Coxeter polytopes with a unique pair of non-intersecting facets
Metric Geometry
2022-09-13 v2 Combinatorics
Group Theory
Abstract
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d+3 facets. In view of results of Lann\'er, Kaplinskaja, Esselmann, and the second author, this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and in dimension 8.
Keywords
Cite
@article{arxiv.0706.3964,
title = {Coxeter polytopes with a unique pair of non-intersecting facets},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:0706.3964},
year = {2022}
}