Hyperbolic Coxeter n-polytopes with n+3 facets

Details Hyperbolic Coxeter n-polytopes with n+3 facets Hyperbolic Coxeter n-polytopes with n+3 facets

2003-11-16

arxiv.org/abs/math/0311272v2

Mathematics

Metric Geometry

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

Scientific paper

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

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