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On this page are computer-accessible forms for the graph C4[ 120, 36 ] = PL(CSI(Octahedron[3^4],5)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {27, 63} under the group generated by the following permutations:

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

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

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