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 census
All minimal triangulations of all closed orientable prime 3-manifolds
≤ 10 tetrahedra
Tabulated by Burton closed-or-census.rga 699
All minimal triangulations of all closed orientable prime 3-manifolds
≤ 11 tetrahedra (too large to ship with Regina)
closed-or-census-11.rga 1906
All minimal triangulations of all closed non-orientable P2-irreducible 3-manifolds
≤ 11 tetrahedra
closed-nor-census.rga 389
Closed hyperbolic census
Smallest known closed hyperbolic 3-manifolds
3000 orientable, 18 non-orientable
Tabulated by Hodgson and Weeks closed-hyp-census.rga 310
Smallest known closed hyperbolic 3-manifolds
11031 orientable, 18 non-orientable (too large to ship with Regina)
closed-hyp-census-full.rga 1275
Cusped hyperbolic census
All minimal triangulations of all cusped hyperbolic orientable 3-manifolds
≤ 7 tetrahedra
Tabulated by Burton cusped-hyp-or-census.rga 354
All minimal triangulations of all cusped hyperbolic non-orientable 3-manifolds
≤ 7 tetrahedra
cusped-hyp-nor-census.rga 179
All minimal triangulations of all cusped hyperbolic orientable 3-manifolds
≤ 9 tetrahedra (too large to ship with Regina)
cusped-hyp-or-census-9.rga 7902
All minimal triangulations of all cusped hyperbolic non-orientable 3-manifolds
≤ 9 tetrahedra (too large to ship with Regina)
cusped-hyp-nor-census-9.rga 3571
Knot and link complements
All hyperbolic knot complements (≤ 11 crossings) and link complements (≤ 10 crossings) Tabulated by Christy
Shipped with Snap 1.9
hyp-knot-link-census.rga 132

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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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