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On this page are computer-accessible forms for the graph C4[ 42, 5 ] = PL(PS(3,7;2)[3^14]).

(I) Following is a form readable by MAGMA:

g:=Graph<42|{ {8, 10}, {32, 34}, {20, 22}, {8, 11}, {32, 35}, {20, 23}, {1, 5}, {33, 37}, {19, 23}, {25, 29}, {1, 4}, {19, 22}, {25, 28}, {2, 4}, {33, 39}, {26, 28}, {2, 5}, {26, 29}, {4, 12}, {18, 26}, {18, 27}, {21, 28}, {6, 12}, {17, 27}, {17, 26}, {21, 30}, {2, 14}, {37, 41}, {7, 11}, {6, 10}, {3, 15}, {2, 15}, {37, 40}, {7, 10}, {3, 14}, {19, 30}, {4, 10}, {38, 40}, {19, 28}, {38, 41}, {7, 18}, {13, 24}, {7, 16}, {15, 24}, {12, 20}, {9, 16}, {15, 22}, {12, 21}, {9, 18}, {13, 22}, {13, 17}, {13, 16}, {11, 21}, {14, 16}, {11, 20}, {14, 17}, {5, 36}, {6, 36}, {6, 35}, {5, 35}, {1, 40}, {3, 42}, {1, 42}, {3, 40}, {8, 38}, {9, 39}, {8, 39}, {9, 38}, {29, 41}, {30, 42}, {23, 33}, {23, 32}, {30, 41}, {29, 42}, {24, 32}, {31, 39}, {24, 33}, {27, 34}, {31, 37}, {25, 34}, {31, 35}, {25, 36}, {31, 34}, {27, 36} }>;

(II) A more general form is to represent the graph as the orbit of {8, 10} under the group generated by the following permutations:

(2, 3)(4, 42, 5, 40)(6, 41)(7, 19, 27, 33)(8, 21, 25, 31)(9, 20, 26, 32)(10, 30, 36, 37)(11, 28, 34, 39)(12, 29, 35, 38)(14, 15)(16, 22, 17, 24)(18, 23)
(2, 3)(4, 40)(5, 42)(6, 41)(7, 9)(10, 38)(11, 39)(12, 37)(19, 32)(20, 33)(21, 31)(22, 24)(26, 27)(28, 34)(29, 36)(30, 35)
(1, 2)(7, 8)(13, 41)(14, 40)(15, 42)(16, 38)(17, 37)(18, 39)(20, 21)(22, 30)(23, 28)(24, 29)(25, 32)(26, 33)(27, 31)(35, 36)
(1, 4, 2, 5)(3, 6)(7, 17, 25, 30, 20, 24, 31, 38)(8, 16, 27, 29, 21, 22, 32, 37)(9, 18, 26, 28, 19, 23, 33, 39)(10, 14, 36, 42, 12, 15, 35, 40)(11, 13, 34, 41)

(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[ 42, 5 ]
42
-1 4 5 40 42
-2 14 4 15 5
-3 14 15 40 42
-4 1 12 2 10
-5 1 2 35 36
-6 12 35 36 10
-7 11 16 18 10
-8 11 38 39 10
-9 16 38 39 18
-10 4 6 7 8
-11 7 8 20 21
-12 4 6 20 21
-13 22 24 16 17
-14 2 3 16 17
-15 22 2 24 3
-16 13 14 7 9
-17 13 14 26 27
-18 26 27 7 9
-19 22 23 28 30
-20 11 22 12 23
-21 11 12 28 30
-22 13 15 19 20
-23 33 19 20 32
-24 33 13 15 32
-25 34 36 28 29
-26 17 28 18 29
-27 34 36 17 18
-28 25 26 19 21
-29 25 26 41 42
-30 19 41 42 21
-31 34 35 37 39
-32 23 34 24 35
-33 23 24 37 39
-34 25 27 31 32
-35 5 6 31 32
-36 25 5 27 6
-37 33 40 41 31
-38 40 8 41 9
-39 33 8 9 31
-40 1 3 37 38
-41 37 38 29 30
-42 1 3 29 30
0

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