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On this page are computer-accessible forms for the graph C4[ 160, 10 ] = PS(20,16;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 18} under the group generated by the following permutations:

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

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

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