The following construction of Tutte's 8-cage uses the technique described in P. Lorimer, J. of Graph Theory, 13, 5 (1989), 553-557. The graph is constructed so that it has in its representation of degree 30 as its automorphism group. The vertices of the graph correspond to the points on which G acts. The neighbours of vertex 1 are the points lying in the unique orbit of length 3 of the stabilizer of 1. The edges for vertex i are precisely the points where g is an element of G such that .
> G := PermutationGroup< 30 |
> (1, 2)(3, 4)(5, 7)(6, 8)(9, 13)(10, 12)(11, 15)(14, 19)(16, 23)
> (17, 22)(18, 21)(20, 27)(24, 29)(25, 28)(26, 30),
> (1, 24, 28, 8)(2, 9, 17, 22)(3, 29, 19, 15)(4, 5, 21, 25)
> (6, 18, 7, 16)(10, 13, 30, 11)(12, 14)(20, 23)(26, 27) >;
> N1 := rep{ o : o in Orbits(Stabilizer(G, 1)) | #o eq 3 };
> tutte := Graph< 30 | <1, N1>^G >;
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