A census of tetrahedral hyperbolic manifolds

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.

26 pages, 5 Figures, 2 Tables; version 2 addresses referee's comments, in particular a rewrite of section 5

References in corpus (3)

• The Pachner graph and the simplification of 3-sphere triangulations
• Regular Tessellation Link Complements
• An edge-based framework for enumerating 3-manifold triangulations

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• Enumeration and Identification of Unique 3D Spatial Topologies of Interconnected Engineering Systems Using Spatial Graphs
• Many cusped hyperbolic 3-manifolds do not bound geometrically
• Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds
• Complexity of 3-manifolds obtained by Dehn filling
• Hyperbolic three-manifolds that embed geodesically
• Corks and automorphisms of 3-manifolds
• Links in the spherical 3-manifold obtained from the quaternion group and their lifts
• Complexity of virtual 3-manifolds