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On this page are computer-accessible forms for the graph C4[ 160, 27 ] = MSY(4,40,21,4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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