# On right-angled reflection groups in hyperbolic spaces

@article{Potyagailo2005OnRR,
title={On right-angled reflection groups in hyperbolic spaces},
author={Leonid Potyagailo and {\`E}rnest B. Vinberg},
journal={Commentarii Mathematici Helvetici},
year={2005},
volume={80},
pages={63-73}
}
• Published 31 March 2005
• Mathematics
• 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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