The special cuts of 600-cell

TL;DR

This paper investigates the class of 4-dimensional regular-faced polytopes derived from the 600-cell by removing non-adjacent vertices, enumerating all such polytopes up to isomorphism.

Contribution

It provides a complete enumeration of the polytopes obtained from the 600-cell by deleting independent vertex sets, expanding understanding of regular-faced polytopes.

Findings

Number of such polytopes is 314,248,344.

All polytopes are obtained by removing non-adjacent vertices.

Enumeration is up to isomorphism.

Abstract

A polytope is called {\em regular-faced} if every one of its facets is a regular polytope. The 4-dimensional regular-faced polytopes were determined by G. Blind and R. Blind \cite{BlBl2,roswitha,roswitha2}. The last class of such polytopes is the one which consists of polytopes obtained by removing a set of non-adjacent vertices (an independent set) of the 600-cell. These independent sets are enumerated up to isomorphism and it is determined that the number of polytopes in this last class is $314,248,344$.