Coxeter polytopes with a unique pair of non-intersecting facets

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Felikson, Anna¹  Tumarkin, Pavel² 

[1] Independent Univ Moscow, Moscow 119002, Russia

[2] Univ Fribourg, Dept Math, CH-1700 Fribourg, Switzerland

关键词: Coxeter polytope;    Missing face;    Simple polytope;    Coxeter diagram;   

DOI  :  10.1016/j.jcta.2008.10.008

来源: Elsevier

【 摘 要 】

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 [P. Tumarkin, Compact hyperbolic Coxeter n-polytopes with n + 3 facets, Electron. J. Combin. 14 (2007), R69. 36 pp.], this implies that compact hyperbolic Coxeter polytopes with a unique pair of non-intersecting facets are completely classified. They do exist only tip to dimension 6 and in dimension 8. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free