English

Hyperbolic Coxeter n-polytopes with n+3 facets

Metric Geometry 2019-10-30 v2

Abstract

A polytope is called a Coxeter polytope if its dihedral angles are integer parts of π\pi. In this paper we prove that if a non-compact Coxeter polytope of finite volume in HnH^n has exactly n+3n+3 facets then n16n\le 16. We also find an example in H16H^{16} and show that it is unique.

Keywords

Cite

@article{arxiv.math/0311272,
  title  = {Hyperbolic Coxeter n-polytopes with n+3 facets},
  author = {Pavel Tumarkin},
  journal= {arXiv preprint arXiv:math/0311272},
  year   = {2019}
}

Comments

This is the short version (3 pages) published in Russian Math. Surveys, 58 (2003). The full version will appear in Trans. Moscow Math. Soc., 2004