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On this page are computer-accessible forms for the graph C4[ 160, 84 ] = SS[160,30].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

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

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

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