Regina - Supporting Data

Census data Weber-Seifert dodecahedral space Related articles Back to main page ...

Census Data

Here you can download additional census files that are too large to ship with Regina. You can also find the standard files that are shipped, in case you have an older version of Regina that did not include them.

You can open each of these data files directly within Regina. Each file begins with a text packet that describes what the census contains and where the data originally came from.

Census	Origin	Download	Size (kB)
Closed hyperbolic 3-manifolds (3000 orientable, 18 non-orientable)	Tabulated by Hodgson and Weeks, shipped with SnapPea 3.0d3	closed-hyp-census.rga	365
Closed hyperbolic 3-manifolds (10986 orientable, 18 non-orientable; not shipped with Regina due to size constraints)		closed-hyp-census-large.rga	1503
Closed orientable prime minimal triangulations (≤ 9 tetrahedra)	Tabulated by Burton using Regina	closed-or-census.rga	378
Closed orientable prime minimal triangulations (≤ 10 tetrahedra)		closed-or-census-large.rga	687
Closed orientable prime minimal triangulations (≤ 11 tetrahedra; not shipped with Regina due to size constraints)		closed-or-census-11.rga	1848
Closed non-orientable minimal P2-irreducible triangulations (≤ 11 tetrahedra)		closed-nor-census.rga	387
Cusped hyperbolic 3-manifolds (≤ 7 tetrahedra)	Tabulated by Callahan, Hildebrand and Weeks, shipped with SnapPea 3.0d3	snappea-census.rga	214
Hyperbolic knot complements (≤ 11 crossings) and link complements (≤ 10 crossings)	Tabulated by Christy, shipped with Snap 1.9	knot-link-census.rga	132
Splitting surface signatures with enclosing closed 3-manifold triangulations (≤ 7 tetrahedra)	Tabulated by Burton using Regina	sig-3mfd-census.rga	58
Splitting surface signatures with enclosing closed prime minimal 3-manifold triangulations (≤ 8 tetrahedra)		sig-prime-min-census.rga	3

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Weber-Seifert dodecahedral space

• B.B., J. Hyam Rubinstein and Stephan Tillmann, The Weber-Seifert dodecahedral space is non-Haken, Trans. Amer. Math. Soc. 364 (2012), no. 2, 911–932.

Because the proof involves computation, there is a fair amount of supporting data, including the 23-tetrahedron triangulation of the Weber-Seifert dodecahedral space and its 1751 standard vertex normal surfaces. This is stored in a Regina data file, which you can download here:

• Download weber-seifert.rga (162 kb)

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Related Articles

• Normal surface enumeration:
  • B.B., Quadrilateral-octagon coordinates for almost normal surfaces, Experiment. Math. 19 (2010), no. 3, 285 315
  • B.B., Converting between quadrilateral and standard solution sets in normal surface theory, Algebr. Geom. Topol. 9 (2009), no. 4, 2121–2174
  • B.B., Optimizing the double description method for normal surface enumeration, Math. Comp. 79 (2010), no. 269, 453–484
  • B.B., Fundamental normal surfaces and the enumeration of Hilbert bases, Preprint, arXiv:1111.7055, November 2011
  • Jeffrey L. Tollefson, Normal surface Q-theory, Pacific J. Math. 183 (1998), no. 2, 359–374
• Decompositions of manifolds:
  • William Jaco and J. Hyam Rubinstein, 0-efficient triangulations of 3-manifolds, J. Differential Geom. 65 (2003), no. 1, 61–168
• Cellular information and embeddings in S⁴:
  • Ryan Budney, Embeddings of 3-manifolds in S⁴ from the point of view of the 11-tetrahedron census, Preprint, arXiv:0810.2346, October 2008
• Census enumeration:
  • B.B., Detecting genus in vertex links for the fast enumeration of 3-manifold triangulations, in "ISSAC 2011: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation", ACM, 2011, pp. 59–66
  • B.B., Enumeration of non-orientable 3-manifolds using face-pairing graphs and union-find, Discrete Comput. Geom. 38 (2007), no. 3, 527–571
  • B.B., Face pairing graphs and 3-manifold enumeration, J. Knot Theory Ramifications 13 (2004), no. 8, 1057–1101

Burton's PhD thesis contains more detailed descriptions of some of the topological structures, concepts and algorithms used in Regina. You can download it from his website.

This list is by no means complete. For more relevant papers, see the bibliography in the handbook, or Regina's summary article in Experimental Mathematics.

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