The interlacing number for alternating semiregular polytopes
In the classical setting, a convex polytope is said to be semiregular if its facets are regular and its symmetry group is transitive on vertices. This paper continues our study of ‘alternating’ semiregular abstract polytopes. These structures have abstract regular facets, still with combinatorial automorphism group transitive on vertices and with two kinds of regular facets occurring in an alternating fashion. Here we investigate a parameter called the interlacing number k for a compatible pair of regular n-polytopes P and Q: in what circumstances can we have k copies each of P and Q occuring in alternating fashion as the facets of a semiregular (n+1)-polytope S?