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On this page are computer-accessible forms for the graph C4[ 24, 7 ] = SDD(Octahedron).

(I) Following is a form readable by MAGMA:

g:=Graph<24|{ {6, 7}, {1, 3}, {20, 22}, {17, 19}, {4, 7}, {9, 10}, {2, 6}, {8, 13}, {2, 4}, {19, 21}, {18, 20}, {9, 14}, {18, 21}, {10, 13}, {16, 23}, {17, 22}, {7, 15}, {5, 12}, {1, 11}, {2, 9}, {5, 14}, {3, 15}, {4, 8}, {1, 12}, {6, 11}, {6, 8}, {4, 11}, {23, 24}, {10, 24}, {3, 16}, {7, 20}, {5, 22}, {1, 23}, {5, 19}, {14, 24}, {3, 20}, {15, 22}, {2, 24}, {11, 16}, {12, 16}, {8, 21}, {12, 17}, {15, 18}, {9, 23}, {13, 19}, {10, 21}, {13, 18}, {14, 17} }>;

(II) A more general form is to represent the graph as the orbit of {6, 7} under the group generated by the following permutations:

a: (13, 21)
b: (3, 12)(4, 9)(5, 15)(6, 24)(7, 14)(8, 10)(11, 23)(17, 20)(18, 19)
c: (2, 7)(3, 23)(9, 15)(10, 18)(14, 22)(20, 24)
d: (15, 20)
e: (1, 4)(2, 3)(5, 13)(6, 16)(7, 23)(8, 12)(9, 15)(10, 22)(14, 18)(17, 21)(20, 24)
f: (5, 17)
g: (2, 14)(4, 5)(6, 17)(7, 22)(8, 19)(11, 12)
h: (1, 13)(3, 18)(8, 11)(10, 23)(12, 19)(16, 21)

(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[ 24, 7 ]
24
-1 11 12 23 3
-2 24 4 6 9
-3 1 15 16 20
-4 11 2 7 8
-5 22 12 14 19
-6 11 2 7 8
-7 4 15 6 20
-8 13 4 6 21
-9 23 2 14 10
-10 13 24 9 21
-11 1 4 16 6
-12 1 5 16 17
-13 18 8 19 10
-14 24 5 17 9
-15 22 3 7 18
-16 11 12 23 3
-17 22 12 14 19
-18 13 15 20 21
-19 13 5 17 21
-20 22 3 7 18
-21 18 8 19 10
-22 15 5 17 20
-23 1 24 16 9
-24 23 2 14 10
0

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