
The tables are plain text CSV (commaseparated 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 habcadebcfgedgfvvbZa. Knot signatures uniquely identify a diagram on the 2sphere 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 DowkerThistlethwaite (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 DowkerThistlethwaite 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 righthand 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 Benjamin A. Burton, “The next 350 million knots”, which should appear on the arXiv in June 2018.
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  
nonalternating  1 knot  —  2 knots  
9  alternating  1 knot  —  40 knots  
nonalternating  —  —  8 knots  
10  alternating  —  —  123 knots  
nonalternating  1 knot  —  41 knots  
11  alternating  1 knot  —  366 knots  
nonalternating  —  —  185 knots  
12  alternating  —  —  1,288 knots  
nonalternating  —  —  888 knots  
13  alternating  1 knot  —  4,877 knots  
nonalternating  —  2 knots  5,108 knots  
14  alternating  —  —  19,536 knots  
nonalternating  1 knot  2 knots  27,433 knots  
15  alternating  1 knot  —  85,262 knots  (1.6 MB) 
nonalternating  1 knot  6 knots  168,023 knots  (4.0 MB)  
16  alternating  —  —  379,799 knots  (7.9 MB) 
nonalternating  1 knot  10 knots  1,008,895 knots  (27 MB)  
17  alternating  1 knot  —  1,769,978 knots  (41 MB) 
nonalternating  —  29 knots  6,283,385 knots  (184 MB)  
18  alternating  —  —  8,400,285 knots  (215 MB) 
nonalternating  —  86 knots  39,866,095 knots  (1.3 GB)  
19  alternating  1 knot  —  40,619,384 knots  (1.1 GB) 
nonalternating  —  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 3manifolds ≤ 10 tetrahedra 
Tabulated by Burton  closedorcensus.rga  699 
All minimal triangulations of all closed orientable
prime 3manifolds ≤ 11 tetrahedra (too large to ship with Regina) 
closedorcensus11.rga  1906  
All minimal triangulations of all closed nonorientable
P^{2}irreducible 3manifolds ≤ 11 tetrahedra 
closednorcensus.rga  389  
Closed hyperbolic census  
Smallest known closed hyperbolic 3manifolds 3000 orientable, 18 nonorientable 
Tabulated by Hodgson and Weeks  closedhypcensus.rga  310 
Smallest known closed hyperbolic 3manifolds 11031 orientable, 18 nonorientable (too large to ship with Regina) 
closedhypcensusfull.rga  1275  
Cusped hyperbolic census  
All minimal triangulations of all cusped hyperbolic
orientable 3manifolds ≤ 7 tetrahedra 
Tabulated by Burton  cuspedhyporcensus.rga  354 
All minimal triangulations of all cusped hyperbolic
nonorientable 3manifolds ≤ 7 tetrahedra 
cuspedhypnorcensus.rga  179  
All minimal triangulations of all cusped hyperbolic
orientable 3manifolds ≤ 9 tetrahedra (too large to ship with Regina) 
cuspedhyporcensus9.rga  7902  
All minimal triangulations of all cusped hyperbolic
nonorientable 3manifolds ≤ 9 tetrahedra (too large to ship with Regina) 
cuspedhypnorcensus9.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 
hypknotlinkcensus.rga  132 
Because the proof involves computation, there is a fair amount of supporting data, including the 23tetrahedron triangulation of the WeberSeifert dodecahedral space and its 1751 standard vertex normal surfaces. This is stored in a Regina data file, which you can download here:
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.