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On this page are computer-accessible forms for the graph C4[ 160, 60 ] = SDD(W(20,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 125} under the group generated by the following permutations:

a: (27, 35)
b: (5, 11)(42, 57)(83, 86)(94, 109)(101, 117)(111, 123)
c: (77, 79)(78, 80)(144, 150)(146, 152)(157, 159)(158, 160)
d: (59, 64)
e: (29, 44)(47, 58)(101, 111)(117, 123)(131, 141)(137, 147)
f: (8, 17)
g: (49, 55)(51, 60)(120, 126)(122, 128)(144, 152)(146, 150)
h: (8, 18)(17, 22)(91, 105)(92, 99)(98, 115)(106, 108)
m: (37, 52)
n1: (55, 60)
a1: (73, 74)
b1: (79, 80)
c1: (11, 57)
d1: (18, 22)
e1: (16, 27)(33, 35)(91, 98)(105, 115)(121, 130)(127, 136)
f1: (61, 62)
g1: (65, 72)(75, 76)(131, 137)(141, 147)(145, 151)(154, 155)
h1: (48, 59)(63, 64)(119, 125)(129, 135)(143, 153)(149, 156)
m1: (49, 51)
n2: (66, 73)(68, 74)(132, 138)(142, 148)(143, 149)(153, 156)
a2: (25, 56)
b2: (72, 76)
c2: (44, 58)
d2: (13, 24)(28, 43)(88, 95)(100, 110)(119, 129)(125, 135)
e2: (14, 25)(21, 56)(89, 96)(103, 113)(120, 128)(122, 126)
f2: (4, 40)
g2: (3, 7)(23, 38)(84, 90)(87, 97)(89, 103)(96, 113)
h2: (9, 19)(31, 39)(92, 106)(99, 108)(104, 116)(107, 114)
m2: (6, 12)(15, 26)(84, 87)(90, 97)(102, 118)(112, 124)
n3: (10, 20)
a3: (50, 54)
b3: (30, 45)(36, 46)(102, 112)(118, 124)(132, 142)(138, 148)
c3: (14, 21)
d3: (19, 39)
e3: (12, 26)
f3: (67, 69)(70, 71)(133, 139)(134, 140)(157, 160)(158, 159)
g3: (1, 2)(3, 8)(4, 10)(5, 13)(6, 16)(7, 18)(9, 14)(11, 24)(12, 27)(15, 33)(17, 38)(19, 25)(20, 40)(21, 31)(22, 23)(26, 35)(28, 42)(29, 48)(30, 50)(32, 49)(34, 53)(36, 54)(37, 55)(39, 56)(41, 51)(43, 57)(44, 59)(45, 61)(46, 62)(47, 63)(52, 60)(58, 64)(65, 66)(67, 77)(68, 75)(69, 79)(70, 78)(71, 80)(72, 73)(74, 76)(82, 85)(83, 88)(84, 91)(86, 95)(87, 98)(89, 92)(90, 105)(94, 100)(96, 106)(97, 115)(99, 103)(101, 119)(102, 121)(104, 120)(107, 122)(108, 113)(109, 110)(111, 125)(112, 127)(114, 126)(116, 128)(117, 129)(118, 130)(123, 135)(124, 136)(131, 149)(132, 151)(133, 144)(134, 146)(137, 143)(138, 145)(139, 150)(140, 152)(141, 156)(142, 155)(147, 153)(148, 154)(159, 160)
h3: (69, 71)
m3: (66, 68)
n4: (2, 5)(3, 9)(4, 11)(6, 8)(7, 19)(12, 18)(13, 29)(14, 32)(15, 17)(16, 30)(21, 41)(22, 26)(23, 39)(24, 44)(25, 37)(27, 45)(28, 47)(31, 38)(33, 36)(34, 42)(35, 46)(40, 57)(43, 58)(48, 65)(49, 67)(50, 66)(51, 70)(52, 56)(54, 68)(55, 69)(59, 72)(60, 71)(61, 73)(62, 74)(63, 75)(64, 76)(81, 83)(82, 86)(84, 92)(85, 94)(87, 99)(88, 101)(89, 104)(90, 106)(91, 102)(93, 109)(95, 111)(96, 114)(97, 108)(98, 112)(100, 117)(103, 116)(105, 118)(107, 113)(110, 123)(115, 124)(119, 131)(120, 133)(121, 132)(122, 134)(125, 137)(126, 139)(127, 138)(128, 140)(129, 141)(130, 142)(135, 147)(136, 148)(143, 155)(144, 157)(145, 156)(146, 158)(149, 151)(150, 159)(152, 160)(153, 154)
a4: (2, 4)(34, 40)(81, 82)(85, 93)(88, 100)(95, 110)
b4: (32, 37)(41, 52)(104, 114)(107, 116)(133, 140)(134, 139)
c4: (30, 36)
d4: (7, 23)
e4: (77, 78)
f4: (50, 61)(54, 62)(121, 127)(130, 136)(145, 154)(151, 155)
g4: (24, 43)
h4: (45, 46)

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

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