Coxeter polytopes with a unique pair of non-intersecting facets
- Felikson, Anna Independent University of Moscow, Russia
- Tumarkin, Pavel Department of Mathematics, University of Fribourg, Switzerland
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19.12.2008
Published in:
- Journal of Combinatorial Theory, Series A. - 2009, vol. 116, no. 4, p. 875-902
English
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 up to dimension 6 and in dimension 8.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 12557
- DOI 10.1016/j.jcta.2008.10.008
- Persistent URL
- https://folia.unifr.ch/unifr/documents/301259
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