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On this page are computer-accessible forms for the graph C4[ 160, 59 ] = SDD(PX(5,3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {80, 88} under the group generated by the following permutations:

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

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

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