Non-flat regular polytopes and restrictions on chiral polytopes
Combinatorics
2017-06-06 v1
Abstract
An abstract polytope is \emph{flat} if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures. We then determine the three smallest non-flat regular polytopes in each rank, and use this to show that for , a chiral -polytope has at least flags.
Keywords
Cite
@article{arxiv.1706.00940,
title = {Non-flat regular polytopes and restrictions on chiral polytopes},
author = {Gabe Cunningham},
journal= {arXiv preprint arXiv:1706.00940},
year = {2017}
}