Compact hyperbolic Coxeter n-polytopes with n+3 facets

Abstract

We use methods of combinatorics of polytopes together with geometrical and computational ones to obtain the complete list of compact hyperbolic Coxeter n-polytopes with n+3 facets, 3<n<8. Combined with results of Esselmann (1994), Andreev (1970) and Poincare (1882) this gives the classification of all compact hyperbolic Coxeter n-polytopes with n+3 facets.

v4: paper is rewritten. Complete proofs added, errors corrected. 36 pages, a lot of figures

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