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The Moscow-Soicher graph is a weakly regular graph on 672 vertices with parameters (nu,k,lambda,mu)=(672,110,28,(0,18)). It is distance-regular but not distance-transitive ...

The biggest little polygon with n sides is the convex plane n-gon of unit polygon diameter having largest possible area. Reinhardt (1922) showed that for n odd, the regular ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

The lines containing the three points of the intersection of the three pairs of opposite sides of a (not necessarily regular) hexagon. There are 6! (i.e., 6 factorial) ...

The Janko-Kharaghani graphs are two strongly regular graph on 936 and 1800 vertices. They have regular parameters (nu,k,lambda,mu)=(936,375,150,150) and (1800,1029,588,588), ...

The Coxeter graph is a nonhamiltonian cubic symmetric graph on 28 vertices and 42 edges which can be constructed as illustrated above. It can also be constructed as the graph ...

A compound of five regular dodecahedra with the symmetry of the icosahedron (Wenninger 1983, pp. 145-147) can be constructed by taking a dodecahedron with top and bottom ...

A number of attractive tetrahedron 6-compounds can be constructed. The first compound (left figures) is obtained by combining three stella octangula. A second can be obtained ...

A cubic symmetric graph is a symmetric cubic (i.e., regular of order 3). Such graphs were first studied by Foster (1932). They have since been the subject of much interest ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...