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Abstract
A convex polytope admits a Coxeter decomposition if it is tiled by finitely many Coxeter polytopes such that any two tiles having a common facet are symmetric with respect to this facet. In this paper, we classify all Coxeter decompositions of compact hyperbolic Coxeter n-polytopes with n + 2 facets. Furthermore, going out from Schläfli‘s reduction formula for simplices we construct in a purely combinatorial way a volume formula for arbitrary polytopes and compute the volumes of all compact Coxeter polytopes in ℍ4 which are products of simplices.
Received: 2005-07-15
Published Online: 2007-06-18
Published in Print: 2007-04-19
© Walter de Gruyter
