On hyperbolic Coxeter polytopes with mutually intersecting facets

Details On hyperbolic Coxeter polytopes with mutually intersecting facets On hyperbolic Coxeter polytopes with mutually intersecting facets

2006-04-11

arxiv.org/abs/math/0604248v3

J. Combin. Theory A 115 (2008), 121--146

Mathematics

Metric Geometry

v3: accepted version, updated according to referee's comments. 37 pages, a lot of figures. To appear in J. Combinatorial Theor

Scientific paper

10.1016/j.jcta.2007.04.006

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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