Compact Hyperbolic Coxeter n-Polytopes with n+3 Facets

We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter npolytopes with n + 3 facets, 4 ≤ n ≤ 7. Combined with results of Esselmann this gives the classification of all compact hyperbolic Coxeter n-polytopes with n + 3 facets, n ≥ 4. Polytopes in dimensions 2 and 3 were classified by Poincar´e and Andreev.

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Pavel Tumarkin
• Keywords: COMBINATORICS 2007, Compact Hyperbolic Coxeter, Computational Ones, Polytopes