Infinite series of combinatorially regular polyhedra in three-space

✍ Scribed by P. McMullen; E. Schulte; J. M. Wills

• Publisher: Springer
• Year: 1988
• Tongue: English
• Weight: 379 KB
• Volume: 26
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00183021

✦ Synopsis

The paper discusses polyhedral realizations in ordinary Euclidean 3-space of Coxeter's regular skew polyhedra {4,pl4 tp/21-1} and their duals on an orientable surface of genus 2 v-3 (p -4) + 1. Our considerations are based on work of Coxeter, Ringel and McMuUen et al., revealing that certain polyhedral manifolds discovered by the last three authors are in fact the polyhedra in question. We also describe Kepler-Poinsot-type polyhedra in 3-space obtained by projections from Coxeter's regular skew star-polyhedra in 4 dimensions.