Compact Hyperbolic Coxeter n-Polytopes with n+3 Facets
نویسنده
چکیده
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 Andreev.
منابع مشابه
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 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 کاملM ay 2 00 7 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 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 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 کاملJu n 20 07 Coxeter polytopes with a unique pair of non - intersecting facets
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d + 3 facets. In view of [L], [K], [E2], and [T], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only up to dimension 6 and ...
متن کاملCoxeter polytopes with a unique pair of non-intersecting facets
We consider compact hyperbolic Coxeter polytopes whose Coxeter diagram contains a unique dotted edge. We prove that such a polytope in d-dimensional hyperbolic space has at most d + 3 facets. In view of results by Kaplinskaja [I.M. Kaplinskaya, Discrete groups generated by reflections in the faces of simplicial prisms in Lobachevskian spaces, Math. Notes 15 (1974) 88–91] and the second author [...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007