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If you want more, then here you can download the tables of all 352,152,252 prime non-trivial knots with up to 19 crossings.
The tables are plain text CSV (comma-separated value) files which you can load into a spreadsheet and/or process with a text editor, and have been compressed with bzip2. The fields include:
name: The name of the knot, using a naming scheme specific to these tables. An example name is 12nh_137. In general the name is of the form c[an][tsh]_k, where:
The torus and satellite knots are sorted according to their structure. The hyperbolic knots are sorted roughly by volume, but take care—although the distinctness and hyperbolicity of the knots are proven using exact computation, the final sorting order is based on approximate volume computation only.
knot_sig: The knot diagram, expressed as a native Regina knot signature. An example signature (for the knot 7ah_5) is habcadebcfgedgfvvb-Za. Knot signatures uniquely identify a diagram on the 2-sphere up to relabelling and/or reflection. In Regina 5.2 or later you can reconstruct a knot from a signature through the GUI, or by calling Link.fromKnotSig() in python.
dt_code: The knot diagram, expressed as an alphabetical Dowker-Thistlethwaite (DT) code An example DT code (again for the knot 7ah_5) is fdgeacb.
dt_name: Identifies the knot in other online databases such as Knotinfo and Knotscape (this field only appears in the tables for ≤ 12 crossings). This field uses the Dowker-Thistlethwaite naming convention, where knots are numbered according to their minimal DT codes.
structure: Gives the full structure of a torus or satellite knot (this field does not appear in the hyperbolic tables). An example is Trefoil[-3/2], indicating a satellite formed by inserting the rational tangle -3/2 into the double of the right-hand trefoil. See the paper below for a full explanation of what the various structure descriptions mean.
Citation: If you wish to cite this data, please reference:
Download all 3–12 crossing knots at once (56 kB)
Download all 13–16 crossing knots at once (41 MB)
Download individual tables (up to 19 crossings) below:
| Crossings | Torus | Satellite | Hyperbolic | ||
|---|---|---|---|---|---|
| 3 | alternating | 1 knot | — | — | |
| 4 | alternating | — | — | 1 knot | |
| 5 | alternating | 1 knot | — | 1 knot | |
| 6 | alternating | — | — | 3 knots | |
| 7 | alternating | 1 knot | — | 6 knots | |
| 8 | alternating | — | — | 18 knots | |
| non-alternating | 1 knot | — | 2 knots | ||
| 9 | alternating | 1 knot | — | 40 knots | |
| non-alternating | — | — | 8 knots | ||
| 10 | alternating | — | — | 123 knots | |
| non-alternating | 1 knot | — | 41 knots | ||
| 11 | alternating | 1 knot | — | 366 knots | |
| non-alternating | — | — | 185 knots | ||
| 12 | alternating | — | — | 1,288 knots | |
| non-alternating | — | — | 888 knots | ||
| 13 | alternating | 1 knot | — | 4,877 knots | |
| non-alternating | — | 2 knots | 5,108 knots | ||
| 14 | alternating | — | — | 19,536 knots | |
| non-alternating | 1 knot | 2 knots | 27,433 knots | ||
| 15 | alternating | 1 knot | — | 85,262 knots | (1.6 MB) |
| non-alternating | 1 knot | 6 knots | 168,023 knots | (4.0 MB) | |
| 16 | alternating | — | — | 379,799 knots | (7.9 MB) |
| non-alternating | 1 knot | 10 knots | 1,008,895 knots | (27 MB) | |
| 17 | alternating | 1 knot | — | 1,769,978 knots | (41 MB) |
| non-alternating | — | 29 knots | 6,283,385 knots | (184 MB) | |
| 18 | alternating | — | — | 8,400,285 knots | (215 MB) |
| non-alternating | — | 86 knots | 39,866,095 knots | (1.3 GB) | |
| 19 | alternating | 1 knot | — | 40,619,384 knots | (1.1 GB) |
| non-alternating | — | 245 knots | 253,510,828 knots | (8.7 GB) | |
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 | 848 |
| 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 | 537 | |
| 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 | |||
| Christy's collection of knot complements (≤ 11 crossings) and link complements (≤ 10 crossings) | Collected by Christy Shipped with Snap 1.9 |
hyp-knot-link-census.rga | 132 |
In older versions of Regina, Christy's collection used to be called “hyperbolic knot / link complements”; however, it also contains some (but not all) non-hyperbolic cases. It also contains the duplicate Perko pair.
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: