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On this page are computer-accessible forms for the graph C4[ 72, 25 ] = PL(CS(DW(3,3)[6^3],1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {35, 49} under the group generated by the following permutations:

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

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

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