On right-angled reflection groups in hyperbolic spaces

  title={On right-angled reflection groups in hyperbolic spaces},
  author={Leonid Potyagailo and {\`E}rnest B. Vinberg},
  journal={Commentarii Mathematici Helvetici},
We show that the right-angled hyperbolic polyhedra of finite volume in the hyperbolic space $\Bbb H^n$ may only exist if $n\leq 14.$ We also provide a family of such polyhedra of dimensions $n=3,4,...,8$. We prove that for $n=3,4$ 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 

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