[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 160, 66 ] = SDD(PS(8,5;2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 115} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 160, 66 ]
160
-1 121 81 127 87
-2 121 90 81 130
-3 121 81 158 118
-4 121 81 159 119
-5 122 82 126 86
-6 88 122 82 128
-7 122 82 159 119
-8 122 82 160 120
-9 123 83 127 87
-10 89 123 83 129
-11 123 156 83 116
-12 123 83 160 120
-13 88 124 84 128
-14 90 124 84 130
-15 156 124 116 84
-16 124 157 84 117
-17 125 126 85 86
-18 89 125 85 129
-19 157 125 117 85
-20 125 158 85 118
-21 133 93 126 86
-22 134 126 94 86
-23 134 94 127 87
-24 135 127 95 87
-25 88 91 128 131
-26 88 135 95 128
-27 89 91 129 131
-28 132 89 92 129
-29 132 90 92 130
-30 133 90 93 130
-31 91 137 97 131
-32 100 91 140 131
-33 132 92 136 96
-34 132 92 138 98
-35 133 93 137 97
-36 99 133 93 139
-37 134 94 138 98
-38 100 134 94 140
-39 135 136 95 96
-40 99 135 95 139
-41 143 103 136 96
-42 144 136 104 96
-43 144 104 137 97
-44 145 137 105 97
-45 101 138 141 98
-46 145 105 138 98
-47 99 101 139 141
-48 99 102 139 142
-49 100 102 140 142
-50 143 100 103 140
-51 101 147 107 141
-52 110 101 150 141
-53 102 146 106 142
-54 102 148 108 142
-55 143 103 147 107
-56 143 103 149 109
-57 144 104 148 108
-58 110 144 104 150
-59 145 146 105 106
-60 145 105 149 109
-61 113 146 106 153
-62 154 146 114 106
-63 154 114 147 107
-64 155 147 115 107
-65 111 148 151 108
-66 155 115 148 108
-67 111 149 151 109
-68 112 149 152 109
-69 110 112 150 152
-70 110 113 150 153
-71 111 157 117 151
-72 111 160 151 120
-73 112 156 116 152
-74 112 158 118 152
-75 113 157 117 153
-76 113 159 119 153
-77 154 114 158 118
-78 154 114 160 120
-79 155 156 115 116
-80 155 115 159 119
-81 1 2 3 4
-82 5 6 7 8
-83 11 12 9 10
-84 13 14 15 16
-85 17 18 19 20
-86 22 5 17 21
-87 1 23 24 9
-88 13 25 26 6
-89 27 28 18 10
-90 2 14 29 30
-91 25 27 31 32
-92 33 34 28 29
-93 35 36 30 21
-94 22 23 37 38
-95 24 26 39 40
-96 33 39 41 42
-97 44 35 31 43
-98 34 45 46 37
-99 36 47 48 40
-100 38 49 50 32
-101 45 47 51 52
-102 48 49 53 54
-103 55 56 50 41
-104 57 58 42 43
-105 44 46 59 60
-106 59 61 62 53
-107 55 51 63 64
-108 66 57 54 65
-109 56 67 68 60
-110 58 69 70 52
-111 67 71 72 65
-112 68 69 73 74
-113 70 61 75 76
-114 77 78 62 63
-115 66 79 80 64
-116 11 79 15 73
-117 16 71 19 75
-118 77 3 74 20
-119 80 4 7 76
-120 12 78 72 8
-121 1 2 3 4
-122 5 6 7 8
-123 11 12 9 10
-124 13 14 15 16
-125 17 18 19 20
-126 22 5 17 21
-127 1 23 24 9
-128 13 25 26 6
-129 27 28 18 10
-130 2 14 29 30
-131 25 27 31 32
-132 33 34 28 29
-133 35 36 30 21
-134 22 23 37 38
-135 24 26 39 40
-136 33 39 41 42
-137 44 35 31 43
-138 34 45 46 37
-139 36 47 48 40
-140 38 49 50 32
-141 45 47 51 52
-142 48 49 53 54
-143 55 56 50 41
-144 57 58 42 43
-145 44 46 59 60
-146 59 61 62 53
-147 55 51 63 64
-148 66 57 54 65
-149 56 67 68 60
-150 58 69 70 52
-151 67 71 72 65
-152 68 69 73 74
-153 70 61 75 76
-154 77 78 62 63
-155 66 79 80 64
-156 11 79 15 73
-157 16 71 19 75
-158 77 3 74 20
-159 80 4 7 76
-160 12 78 72 8
0

**************