
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.