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On this page are computer-accessible forms for the graph C4[ 144, 72 ] = SS[144,26].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {1, 3} under the group generated by the following permutations:

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

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

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