Regular Polyhedra of Index Two, II
Metric Geometry
2010-11-15 v1 Combinatorics
Abstract
A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular and its geometric symmetry group has index 2 in its combinatorial automorphism group; thus its automorphism group is flag-transitive but its symmetry group has two flag orbits. The present paper completes the classification of finite regular polyhedra of index 2 in 3-space. In particular, this paper enumerates the regular polyhedra of index 2 with vertices on one orbit under the symmetry group. There are ten such polyhedra.
Keywords
Cite
@article{arxiv.1011.3034,
title = {Regular Polyhedra of Index Two, II},
author = {Anthony M. Cutler},
journal= {arXiv preprint arXiv:1011.3034},
year = {2010}
}
Comments
33 pages; 5 figures; to appear in "Contributions to Algebra and Geometry"