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On this page are computer-accessible forms for the graph C4[ 80, 29 ] = SS[80,6].

(I) Following is a form readable by MAGMA:

g:=Graph<80|{ {1, 3}, {32, 34}, {1, 2}, {1, 5}, {1, 4}, {67, 74}, {32, 42}, {64, 77}, {68, 73}, {66, 79}, {65, 80}, {32, 52}, {32, 56}, {20, 52}, {26, 59}, {27, 58}, {9, 43}, {9, 42}, {25, 58}, {10, 46}, {10, 47}, {23, 50}, {21, 48}, {26, 63}, {7, 33}, {19, 53}, {31, 57}, {6, 33}, {22, 49}, {16, 55}, {28, 59}, {17, 57}, {27, 51}, {8, 33}, {15, 38}, {13, 36}, {12, 37}, {30, 55}, {14, 36}, {18, 56}, {31, 53}, {16, 59}, {24, 51}, {22, 61}, {21, 62}, {29, 54}, {19, 63}, {9, 36}, {21, 56}, {29, 48}, {11, 37}, {16, 62}, {28, 50}, {10, 37}, {22, 57}, {30, 49}, {24, 40}, {25, 41}, {26, 42}, {29, 45}, {15, 61}, {25, 43}, {26, 40}, {28, 46}, {30, 44}, {20, 39}, {18, 38}, {27, 47}, {31, 43}, {9, 60}, {24, 45}, {19, 38}, {15, 58}, {10, 60}, {17, 39}, {8, 63}, {16, 39}, {6, 62}, {15, 54}, {20, 45}, {27, 34}, {6, 60}, {12, 54}, {6, 61}, {23, 44}, {12, 55}, {13, 49}, {21, 41}, {18, 46}, {14, 50}, {30, 34}, {31, 35}, {13, 48}, {14, 51}, {11, 53}, {23, 41}, {22, 40}, {17, 47}, {29, 35}, {11, 52}, {19, 44}, {28, 35}, {7, 68}, {2, 70}, {2, 71}, {7, 66}, {7, 65}, {2, 69}, {4, 76}, {8, 64}, {5, 77}, {3, 74}, {13, 68}, {3, 73}, {5, 79}, {4, 78}, {3, 72}, {8, 67}, {14, 67}, {5, 75}, {11, 68}, {12, 67}, {17, 66}, {18, 65}, {4, 80}, {20, 64}, {23, 66}, {24, 65}, {25, 64}, {39, 71}, {38, 71}, {47, 78}, {36, 71}, {37, 70}, {46, 77}, {33, 69}, {44, 72}, {42, 79}, {45, 72}, {35, 69}, {34, 69}, {55, 80}, {40, 70}, {41, 70}, {61, 76}, {63, 78}, {56, 74}, {59, 73}, {57, 74}, {58, 73}, {60, 72}, {62, 75}, {51, 75}, {52, 76}, {54, 79}, {43, 80}, {49, 77}, {48, 78}, {53, 75}, {50, 76} }>;

(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: (6, 9)(7, 14)(8, 13)(11, 12)(15, 31)(16, 32)(17, 27)(18, 28)(19, 29)(20, 30)(21, 26)(22, 25)(23, 24)(33, 36)(34, 39)(35, 38)(40, 41)(42, 62)(43, 61)(44, 45)(48, 63)(49, 64)(50, 65)(51, 66)(52, 55)(53, 54)(56, 59)(57, 58)(67, 68)(69, 71)(73, 74)(75, 79)(76, 80)
b: (3, 5, 4)(6, 32, 31)(7, 30, 29)(8, 27, 28)(10, 26, 25)(11, 22, 21)(12, 24, 23)(15, 18, 19)(16, 20, 17)(33, 34, 35)(37, 40, 41)(42, 43, 60)(44, 54, 65)(45, 66, 55)(46, 63, 58)(47, 59, 64)(48, 68, 49)(50, 67, 51)(52, 57, 62)(53, 61, 56)(72, 79, 80)(73, 77, 78)(74, 75, 76)
c: (2, 5, 4)(6, 9)(7, 32, 15, 14, 16, 31)(8, 26, 22, 13, 21, 25)(11, 18, 27, 12, 28, 17)(19, 24, 30, 29, 23, 20)(33, 42, 61, 36, 62, 43)(34, 54, 50, 39, 53, 65)(35, 66, 52, 38, 51, 55)(37, 46, 47)(40, 49, 48, 41, 64, 63)(44, 45)(56, 58, 67, 59, 57, 68)(69, 79, 76, 71, 75, 80)(70, 77, 78)(73, 74)
d: (3, 4)(9, 15)(10, 22)(11, 24)(12, 26)(13, 18)(14, 19)(27, 31)(28, 30)(29, 32)(34, 35)(36, 38)(37, 40)(42, 54)(43, 58)(44, 50)(45, 52)(46, 49)(47, 57)(48, 56)(51, 53)(55, 59)(60, 61)(63, 67)(65, 68)(72, 76)(73, 80)(74, 78)
e: (4, 5)(7, 8)(9, 10)(11, 14)(12, 13)(15, 21)(16, 22)(17, 26)(18, 25)(19, 23)(20, 24)(27, 32)(28, 31)(36, 37)(38, 41)(39, 40)(42, 47)(43, 46)(48, 54)(49, 55)(50, 53)(51, 52)(56, 58)(57, 59)(61, 62)(63, 66)(64, 65)(67, 68)(70, 71)(73, 74)(75, 76)(77, 80)(78, 79)
f: (4, 5)(6, 7)(9, 11)(10, 13)(12, 14)(15, 23)(16, 24)(17, 22)(18, 21)(19, 25)(20, 26)(27, 30)(28, 29)(36, 37)(38, 41)(39, 40)(42, 52)(43, 53)(44, 58)(45, 59)(46, 48)(47, 49)(50, 54)(51, 55)(60, 68)(61, 66)(62, 65)(63, 64)(70, 71)(72, 73)(75, 80)(76, 79)(77, 78)
g: (1, 6, 70, 8, 71, 7)(2, 33)(3, 60, 37, 67, 36, 68)(4, 62, 40, 64, 38, 66)(5, 61, 41, 63, 39, 65)(9, 11, 74)(10, 12, 14, 13, 73, 72)(15, 23, 78, 16, 24, 77)(17, 80, 75, 22, 25, 19)(18, 79, 76, 21, 26, 20)(27, 30)(28, 29)(42, 52, 56)(43, 53, 57)(44, 47, 55, 51, 49, 58)(45, 46, 54, 50, 48, 59)
h: (4, 5)(15, 16)(17, 18)(19, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(34, 35)(38, 39)(40, 41)(42, 43)(44, 45)(46, 47)(48, 49)(50, 51)(52, 53)(54, 55)(56, 57)(58, 59)(61, 62)(63, 64)(65, 66)(75, 76)(77, 78)(79, 80)

(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[ 80, 29 ]
80
-1 2 3 4 5
-2 1 69 70 71
-3 1 72 73 74
-4 1 78 80 76
-5 77 1 79 75
-6 33 60 61 62
-7 33 66 68 65
-8 33 67 63 64
-9 36 60 42 43
-10 46 47 37 60
-11 68 37 52 53
-12 55 67 37 54
-13 68 36 48 49
-14 67 36 50 51
-15 58 38 61 54
-16 55 59 39 62
-17 66 57 47 39
-18 56 46 38 65
-19 44 38 63 53
-20 45 39 52 64
-21 56 48 62 41
-22 57 49 61 40
-23 44 66 50 41
-24 45 40 51 65
-25 58 41 64 43
-26 59 40 63 42
-27 34 47 58 51
-28 35 46 59 50
-29 45 35 48 54
-30 44 55 34 49
-31 35 57 53 43
-32 34 56 52 42
-33 69 6 7 8
-34 69 27 30 32
-35 69 28 29 31
-36 13 14 71 9
-37 11 12 70 10
-38 15 71 18 19
-39 16 71 17 20
-40 22 24 26 70
-41 23 25 70 21
-42 79 26 9 32
-43 25 80 9 31
-44 23 72 19 30
-45 24 72 29 20
-46 77 28 18 10
-47 78 27 17 10
-48 78 13 29 21
-49 22 77 13 30
-50 23 14 28 76
-51 24 14 27 75
-52 11 20 32 76
-53 11 19 31 75
-54 12 79 15 29
-55 12 80 16 30
-56 18 74 21 32
-57 22 17 74 31
-58 25 15 27 73
-59 26 16 28 73
-60 6 72 9 10
-61 22 15 6 76
-62 16 6 75 21
-63 78 26 8 19
-64 77 25 8 20
-65 24 80 7 18
-66 23 79 17 7
-67 12 14 8 74
-68 11 13 7 73
-69 33 34 2 35
-70 2 37 40 41
-71 2 36 38 39
-72 44 45 3 60
-73 68 3 58 59
-74 56 67 57 3
-75 5 51 62 53
-76 4 50 61 52
-77 46 5 49 64
-78 47 4 48 63
-79 66 5 42 54
-80 55 4 43 65
0

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