منابع مشابه
On hyperbolic Coxeter n-cubes
Beside simplices, n-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n-cubes are not classified. In this work, we first show that there are no Coxeter n-cubes in H for n ≥ 10. Then, we show that the ideal ones exist only for n = 2 and 3, and provide a classification. The methods used are of combinatorial and algebraic nature, using prope...
متن کاملCompact 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...
متن کاملHyperbolic Coxeter N-polytopes with N + 2 Facets
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 کاملEssential Hyperbolic Coxeter Polytopes
We introduce a notion of essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimens...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2018
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.04.001