A census of tetrahedral hyperbolic manifolds

Evgeny Fominykh, Stavros Garoufalidis, Matthias Goerner, Vladimir Tarkaev, Andrei Vesnin

Research output

17 Citations (Scopus)


We call a cusped hyperbolic 3-manifold tetrahedral if it can be decomposed into regular ideal tetrahedra. Following an earlier publication by three of the authors, we give a census of all tetrahedral manifolds and all of their combinatorial tetrahedral tessellations with at most 25 (orientable case) and 21 (non-orientable case) tetrahedra. Our isometry classification uses certified canonical cell decompositions (based onwork by Dunfield, Hoffman, and Licata) and isomorphism signatures (an improvement of dehydration sequences by Burton). The tetrahedral census comes in Regina as well as SnapPy format, and we illustrate its features.

Original languageEnglish
Pages (from-to)466-481
Number of pages16
JournalExperimental Mathematics
Issue number4
Publication statusPublished - 1 Jan 2016

Scopus subject areas

  • Mathematics(all)

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