118, 145)(120, 159)(121, 146)(122, 138)(124, 160)(126, 166)(127, 133)(132, 139)(136, 137)(140, 162)(142, 167)(144, 150)(149, 151)(152, 161)(154, 165)(155, 158)

(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.

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&Graph
C4[ 168, 66 ]
168
-1 143 105 140 162
-2 88 90 127 140
-3 121 168 94 105
-4 134 127 119 142
-5 143 102 103 128
-6 121 101 156 109
-7 88 89 135 131
-8 113 157 159 162
-9 100 114 107 119
-10 133 167 103 114
-11 167 92 94 149
-12 154 90 129 163
-13 132 156 91 136
-14 89 101 85 108
-15 99 113 136 137
-16 138 139 85 142
-17 146 128 97 163
-18 89 168 104 116
-19 100 136 118 164
-20 165 124 114 151
-21 154 149 160 119
-22 166 123 136 163
-23 111 157 151 142
-24 128 161 152 109
-25 113 150 98 131
-26 134 103 125 106
-27 100 145 102 137
-28 110 165 101 93
-29 137 117 139 97
-30 121 159 160 139
-31 135 148 96 163
-32 133 157 116 118
-33 110 111 94 129
-34 115 117 107 131
-35 123 167 91 148
-36 132 122 167 96
-37 101 126 137 87
-38 122 166 156 135
-39 165 156 125 159
-40 154 106 97 120
-41 166 149 152 98
-42 112 104 149 151
-43 90 124 128 108
-44 112 102 113 96
-45 132 106 129 108
-46 89 126 138 97
-47 132 124 146 120
-48 99 112 85 164
-49 88 99 144 130
-50 145 85 96 118
-51 121 155 146 158
-52 144 166 114 158
-53 145 92 127 141
-54 154 165 100 104
-55 159 116 98 153
-56 135 104 115 141
-57 110 125 148 139
-58 133 93 162 131
-59 88 91 168 107
-60 155 126 150 119
-61 92 103 158 98
-62 93 150 118 153
-63 93 148 160 109
-64 143 123 147 87
-65 117 108 87 142
-66 91 116 117 141
-67 122 105 138 95
-68 144 90 145 86
-69 102 125 95 161
-70 126 161 151 130
-71 99 92 140 120
-72 143 134 109 164
-73 122 162 86 87
-74 95 106 152 164
-75 112 124 160 107
-76 155 134 157 130
-77 133 144 94 152
-78 111 127 150 161
-79 155 168 147 129
-80 110 147 158 115
-81 123 138 140 153
-82 111 146 115 105
-83 86 130 141 120
-84 147 95 86 153
-85 14 48 16 50
-86 68 83 73 84
-87 37 73 64 65
-88 2 59 49 7
-89 46 14 7 18
-90 12 2 68 43
-91 66 13 35 59
-92 11 71 61 53
-93 58 28 62 63
-94 11 33 77 3
-95 67 69 84 74
-96 44 36 50 31
-97 46 17 29 40
-98 55 25 61 41
-99 15 48 49 71
-100 27 19 9 54
-101 14 37 6 28
-102 44 69 5 27
-103 26 5 61 10
-104 56 18 42 54
-105 1 67 3 82
-106 45 26 40 74
-107 34 59 9 75
-108 45 14 43 65
-109 24 6 72 63
-110 33 57 80 28
-111 33 23 78 82
-112 44 48 42 75
-113 44 25 15 8
-114 52 9 20 10
-115 34 56 80 82
-116 55 66 18 32
-117 66 34 29 65
-118 50 62 19 32
-119 4 60 9 21
-120 47 71 83 40
-121 3 6 51 30
-122 67 36 38 73
-123 22 35 81 64
-124 47 20 75 43
-125 57 69 26 39
-126 46 37 70 60
-127 78 2 4 53
-128 24 5 17 43
-129 33 12 45 79
-130 70 49 83 76
-131 34 25 58 7
-132 45 13 36 47
-133 77 58 10 32
-134 4 26 72 76
-135 56 38 7 31
-136 22 13 15 19
-137 15 37 27 29
-138 67 46 81 16
-139 57 16 29 30
-140 1 2 81 71
-141 66 56 83 53
-142 23 4 16 65
-143 1 5 72 64
-144 77 68 49 52
-145 68 27 50 53
-146 47 82 17 51
-147 79 80 84 64
-148 35 57 63 31
-149 11 41 42 21
-150 78 25 60 62
-151 23 70 20 42
-152 77 24 41 74
-153 55 81 62 84
-154 12 40 21 54
-155 79 60 51 76
-156 13 38 6 39
-157 23 8 32 76
-158 80 61 51 52
-159 55 39 8 30
-160 30 63 75 21
-161 78 24 69 70
-162 1 58 73 8
-163 22 12 17 31
-164 48 72 19 74
-165 28 39 20 54
-166 22 38 41 52
-167 11 35 36 10
-168 79 3 59 18
0

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