We show that the right-angled hyperbolic polyhedra of finite volume in the hyperbolic space may only exist if We also provide a family of such polyhedra of dimensions . We prove that for the members of this family have the minimal total number of hyperfaces and cusps among all hyperbolic right-angled polyhedra of the corresponding dimension. This fact is used in the proof of the main result.
Cite this article
Leonid Potyagailo, Ernest Vinberg, On right-angled reflection groups in hyperbolic spaces. Comment. Math. Helv. 80 (2005), no. 1, pp. 63–73DOI 10.4171/CMH/4