Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

Christopher K. Atkinson

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold S3. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schläfli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.

Original languageEnglish (US)
Pages (from-to)177-211
Number of pages35
JournalGeometriae Dedicata
Issue number1
StatePublished - Aug 2011
Externally publishedYes


  • Hyperbolic geometry
  • Polyhedron
  • Volume


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