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On this page are computer-accessible forms for the graph C4[ 160, 81 ] = SS[160,27].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {6, 7} under the group generated by the following permutations:

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

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

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