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On this page are computer-accessible forms for the graph C4[ 80, 16 ] = PL(MC3(8,5,1,4,2,0,1),[8^5,10^4]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 46} under the group generated by the following permutations:

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

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

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