Classifying Regular Polyhedra and Polytopes using Wythoff's Construction
Metric Geometry
2021-12-21 v2 Combinatorics
Abstract
Wythoff's construction associates a uniform polytope to a Coxeter diagram whose vertices are decorated with crosses, which indicate the subgroup stabilizing a generic point. Champagne, Kjiri, Patera, and Sharp remarked that by associating more information to a Coxeter diagram, one can furthermore determine the types and number of faces of such a polytope. This article provides a proof of this result, and uses it to provide a classification of the regular polytopes.
Keywords
Cite
@article{arxiv.2001.09364,
title = {Classifying Regular Polyhedra and Polytopes using Wythoff's Construction},
author = {Spencer Whitehead},
journal= {arXiv preprint arXiv:2001.09364},
year = {2021}
}
Comments
16 pages, 6 figures; revision includes more proofs and fixes some definitions