On hyperbolic Coxeter polytopes with mutually intersecting facets
classification
🧮 math.MG
math.COmath.GR
keywords
coxeterhyperbolicpolytopescompactfacetsapartcombinatoricsconcerning
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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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