On hyperbolic Coxeter polytopes with mutually intersecting facets
Metric Geometry
2007-12-06 v3 Combinatorics
Group Theory
Abstract
We prove that, apart from some well-known low-dimensional examples, any compact hyperbolic Coxeter polytope has a pair of disjoint facets. This is one of very few known general results concerning combinatorics of compact hyperbolic Coxeter polytopes. We also obtain a similar result for simple non-compact polytopes.
Cite
@article{arxiv.math/0604248,
title = {On hyperbolic Coxeter polytopes with mutually intersecting facets},
author = {Anna Felikson and Pavel Tumarkin},
journal= {arXiv preprint arXiv:math/0604248},
year = {2007}
}
Comments
v3: accepted version, updated according to referee's comments. 37 pages, a lot of figures. To appear in J. Combinatorial Theory A