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{\bf Pavel Tumarkin}
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{\bf Compact Hyperbolic Coxeter $n$-Polytopes with $n+3$ Facets}
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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, $4\le n\le 7$.
Combined with results of Esselmann this gives the classification of
all compact hyperbolic Coxeter $n$-polytopes with $n+3$ facets, $n\ge
4$. Polytopes in dimensions $2$ and $3$ were classified by Poincar\'e
and Andreev.
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