The number of cusps of right-angled polyhedra in hyperbolic spaces

Jun Nonaka*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


As was pointed out by Nikulin [8] and Vinberg [10], a right-angled polyhedron of finite volume in the hyperbolic n-space Hn has at least one cusp for n ≥ 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.

Original languageEnglish
Pages (from-to)539-560
Number of pages22
JournalTokyo Journal of Mathematics
Issue number2
Publication statusPublished - 2015 Dec


  • Combinatorics
  • Cusp
  • Hyperbolic space
  • Right-angled polyhedron

ASJC Scopus subject areas

  • Mathematics(all)


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