On hyperbolic Coxeter polytopes with mutually intersecting facets
Abstract
Description
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.
v3: accepted version, updated according to referee's comments. 37 pages, a lot of figures. To appear in J. Combinatorial Theory A
v3: accepted version, updated according to referee's comments. 37 pages, a lot of figures. To appear in J. Combinatorial Theory A