Regina - Supporting Data

Census data
Weber-Seifert dodecahedral space
Related articles
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Census Data

Regina ships with several different censuses of triangulations. You can access most of these censuses by selecting File → Open Example from Regina's main menu.

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

The Weber-Seifert dodecahedral space was one of the first-known examples of a hyperbolic 3-manifold, and Thurston conjectured around 1980 that this space was non-Haken. A proof was obtained in 2009 using a blend of theory and computation, and the details can be found in the following paper:

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:

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Related Articles

The following papers describe some of the algorithms that Regina implements.

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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