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On this page are computer-accessible forms for the graph C4[ 80, 25 ] = PL(CS(C_10(1,3)[10^2],1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {40, 41} under the group generated by the following permutations:

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

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