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

2004
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Transactions of the Moscow Mathematical Society
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Noncompact hyperbolic Coxeter n-polytopes of finite volume and having n + 3 facets are studied in this paper. Unlike the spherical and parabolic cases, no complete classification exists as yet for hyperbolic Coxeter polytopes of finite volume. It has been shown that the dimension of a bounded Coxeter polytope is at most 29 (Vinberg, 1984) , while an upper estimate in the unbounded case is 995 (Prokhorov, 1986) . There is a complete classification of simplexes and of Coxeter n-polytopes of

doi:10.1090/s0077-1554-04-00146-3
fatcat:qiegetbtdbamjl4jc5cyabocgy