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On this page are computer-accessible forms for the graph C4[ 160, 85 ] = SS[160,31].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 17} under the group generated by the following permutations:

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

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

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