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 Schlafli'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.
展开▼
