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On this page are computer-accessible forms for the graph C4[ 40, 10 ] = PL(Br(4,5;2)).

(I) Following is a form readable by MAGMA:

g:=Graph<40|{ {17, 21}, {16, 21}, {16, 24}, {17, 25}, {17, 24}, {18, 25}, {17, 28}, {18, 28}, {19, 29}, {18, 29}, {6, 22}, {7, 23}, {6, 23}, {7, 22}, {8, 26}, {13, 31}, {14, 28}, {8, 27}, {11, 24}, {12, 31}, {15, 28}, {1, 21}, {2, 22}, {12, 24}, {15, 27}, {14, 27}, {8, 30}, {9, 31}, {1, 22}, {9, 30}, {8, 31}, {2, 21}, {12, 23}, {2, 30}, {11, 23}, {7, 27}, {5, 25}, {3, 30}, {7, 26}, {4, 25}, {3, 29}, {4, 26}, {2, 29}, {5, 26}, {1, 33}, {6, 38}, {4, 37}, {6, 39}, {4, 38}, {1, 34}, {5, 33}, {3, 38}, {13, 40}, {3, 37}, {14, 40}, {5, 34}, {10, 34}, {11, 35}, {10, 35}, {14, 39}, {9, 35}, {13, 39}, {9, 34}, {15, 36}, {10, 38}, {12, 32}, {15, 35}, {10, 39}, {13, 32}, {11, 36}, {20, 36}, {20, 37}, {18, 32}, {19, 33}, {19, 32}, {16, 37}, {20, 33}, {19, 36}, {16, 40}, {20, 40} }>;

(II) A more general form is to represent the graph as the orbit of {17, 21} under the group generated by the following permutations:

a: (2, 5)(3, 4)(6, 10)(7, 9)(12, 15)(13, 14)(16, 20)(17, 19)(21, 33)(22, 34)(23, 35)(24, 36)(25, 29)(26, 30)(27, 31)(28, 32)
b: (1, 6, 13, 19)(2, 10, 12, 20)(3, 9, 11, 16)(4, 8, 15, 17)(5, 7, 14, 18)(21, 38, 31, 36)(22, 39, 32, 33)(23, 40, 29, 34)(24, 37, 30, 35)(25, 26, 27, 28)
c: (6, 16)(7, 17)(8, 18)(9, 19)(10, 20)(21, 22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 34)(35, 36)(37, 38)(39, 40)
d: (1, 2, 3, 4, 5)(6, 8, 10, 7, 9)(11, 12, 13, 14, 15)(16, 18, 20, 17, 19)(21, 29, 37, 25, 33)(22, 30, 38, 26, 34)(23, 31, 39, 27, 35)(24, 32, 40, 28, 36)

(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[ 40, 10 ]
40
-1 22 33 34 21
-2 22 29 30 21
-3 37 38 29 30
-4 25 26 37 38
-5 33 34 25 26
-6 22 23 38 39
-7 22 23 26 27
-8 26 27 30 31
-9 34 35 30 31
-10 34 35 38 39
-11 23 24 35 36
-12 23 24 31 32
-13 39 40 31 32
-14 27 28 39 40
-15 35 36 27 28
-16 24 37 40 21
-17 24 25 28 21
-18 25 28 29 32
-19 33 36 29 32
-20 33 36 37 40
-21 1 2 16 17
-22 1 2 6 7
-23 11 12 6 7
-24 11 12 16 17
-25 4 5 17 18
-26 4 5 7 8
-27 14 15 7 8
-28 14 15 17 18
-29 2 3 18 19
-30 2 3 8 9
-31 12 13 8 9
-32 12 13 18 19
-33 1 5 19 20
-34 1 5 9 10
-35 11 15 9 10
-36 11 15 19 20
-37 3 4 16 20
-38 3 4 6 10
-39 13 14 6 10
-40 13 14 16 20
0

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