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DOI: 10.4230/LIPIcs.SoCG.2026.73

The Complete 10-Tetrahedra Census of Orientable Cusped Hyperbolic 3-Manifolds

Authors: Shana Yunsheng Li

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

We extend the complete census of orientable cusped hyperbolic 3-manifolds to 10 tetrahedra, giving the next 150,730 manifolds and their 496,638 minimal ideal triangulations. As applications, we find the precisely 439,898 exceptional Dehn fillings on them, revealing the next 1,849 simplest hyperbolic knot exteriors in S³. We also give the simplest example of an orientable cusped hyperbolic 3-manifold containing a closed totally geodesic surface.

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Shana Yunsheng Li. The Complete 10-Tetrahedra Census of Orientable Cusped Hyperbolic 3-Manifolds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{li:LIPIcs.SoCG.2026.73,
  author =	{Li, Shana Yunsheng},
  title =	{{The Complete 10-Tetrahedra Census of Orientable Cusped Hyperbolic 3-Manifolds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{73:1--73:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.73},
  URN =		{urn:nbn:de:0030-drops-258800},
  doi =		{10.4230/LIPIcs.SoCG.2026.73},
  annote =	{Keywords: hyperbolic manifolds, 3-manifolds, triangulation, census, tabulation, exact computation, computational topology, low-dimensional topology}
}

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The Complete 10-Tetrahedra Census of Orientable Cusped Hyperbolic 3-Manifolds

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