1. Hyperbolic Coxeter n-polytopes with n+3 facets
- Author
-
P. Tumarkin
- Subjects
Mathematics::Combinatorics ,Coxeter notation ,Coxeter group ,Uniform polytope ,Uniform k 21 polytope ,Metric Geometry (math.MG) ,Point group ,Combinatorics ,Mathematics::Group Theory ,Mathematics (miscellaneous) ,Mathematics - Metric Geometry ,Coxeter complex ,FOS: Mathematics ,Mathematics::Metric Geometry ,Coxeter element ,Regular polytope ,Mathematics - Abstract
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., Comment: 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
- Published
- 2003