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On this page are computer-accessible forms for the graph C4[ 160, 32 ] = PL(MC3(10,8,1,5,3,0,1),[4^20,10^8]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 84} under the group generated by the following permutations:

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

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