
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 3manifolds (3000 orientable, 18 nonorientable)  Tabulated by Hodgson and Weeks, shipped with SnapPea 3.0d3  closedhypcensus.rga  365 
Closed hyperbolic 3manifolds (10986 orientable, 18 nonorientable; not shipped with Regina due to size constraints)  closedhypcensuslarge.rga  1503  
Closed orientable prime minimal triangulations (≤ 9 tetrahedra)  Tabulated by Burton using Regina  closedorcensus.rga  378 
Closed orientable prime minimal triangulations (≤ 10 tetrahedra)  closedorcensuslarge.rga  687  
Closed orientable prime minimal triangulations (≤ 11 tetrahedra; not shipped with Regina due to size constraints)  closedorcensus11.rga  1848  
Closed nonorientable minimal P^{2}irreducible triangulations (≤ 11 tetrahedra)  closednorcensus.rga  387  
Cusped hyperbolic 3manifolds (≤ 7 tetrahedra)  Tabulated by Callahan, Hildebrand and Weeks, shipped with SnapPea 3.0d3  snappeacensus.rga  214 
Hyperbolic knot complements (≤ 11 crossings) and link complements (≤ 10 crossings)  Tabulated by Christy, shipped with Snap 1.9  knotlinkcensus.rga  132 
Splitting surface signatures with enclosing closed 3manifold triangulations (≤ 7 tetrahedra)  Tabulated by Burton using Regina  sig3mfdcensus.rga  58 
Splitting surface signatures with enclosing closed prime minimal 3manifold triangulations (≤ 8 tetrahedra)  sigprimemincensus.rga  3 
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.