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On this page are computer-accessible forms for the graph C4[ 162, 18 ] = XI(Rmap(81,3){3,6|6}_18).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {81, 91} under the group generated by the following permutations:

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

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

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