M G ] 1 4 O ct 2 00 6 On hyperbolic Coxeter polytopes with mutually intersecting facets

@inproceedings{Felikson2006MG,
  title={M G ] 1 4 O ct 2 00 6 On hyperbolic Coxeter polytopes with mutually intersecting facets},
  author={Anna Felikson and Pavel Tumarkin},
  year={2006}
}
We prove that any compact hyperbolic Coxeter polytope except some well-known low-dimensional examples 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.