Hyperbolic Coxeter $n$-polytopes with $n+3$ facets
نویسندگان
چکیده
منابع مشابه
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 Poincaré and And...
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In this paper, we classify all the hyperbolic non-compact Coxeter polytopes of finite volume combinatorial type of which is either a pyramid over a product of two simplices or a product of two simplices of dimension greater than one. Combined with results of Kaplinskaja [5] and Esselmann [3] this completes the classification of hyperbolic Coxeter n-polytopes of finite volume with n + 2 facets.
متن کاملHYPERBOLIC COXETER n-POLYTOPES WITH n+ 3 FACETS
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 (Pr...
متن کاملCoxeter 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 n-polytopes with n + 3 facets, 4 ≤ n ≤ 7. Combined with results of Esselmann [E1] 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 Poincaré [...
متن کامل. M G ] 1 1 Ju n 20 04 Hyperbolic Coxeter n - polytopes with n + 3 facets
A polytope is called a Coxeter polytope if its dihedral angles are integer parts of π. In this paper we prove that if a noncompact Coxeter polytope of finite volume in IH has exactly n+3 facets then n ≤ 16. We also find an example in IH and show that it is unique. 1. Consider a convex polytope P in n-dimensional hyperbolic space IH. A polytope is called a Coxeter polytope if its dihedral angles...
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ژورنال
عنوان ژورنال: Transactions of the Moscow Mathematical Society
سال: 2004
ISSN: 0077-1554,1547-738X
DOI: 10.1090/s0077-1554-04-00146-3