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On this page are computer-accessible forms for the graph C4[ 160, 78 ] = SS[160,21].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {112, 113} under the group generated by the following permutations:

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

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