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On this page are computer-accessible forms for the graph C4[ 128, 28 ] = PL(SoP(4,8)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 93} under the group generated by the following permutations:

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

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

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