Regina - Supporting Data

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

Census Data

Typically you will not need to download any of these files separately. You can find them by:

• running Regina and looking in the File->Open Example menu, or
• looking in /usr/share/regina/examples/ (this location might differ for some installations or GNU/Linux distributions), or
• downloading Regina's source code and looking in the examples/ subdirectory.

On this page you can find some additional census data files that are too large to ship with Regina. You can also find the usual data files that are normally shipped, which may help users with stripped-down installations or older versions of Regina that did not include them.

Each data file includes a text packet containing a full description of the census as well as its origin and literary references where appropriate. Data from external sources (such as the hyperbolic census data shipped with SnapPea) have been converted into Regina data files.

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 (see the notes below)	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
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
All splitting surface signatures (order <= 8). These are plain text files containing signatures only. Note that only order <= 7 is shipped with Regina due to size constraints. Files for order >= 7 are bzipped; the bzip2 utility can be used to uncompress them.		1.sig	0.007
		2.sig	0.03
		3.sig	0.2
		4.sig	1
		5.sig	8
		6.sig	86
		7.sig.bz2	188
		8.sig.bz2	2572

Notes:

• Closed orientable census: Other authors (Matveev, Ovchinnikov, Martelli and Petronio) were the first to construct censuses of closed orientable manifolds. Regina's census extends these results by enumerating all minimal triangulations of these manifolds.
• Closed non-orientable census: Amendola and Martelli independently formed a census of closed non-orientable manifolds of up to 7 tetrahedra, around the same time as Regina's 7-tetrahedron census was released in 2003. Regina's non-orientable census has since been extended to 11 tetrahedra.

Where Regina's censuses overlap those of the authors listed above, the results agree completely.

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Weber-Seifert dodecahedral space

• B.B., J. Hyam Rubinstein and Stephan Tillmann, The Weber-Seifert dodecahedral space is non-Haken, Preprint, arXiv:0909.4625, September 2009

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 and PhD Thesis

• Normal surface enumeration:
  • B.B., Quadrilateral-octagon coordinates for almost normal surfaces, To appear in Experiment. Math., arXiv:0904.3041, April 2009
  • B.B., Converting between quadrilateral and standard solution sets in normal surface theory, To appear in Algebr. Geom. Topol., arXiv:0901.2629, January 2009
  • B.B., Optimizing the double description method for normal surface enumeration, Math. Comp. 79 (2010), no. 269, 453–484
  • 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., 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

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.

The author's PhD thesis contains detailed descriptions of some of the topological structures, concepts and algorithms used in Regina. It can be downloaded in either of the following formats.

• PDF (1.8 Mb)
• Gzipped Postscript (1.1 Mb)

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