-t,--tetrahedra=tetrahedra
Specifies the number of top-dimensional simplices used to build the triangulations. For
2-manifolds, 3-manifolds and 4-manifolds, this specifies the number of triangles, tetrahedra or
pentachora respectively.
-2,--dim2
Build a census of 2-manifold triangulations, not 3-manifold triangulations.
This is incompatible with several options; for other options it simply translates the relevant
constraint into two dimensions. See each individual option for details on how it interacts with
--dim2.
This option cannot be used with --dim4.
-4,--dim4
Build a census of 4-manifold triangulations, not 3-manifold triangulations.
This is incompatible with several options; for other options it simply translates the relevant
constraint into four dimensions. See each individual option for details on how it interacts with
--dim4.
This option cannot be used with --dim2.
-b,--boundary
Only produce triangulations with at least one boundary triangle.
For 2-manifolds or 4-manifolds, this option ensures at least one boundary edge or boundary
tetrahedron respectively.
-i,--internal
Only produce triangulations with all triangles internal (i.e., with no boundary triangles).
For 2-manifolds or 4-manifolds, this option ensures that all edges or tetrahedra respectively are
internal.
-B,--bdryfaces=triangles
Only produce triangulations with the precise number of boundary triangles specified.
For 2-manifolds or 4-manifolds, this specifies the number of boundary edges or boundary tetrahedra
respectively.
-o,--orientable
Only produce orientable triangulations.
-n,--nonorientable
Only produce non-orientable triangulations.
-f,--finite
Only produce finite triangulations (triangulations with no ideal vertices).
This option cannot be used with --dim2.
-d,--ideal
Only produce triangulations with at least one ideal vertex. There might or might not be internal
vertices (whose links are spheres) as well.
This option cannot be used with --dim2.
-m,--minimal
Do not include triangulations that are obviously non-minimal.
This option uses a series of fast tests that try to eliminate non-minimal triangulations, but that
are not always conclusive. If Regina cannot quickly tell whether a triangulation is non-minimal,
it will place the triangulation in the census regardless.
This option cannot be used with --dim4.
-M,--minprime
Do not include triangulations that are obviously non-minimal, non-prime and/or disc-reducible.
This can significantly speed up the census and vastly reduce the final number of triangulations
produced.
As above, this option uses a series of fast tests that are not always conclusive. If Regina
cannot quickly tell whether a triangulation is non-minimal, non-prime or disc-reducible, it will
place the triangulation in the census regardless.
This option cannot be used with --dim2 or --dim4.
-N,--minprimep2
Do not include triangulations that are obviously non-minimal, non-prime, P2-reducible and/or disc-
reducible.
This can significantly speed up the census and vastly reduce the final number of triangulations
produced, even more so than --minprime.
As above, this option uses a series of fast tests that are not always conclusive. If Regina
cannot quickly tell whether a triangulation is non-minimal, non-prime, P2-reducible or disc-
reducible, it will place the triangulation in the census regardless.
This option cannot be used with --dim2 or --dim4.
-h,--minhyp
Do not include triangulations that are obviously not minimal ideal triangulations of cusped
finite-volume hyperbolic 3-manifolds.
This can significantly speed up the census and vastly reduce the final number of triangulations
produced.
As above, this option uses a series of fast tests that are not always conclusive. If Regina
cannot quickly tell whether a triangulation is a minimal ideal triangulation of a cusped finite-
volume hyperbolic 3-manifold, it will place the triangulation in the census regardless.
This option is designed for use with ideal triangulations only (so, for instance, combining it
with --finite or --boundary will produce an error message). This option also cannot be used with
--dim2 or --dim4.
-s,--sigs
Instead of writing a full Regina data file, just output a list of isomorphism signatures.
The output file will be a plain text file. Each line will be a short string of letters, digits
and punctuation that uniquely encodes a triangulation up to combinatorial isomorphism. You can
import this text file from within Regina by selecting File->Import->Isomorphism Signature List
from the menu.
This option is highly recommended for large census enumerations. First, the output file will be
considerably smaller. More importantly, the memory footprint of tricensus will also be much
smaller: triangulations can be written to the output file and forgotten immediately, instead of
being kept in memory to construct a final Regina data file.
-c,--subcontainers
For each facet pairing, a new container will be created, and resultant triangulations will be
placed into these containers. These containers will be created even if the facet pairing results
in no triangulations.
See --genpairs below for further information on facet pairings.
This option cannot be used with --sigs.
-p,--genpairs
Only generate facet pairings, not triangulations. A facet pairing stores which facets of top-
dimension simplices are glued to which others, but it does not store the precise rotations and/or
reflections that are used for each gluing. For 3-manifolds a facet pairing represents a pairing
of tetrahedron faces, for 2-manifolds it represents a pairing of triangle edges, and for
4-manifolds it represents a pairing of pentachoron facets.
The outermost layer of the census code involves pairing off the facets of individual top-
dimensional simplices without determining the corresponding gluing permutations. For each such
facet pairing that is produced, Regina will try many different sets of gluing permutations and
generated the corresponding triangulations.
Facet pairing generation consumes a very small fraction of the total census runtime, and
effectively divides the census into multiple pieces. This option allows you to quickly generate a
complete list of possible facet pairings, so that you can feed subsets of this list to different
machines to work on simultaneously.
The list of all facet pairings will be written to the given output file in text format (though you
may omit the output file from the command line, in which case the facet pairings will be written
to standard output). If you are coordinating your sub-censuses manually, you can use the option
--usepairs to generate triangulations from a subset of these facet pairings.
Options for orientability, finiteness or minimality cannot be used with --genpairs; instead you
should use them later with --usepairs.
This option does not come with progress reporting, though typically it runs fast enough that this
does not matter. You can always track the state of progress by counting lines in the output file.
-P,--usepairs
Use only the given subset of facet pairings to build the triangulations.
Each facet pairing that is processed must be in canonical form, i.e., must be a minimal
representative of its isomorphism class. All facet pairings generated using --genpairs are
guaranteed to satisfy this condition.
Facet pairings should be supplied on standard input, one per line. They should be listed in the
format produced by the option --genpairs.
This option effectively lets you run a subset of a larger census. See --genpairs for further
details on how to split a census into subsets that can run simultaneously on different machines.
Options for the number of top-dimensional simplices (i.e., --tetrahedra) or boundary facets (i.e.,
--boundary or --bdryfaces) cannot be used with --usepairs. Instead you should pass these options
earlier along with --genpairs when you split the original census into pieces.
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