On hyperbolic Coxeter n-polytopes with n + 2 facets

A Felikson, P Tumarkin, T Zehrt
2007 Advances in Geometry  
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
more » ... of all compact Coxeter polytopes in H 4 which are products of simplices.
doi:10.1515/advgeom.2007.011 fatcat:rat2tziut5eafm4ljfnbljm6b4