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On this page are computer-accessible forms for the graph C4[ 40, 12 ] = PL(R_10(7, 6)[4^10]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 6} under the group generated by the following permutations:

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

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

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