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On this page are computer-accessible forms for the graph C4[ 80, 21 ] = PL(Br(8,5;2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {37, 41} under the group generated by the following permutations:

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

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

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