The interlacing number for alternating semiregular polytopes

Authors

DOI:

https://doi.org/10.26493/2590-9770.1406.ec5

Keywords:

Abstract semiregular polytopes, tail-triangle C-groups

Abstract

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?

Published

2022-08-05

Issue

Section

The Marston Conder Issue of ADAM