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On this page are computer-accessible forms for the graph C4[ 144, 53 ] = PL(CSI(Octahedron[3^4],6)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {69, 109} under the group generated by the following permutations:

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

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

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