A census of tetrahedral hyperbolic manifolds

TL;DR

This paper provides a comprehensive census of tetrahedral hyperbolic 3-manifolds, classifying all such manifolds with up to 25 tetrahedra, using advanced computational tools and canonical decompositions.

Contribution

It offers the first complete census of tetrahedral hyperbolic 3-manifolds with explicit classifications and improved isometry detection methods.

Findings

Catalog of all tetrahedral hyperbolic 3-manifolds up to 25 tetrahedra

Implementation of certified canonical cell decompositions for classification

Availability of census data in Regina and SnapPy formats

Abstract

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 on work by Dunfield, Hoffman, 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.