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On this page are computer-accessible forms for the graph C4[ 84, 9 ] = PL(MSZ(6,7,2,2),[3^14,6^7]).

(I) Following is a form readable by MAGMA:

g:=Graph<84|{ {40, 46}, {39, 46}, {34, 46}, {32, 46}, {37, 43}, {33, 52}, {34, 53}, {37, 50}, {35, 58}, {41, 48}, {40, 49}, {39, 61}, {42, 48}, {32, 59}, {39, 60}, {37, 62}, {32, 60}, {33, 61}, {35, 62}, {40, 53}, {38, 57}, {40, 55}, {30, 62}, {10, 43}, {13, 47}, {14, 45}, {15, 44}, {10, 47}, {29, 59}, {31, 57}, {18, 53}, {19, 52}, {3, 43}, {16, 56}, {22, 62}, {25, 48}, {30, 52}, {4, 47}, {26, 49}, {27, 48}, {22, 58}, {30, 50}, {26, 55}, {18, 60}, {22, 56}, {24, 54}, {20, 59}, {2, 50}, {6, 54}, {28, 44}, {2, 51}, {5, 55}, {1, 50}, {12, 63}, {10, 57}, {7, 52}, {31, 44}, {3, 55}, {13, 57}, {8, 60}, {13, 56}, {14, 59}, {24, 45}, {5, 51}, {11, 61}, {7, 49}, {29, 43}, {2, 58}, {14, 54}, {11, 51}, {7, 63}, {5, 63}, {9, 51}, {1, 58}, {22, 45}, {13, 54}, {6, 61}, {3, 63}, {8, 53}, {18, 47}, {17, 44}, {16, 45}, {12, 49}, {6, 56}, {15, 79}, {19, 83}, {11, 73}, {17, 83}, {16, 82}, {1, 66}, {15, 76}, {11, 72}, {4, 71}, {4, 64}, {20, 80}, {23, 83}, {20, 81}, {21, 80}, {1, 71}, {15, 73}, {4, 66}, {3, 69}, {2, 68}, {19, 84}, {9, 65}, {8, 65}, {27, 82}, {9, 67}, {8, 67}, {24, 83}, {25, 82}, {27, 80}, {5, 72}, {9, 68}, {28, 81}, {12, 66}, {6, 73}, {10, 69}, {23, 70}, {31, 78}, {17, 67}, {21, 71}, {19, 65}, {18, 64}, {23, 69}, {28, 78}, {7, 84}, {23, 67}, {26, 78}, {30, 75}, {20, 66}, {26, 76}, {28, 74}, {29, 74}, {24, 65}, {21, 79}, {29, 70}, {12, 80}, {21, 73}, {25, 69}, {27, 71}, {16, 77}, {17, 76}, {14, 81}, {25, 70}, {31, 64}, {36, 68}, {41, 75}, {42, 72}, {37, 70}, {41, 77}, {38, 64}, {42, 77}, {39, 79}, {32, 74}, {33, 75}, {36, 72}, {35, 78}, {38, 75}, {33, 79}, {42, 68}, {36, 74}, {34, 77}, {35, 76}, {34, 82}, {38, 84}, {36, 81}, {41, 84} }>;

(II) A more general form is to represent the graph as the orbit of {40, 46} under the group generated by the following permutations:

a: (3, 41)(5, 42)(6, 28)(7, 25)(10, 38)(11, 36)(12, 27)(13, 31)(14, 15)(16, 26)(17, 24)(19, 23)(20, 21)(22, 35)(29, 33)(30, 37)(32, 39)(34, 40)(43, 75)(44, 54)(45, 76)(47, 64)(48, 63)(49, 82)(51, 68)(52, 70)(55, 77)(56, 78)(59, 79)(61, 74)(65, 67)(66, 71)(69, 84)(73, 81)
b: (1, 2)(3, 7)(4, 9)(5, 12)(6, 14)(8, 18)(10, 19)(11, 20)(13, 24)(15, 28)(17, 31)(21, 36)(23, 38)(25, 41)(27, 42)(29, 33)(30, 37)(32, 39)(43, 52)(45, 56)(47, 65)(49, 55)(51, 66)(57, 83)(59, 61)(64, 67)(68, 71)(69, 84)(70, 75)(72, 80)(73, 81)(74, 79)(76, 78)(77, 82)
c: (1, 3)(2, 5)(4, 10)(6, 8)(7, 30)(9, 11)(12, 37)(13, 18)(14, 32)(15, 17)(16, 34)(19, 33)(20, 29)(21, 23)(22, 40)(24, 39)(25, 27)(26, 35)(43, 66)(45, 46)(49, 62)(50, 63)(53, 56)(54, 60)(55, 58)(57, 64)(61, 65)(67, 73)(68, 72)(69, 71)(70, 80)(74, 81)(75, 84)(79, 83)
d: (2, 4)(3, 41, 6, 28)(5, 38, 11, 31)(7, 33, 15, 26)(9, 18)(10, 42, 13, 36)(12, 30, 21, 35)(14, 29, 25, 16)(17, 40, 19, 39)(20, 37, 27, 22)(23, 34, 24, 32)(43, 48, 56, 81)(44, 55, 84, 61)(45, 59, 70, 82)(46, 83)(47, 68)(49, 52, 79, 76)(50, 71, 58, 66)(51, 64)(53, 65, 60, 67)(54, 74, 69, 77)(57, 72)(62, 80)(63, 75, 73, 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.

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&Graph
C4[ 84, 9 ]
84
-1 66 58 71 50
-2 68 58 50 51
-3 55 69 63 43
-4 66 47 71 64
-5 55 72 51 63
-6 56 61 73 54
-7 49 84 52 63
-8 67 60 53 65
-9 67 68 51 65
-10 57 47 69 43
-11 61 72 51 73
-12 66 80 49 63
-13 56 57 47 54
-14 45 59 81 54
-15 44 79 73 76
-16 77 45 56 82
-17 44 67 83 76
-18 47 60 53 64
-19 83 84 52 65
-20 66 80 59 81
-21 79 80 71 73
-22 45 56 58 62
-23 67 69 70 83
-24 45 83 54 65
-25 69 48 70 82
-26 55 78 49 76
-27 80 48 71 82
-28 44 78 81 74
-29 59 70 74 43
-30 50 62 52 75
-31 44 78 57 64
-32 46 59 60 74
-33 79 61 52 75
-34 77 46 82 53
-35 78 58 62 76
-36 68 81 72 74
-37 70 50 62 43
-38 57 84 64 75
-39 46 79 60 61
-40 55 46 49 53
-41 77 48 84 75
-42 77 68 48 72
-43 3 37 29 10
-44 15 17 28 31
-45 22 24 14 16
-46 34 39 40 32
-47 13 4 18 10
-48 25 27 41 42
-49 12 26 7 40
-50 1 2 37 30
-51 11 2 5 9
-52 33 7 19 30
-53 34 18 40 8
-54 13 24 14 6
-55 3 26 5 40
-56 22 13 16 6
-57 13 38 31 10
-58 22 1 2 35
-59 14 29 20 32
-60 39 18 8 32
-61 11 33 6 39
-62 22 35 37 30
-63 12 3 5 7
-64 4 38 18 31
-65 24 8 19 9
-66 1 12 4 20
-67 23 17 8 9
-68 2 36 9 42
-69 23 3 25 10
-70 23 25 37 29
-71 1 4 27 21
-72 11 36 5 42
-73 11 15 6 21
-74 36 28 29 32
-75 33 38 30 41
-76 35 15 26 17
-77 34 16 41 42
-78 35 26 28 31
-79 33 15 39 21
-80 12 27 20 21
-81 14 36 28 20
-82 34 25 16 27
-83 23 24 17 19
-84 38 7 19 41
0

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