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On this page are computer-accessible forms for the graph C4[ 168, 30 ] = PL(Curtain_21(1,8,13,20,21),[4^21,6^14]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {71, 86} under the group generated by the following permutations:

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

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

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