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On this page are computer-accessible forms for the graph C4[ 168, 31 ] = PL(Curtain_21(1,9,1,2,14),[4^21,14^6]).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {72, 94}, {67, 93}, {65, 96}, {74, 107}, {67, 98}, {64, 98}, {71, 100}, {72, 109}, {69, 107}, {78, 96}, {77, 98}, {84, 123}, {72, 120}, {67, 113}, {81, 100}, {68, 114}, {83, 101}, {70, 112}, {73, 126}, {66, 122}, {75, 114}, {80, 109}, {76, 115}, {82, 109}, {79, 112}, {23, 87}, {56, 120}, {52, 117}, {58, 123}, {35, 97}, {39, 101}, {54, 116}, {33, 98}, {51, 119}, {44, 105}, {60, 121}, {46, 107}, {50, 119}, {18, 85}, {36, 99}, {26, 93}, {41, 110}, {17, 89}, {39, 111}, {34, 106}, {42, 99}, {56, 113}, {47, 101}, {49, 123}, {55, 125}, {22, 93}, {51, 120}, {22, 90}, {63, 115}, {45, 97}, {48, 124}, {50, 126}, {21, 91}, {61, 115}, {16, 95}, {6, 86}, {62, 110}, {36, 116}, {33, 113}, {32, 112}, {45, 125}, {4, 85}, {8, 89}, {8, 90}, {10, 88}, {43, 121}, {37, 118}, {1, 85}, {14, 90}, {2, 86}, {53, 97}, {3, 86}, {33, 116}, {50, 103}, {54, 99}, {56, 109}, {49, 103}, {55, 97}, {1, 86}, {38, 113}, {15, 88}, {7, 95}, {15, 87}, {51, 107}, {59, 99}, {46, 119}, {2, 88}, {3, 89}, {45, 119}, {5, 89}, {35, 127}, {9, 85}, {57, 101}, {2, 95}, {40, 117}, {49, 108}, {1, 95}, {9, 87}, {38, 121}, {44, 115}, {54, 105}, {14, 110}, {30, 126}, {29, 125}, {23, 118}, {61, 92}, {27, 122}, {25, 120}, {20, 118}, {5, 102}, {23, 116}, {17, 114}, {12, 111}, {11, 111}, {12, 104}, {21, 112}, {25, 124}, {8, 110}, {61, 91}, {29, 123}, {24, 126}, {11, 108}, {3, 106}, {31, 118}, {14, 103}, {9, 96}, {4, 111}, {20, 127}, {55, 92}, {10, 102}, {6, 104}, {28, 114}, {5, 106}, {18, 125}, {44, 92}, {11, 122}, {29, 108}, {13, 124}, {47, 94}, {18, 96}, {37, 87}, {22, 100}, {47, 93}, {6, 117}, {28, 104}, {28, 105}, {46, 91}, {10, 124}, {26, 108}, {15, 121}, {17, 105}, {12, 117}, {39, 94}, {37, 92}, {19, 106}, {4, 127}, {32, 91}, {21, 104}, {1, 127}, {38, 88}, {36, 90}, {32, 94}, {26, 100}, {24, 102}, {4, 122}, {24, 103}, {25, 102}, {3, 130}, {2, 128}, {6, 130}, {7, 131}, {19, 150}, {19, 149}, {27, 157}, {25, 159}, {9, 129}, {30, 150}, {42, 162}, {26, 147}, {7, 141}, {10, 128}, {43, 161}, {8, 131}, {35, 168}, {5, 137}, {16, 157}, {13, 131}, {23, 153}, {15, 129}, {45, 163}, {22, 134}, {27, 139}, {24, 137}, {50, 163}, {7, 149}, {17, 131}, {19, 134}, {53, 160}, {48, 166}, {28, 139}, {48, 167}, {11, 147}, {30, 134}, {13, 149}, {12, 148}, {58, 160}, {60, 166}, {16, 139}, {16, 141}, {63, 162}, {60, 161}, {14, 144}, {21, 139}, {31, 128}, {42, 138}, {48, 144}, {37, 132}, {59, 154}, {49, 144}, {36, 134}, {56, 154}, {57, 155}, {63, 156}, {53, 145}, {54, 146}, {41, 140}, {43, 141}, {52, 146}, {53, 147}, {62, 153}, {32, 136}, {62, 150}, {47, 135}, {43, 130}, {52, 157}, {52, 158}, {13, 166}, {42, 129}, {46, 133}, {51, 159}, {40, 133}, {41, 135}, {34, 146}, {59, 138}, {35, 145}, {39, 148}, {40, 155}, {55, 132}, {62, 138}, {40, 157}, {60, 137}, {59, 142}, {20, 162}, {57, 143}, {58, 140}, {18, 165}, {34, 149}, {29, 165}, {61, 133}, {33, 153}, {30, 167}, {20, 168}, {38, 154}, {34, 158}, {57, 133}, {31, 162}, {58, 135}, {31, 161}, {63, 129}, {44, 146}, {27, 164}, {41, 150}, {64, 128}, {84, 148}, {72, 136}, {68, 132}, {75, 138}, {65, 130}, {77, 142}, {67, 135}, {80, 151}, {71, 143}, {80, 152}, {66, 136}, {82, 152}, {71, 140}, {83, 152}, {81, 154}, {79, 132}, {65, 141}, {83, 159}, {66, 143}, {64, 142}, {71, 136}, {76, 156}, {70, 151}, {69, 151}, {77, 159}, {75, 153}, {79, 156}, {69, 145}, {79, 155}, {75, 158}, {77, 152}, {68, 156}, {68, 158}, {78, 148}, {74, 144}, {73, 147}, {82, 137}, {83, 143}, {70, 155}, {81, 140}, {76, 145}, {74, 151}, {81, 142}, {69, 165}, {64, 161}, {70, 163}, {66, 164}, {78, 168}, {65, 168}, {76, 165}, {73, 160}, {78, 164}, {74, 167}, {73, 167}, {84, 164}, {80, 163}, {82, 166}, {84, 160} }>;

(II) A more general form is to represent the graph as the orbit of {72, 94} under the group generated by the following permutations:

a: (2, 4)(3, 18)(5, 29)(6, 9)(7, 35)(8, 45)(10, 11)(12, 15)(13, 53)(14, 50)(16, 20)(17, 55)(19, 69)(21, 23)(22, 51)(24, 49)(25, 26)(27, 31)(28, 37)(30, 74)(32, 33)(34, 76)(36, 46)(38, 39)(40, 42)(41, 80)(43, 78)(47, 56)(48, 73)(52, 63)(54, 61)(57, 59)(58, 82)(60, 84)(62, 70)(64, 66)(67, 72)(71, 77)(75, 79)(81, 83)(85, 86)(87, 104)(88, 111)(89, 125)(90, 119)(91, 116)(92, 105)(93, 120)(94, 113)(95, 127)(96, 130)(97, 131)(98, 136)(99, 133)(100, 159)(101, 154)(102, 108)(106, 165)(107, 134)(109, 135)(110, 163)(112, 153)(114, 132)(115, 146)(117, 129)(118, 139)(121, 148)(122, 128)(123, 137)(124, 147)(126, 144)(138, 155)(140, 152)(141, 168)(142, 143)(145, 149)(150, 151)(156, 158)(157, 162)(160, 166)(161, 164)
b: (1, 2)(3, 6)(4, 10)(5, 12)(7, 16)(8, 21)(9, 15)(11, 25)(13, 27)(14, 32)(17, 28)(18, 38)(19, 40)(20, 31)(22, 46)(23, 37)(24, 39)(26, 51)(29, 56)(30, 57)(33, 55)(34, 52)(35, 64)(36, 61)(41, 70)(42, 63)(43, 65)(44, 54)(45, 67)(47, 50)(48, 66)(49, 72)(53, 77)(58, 80)(59, 76)(60, 78)(62, 79)(68, 75)(69, 81)(71, 74)(73, 83)(82, 84)(85, 88)(89, 104)(90, 91)(92, 116)(93, 119)(94, 103)(96, 121)(97, 98)(99, 115)(100, 107)(101, 126)(102, 111)(106, 117)(108, 120)(109, 123)(110, 112)(113, 125)(122, 124)(127, 128)(131, 139)(132, 153)(133, 134)(135, 163)(136, 144)(137, 148)(138, 156)(140, 151)(142, 145)(143, 167)(147, 159)(149, 157)(150, 155)(152, 160)(154, 165)(161, 168)(164, 166)
c: (1, 3, 8, 22, 47, 32, 61, 37, 15, 10, 24, 49, 11, 12, 28, 54, 33, 56, 51, 45, 18)(2, 5, 14, 26, 39, 21, 44, 23, 38, 25, 50, 29, 4, 6, 17, 36, 67, 72, 46, 55, 9)(7, 19, 41, 71, 57, 79, 63, 31, 60, 48, 73, 84, 27, 52, 75, 59, 77, 80, 69, 35, 65)(13, 30, 58, 66, 40, 68, 42, 64, 82, 74, 53, 78, 16, 34, 62, 81, 83, 70, 76, 20, 43)(85, 86, 89, 90, 93, 94, 91, 92, 87, 88, 102, 103, 108, 111, 104, 105, 116, 113, 120, 119, 125)(95, 106, 110, 100, 101, 112, 115, 118, 121, 124, 126, 123, 122, 117, 114, 99, 98, 109, 107, 97, 96)(127, 130, 131, 134, 135, 136, 133, 132, 129, 128, 137, 144, 147, 148, 139, 146, 153, 154, 159, 163, 165)(138, 142, 152, 151, 145, 168, 141, 149, 150, 140, 143, 155, 156, 162, 161, 166, 167, 160, 164, 157, 158)
d: (3, 7)(5, 13)(6, 16)(12, 27)(23, 42)(24, 48)(33, 59)(37, 63)(39, 66)(45, 69)(47, 71)(50, 74)(55, 76)(67, 81)(86, 95)(87, 129)(89, 131)(92, 115)(93, 100)(94, 136)(97, 145)(98, 142)(99, 116)(101, 143)(102, 124)(103, 144)(104, 139)(106, 149)(107, 119)(111, 122)(113, 154)(117, 157)(118, 162)(125, 165)(126, 167)(130, 141)(132, 156)(135, 140)(137, 166)(138, 153)(148, 164)(151, 163)

(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[ 168, 31 ]
168
-1 127 95 85 86
-2 88 95 128 86
-3 89 106 86 130
-4 111 122 127 85
-5 89 102 137 106
-6 104 117 86 130
-7 149 95 141 131
-8 110 89 90 131
-9 85 96 129 87
-10 88 102 124 128
-11 111 122 147 108
-12 111 104 148 117
-13 166 124 149 131
-14 110 144 90 103
-15 88 121 129 87
-16 157 95 139 141
-17 89 114 105 131
-18 165 125 85 96
-19 134 149 106 150
-20 168 127 118 162
-21 112 91 104 139
-22 100 90 134 93
-23 116 118 87 153
-24 102 103 126 137
-25 102 124 159 120
-26 100 147 93 108
-27 122 157 139 164
-28 114 104 105 139
-29 165 123 125 108
-30 134 167 126 150
-31 128 161 118 162
-32 112 91 136 94
-33 113 116 98 153
-34 146 158 149 106
-35 145 168 127 97
-36 99 90 134 116
-37 132 92 118 87
-38 88 121 154 113
-39 111 101 148 94
-40 133 155 157 117
-41 110 135 150 140
-42 99 138 129 162
-43 121 161 130 141
-44 146 92 115 105
-45 125 97 119 163
-46 133 91 107 119
-47 101 135 93 94
-48 144 166 167 124
-49 144 123 103 108
-50 103 126 119 163
-51 159 107 119 120
-52 146 157 158 117
-53 145 147 160 97
-54 99 146 105 116
-55 132 92 125 97
-56 154 113 109 120
-57 143 133 155 101
-58 123 135 160 140
-59 99 154 138 142
-60 121 166 137 161
-61 133 91 92 115
-62 110 138 150 153
-63 156 115 129 162
-64 128 161 98 142
-65 168 96 130 141
-66 143 122 136 164
-67 113 135 93 98
-68 132 156 114 158
-69 165 145 107 151
-70 155 112 151 163
-71 143 100 136 140
-72 136 94 109 120
-73 167 147 126 160
-74 144 167 107 151
-75 114 158 138 153
-76 165 145 156 115
-77 159 152 98 142
-78 168 148 96 164
-79 132 155 112 156
-80 151 152 163 109
-81 154 100 140 142
-82 166 137 152 109
-83 143 101 159 152
-84 123 148 160 164
-85 1 4 18 9
-86 1 2 3 6
-87 23 15 37 9
-88 2 15 38 10
-89 3 5 17 8
-90 22 14 36 8
-91 46 61 21 32
-92 44 55 37 61
-93 22 67 47 26
-94 47 39 72 32
-95 1 2 16 7
-96 78 18 9 65
-97 55 45 35 53
-98 33 77 67 64
-99 36 59 42 54
-100 22 26 81 71
-101 57 47 39 83
-102 24 25 5 10
-103 24 14 49 50
-104 12 6 28 21
-105 44 17 28 54
-106 34 3 5 19
-107 46 69 51 74
-108 11 26 49 29
-109 56 80 82 72
-110 14 62 8 41
-111 11 12 4 39
-112 79 70 21 32
-113 33 56 67 38
-114 68 17 28 75
-115 44 61 63 76
-116 33 23 36 54
-117 12 6 40 52
-118 23 37 20 31
-119 45 46 50 51
-120 56 25 72 51
-121 15 38 60 43
-122 11 66 4 27
-123 58 49 29 84
-124 13 25 48 10
-125 55 45 18 29
-126 24 50 73 30
-127 1 35 4 20
-128 2 31 64 10
-129 15 63 9 42
-130 3 6 43 65
-131 13 17 7 8
-132 55 68 79 37
-133 46 57 61 40
-134 22 36 19 30
-135 67 47 58 41
-136 66 71 72 32
-137 24 5 60 82
-138 59 62 42 75
-139 16 27 28 21
-140 58 81 71 41
-141 16 7 43 65
-142 77 59 81 64
-143 66 57 71 83
-144 14 48 49 74
-145 35 69 53 76
-146 44 34 52 54
-147 11 26 73 53
-148 12 78 39 84
-149 34 13 7 19
-150 62 19 30 41
-151 69 80 70 74
-152 77 80 82 83
-153 33 23 62 75
-154 56 59 81 38
-155 57 79 70 40
-156 68 79 63 76
-157 16 27 40 52
-158 34 68 52 75
-159 77 25 83 51
-160 58 73 84 53
-161 60 31 64 43
-162 63 20 31 42
-163 45 80 70 50
-164 66 78 27 84
-165 69 18 29 76
-166 13 48 60 82
-167 48 73 30 74
-168 78 35 20 65
0

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