On hyperbolic Coxeter polytopes with mutually intersecting facets |
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Authors: | Anna Felikson |
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Affiliation: | Independent University of Moscow, B. Vlassievskii 11, 119002 Moscow, Russia |
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Abstract: | We prove that, apart from some well-known low-dimensional examples, any compact hyperbolic Coxeter polytope has a pair of disjoint facets. This is one of very few known general results concerning combinatorics of compact hyperbolic Coxeter polytopes. We also obtain a similar result for simple non-compact polytopes. |
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Keywords: | Coxeter polytope Missing face Gale diagram Simple polytope |
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