The growth rates of ideal coxeter polyhedra in hyperbolic 3-space

Jun Nonaka, Ruth Kellerhals

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In [7], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by compact hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture holds in the context of ideal Coxeter polyhedra in H3. Our methods allow us to bound from below the growth rates of composite ideal Coxeter polyhedra by the growth rates of its ideal Coxeter polyhedral constituents.

Original languageEnglish
Pages (from-to)379-391
Number of pages13
JournalTokyo Journal of Mathematics
Issue number2
Publication statusPublished - 2017 Dec


  • Cusp
  • Growth rate
  • Hyperbolic Coxeter polyhedron
  • Perron number

ASJC Scopus subject areas

  • Mathematics(all)


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