Abstract
As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic $n$-space $\mathbf{H}^n$ has at least one cusp for $n\geq 5$. We obtain non-trivial lower bounds on the number of cusps of such polyhedra. For example, right-angled polyhedra of finite volume must have at least three cusps for $n=6$. Our theorem also says that the higher the dimension of a right-angled polyhedron becomes, the more cusps it must have.
Citation
Jun NONAKA. "The Number of Cusps of Right-angled Polyhedra in Hyperbolic Spaces." Tokyo J. Math. 38 (2) 539 - 560, December 2015. https://doi.org/10.3836/tjm/1452806056
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