2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143642We 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 AMetric GeometryCombinatoricsGroup Theory51F15; 51M20; 20F55text