# Command Line: Specialised Utilities

The main applications `regina-gui` and `regina-python` are documented in the previous chapter. This chapter documents the more specialised command-line utilities that ®ina; provides.

censuslookup

1

censuslookup

Search for triangulations in ®ina;'s census databases

        censuslookup
        isosig

### Description

This utility searches for the given 3-manifold triangulations in the various census databases that are shipped with®ina;.

You should present the trianguations using their isomorphism signatures. These are short text strings that identify the triangulation uniquely up to combinatorial isomorphism (i.e., up to relabellings of the tetrahedra and/or their vertices).

From the graphical user interface, you can view the isomorphism signature of a triangulation by switching to the Composition tab in the triangulation viewer. From &python; you can fetch the isomorphism signature of the triangulation `x` by calling `x.isoSig()`. For a full and precise specification of isomorphism signatures, see Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations, Burton, 2011, arXiv:1110.6080.

All database matches (if any) will be written to standard output.

### Example

        example$ censuslookup fvPQcdecedekrsnrs dLQbcccajqs cPcbbbiht
        fvPQcdecedekrsnrs: 1 hit
            SFS [S2: (2,1) (3,1) (5,-4)] : #1 -- Closed census (orientable)

        dLQbcccajqs: 0 hits

        cPcbbbiht: 2 hits
            m004 : #1 -- Cusped hyperbolic census (orientable)
            L104001 -- Hyperbolic knot and link complements

        example$

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/censuslookup`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\censuslookup.exe`.

### See Also

regina-gui. trisetcmp,

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

regconcat

1

regconcat

Combine several ®ina; data files

        regconcat
        -o output-file
        input-file

### Description

This utility combines several individual ®ina; data files into a single larger data file. The new file will have a container as its top-level packet, and beneath this container will be the packet trees from each of the input files that you supply.

If an output file is specified through option `-o`, the new file will be written as compressed &xml; to this output file. Otherwise the new file will be written as uncompressed &xml; to standard output.

### Options

`-o` `output-file`

- Specifies that the new combined data file should be written as compressed &xml; to the given output file.

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/regconcat`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\regconcat.exe`.

### See Also

regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

regconvert

1

regconvert

Convert between different ®ina; file formats

        regconvert

         -x
         -u

        old-file
        new-file

### Description

This utility converts back and forth between different ®ina; file formats.

As of September 2013, the ancient binary file format that was used with ®ina; 2.x is no longer supported. This format has not been in use for over a decade now. If you still have files in this format, you will need to download ®ina; 4.93 to convert them.

The argument `old-file` should be the file to read and convert; the argument `new-file` should be the name of the new converted file to write. These two filenames may be the same, in which case the old file will be replaced with the new.

If the argument `new-file` is missing then the new file will be written to standard output, which forces the output to be uncompressed &xml; (see option `-u`).

### Options

`-x` (default)

- Convert to compressed &xml;.

`-u`

- Convert to plain (uncompressed) &xml;.

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/regconvert`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\regconvert.exe`.

### See Also

regfiletype, regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

regfiledump

1

regfiledump

Dump the contents of a ®ina; data file

        regfiledump

         -f
         -l
         -n

        -c
        file
        packet-label

### Description

This utility dumps the contents of the given ®ina; data file to standard output in a human-readable format.

If a list of packet labels is given on the command-line, only those packets will be output. Otherwise all packets in the given file will be output.

### Options

`-f` (default)

- Output full packet details. The output for each packet will cover several lines, beginning with basic details (such as the packet label and type) followed by the packet's long description.

`-l`

- Output a list of packet labels and types only, one packet per line.

`-n`

- Don't output any packets at all; this option forces a packet count (see option `-c`).

`-c`

- Finish the output with a total count of all packets in the file.

&submani18n;

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/regfiledump`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\regfiledump.exe`.

### See Also

regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

regfiletype

1

regfiletype

Identify the formats of ®ina; data files

        regfiletype
        file

### Description

This utility determines which file format a given ®ina; data file is in. You may pass multiple files on the command line; the format of each file will be written to standard output.

Only ®ina;'s modern &xml;-based file formats are recognised (both compressed and uncompressed). In its very early years, ®ina; used an impenetrable and undocumented binary format; this was replaced with &xml; in 2002 (®ina; 3.0), and support for this format was removed completely in 2013 (®ina; 4.94). If you still need to recognise and/or read files in this ancient binary format, you will need to download ®ina; 4.93.

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/regfiletype`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\regfiletype.exe`.

### See Also

regconvert, regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

retriangulate

1

retriangulate

Exhaustively retriangulate a given manifold

        retriangulate
        -h, --height=height
        -t, --threads=threads
        -4, --dim4
        isosig

        retriangulate
        --help

### Description

Given a 3-manifold or 4-manifold triangulation, this utility uses Pachner moves to exhaustively search for other triangulations of the same manifold that are the same size or smaller.

Specifically, suppose the input triangulation contains `n` tetrahedra (for a 3-manifold) or pentachora (for a 4-manifold). Then this utility will exhaustively retriangulate the manifold using repeated Pachner moves, without ever exceeding `n` + `height` tetrahedra/pentachora in total. Moreover, all such retriangulations are guaranteed to be found, each once and only once.

For 3-manifold triangulations, this utility will only attempt 2-3 and 2-3 Pachner moves, never 1-4 or 4-1 moves. For 4-manifold triangulations, all types of Pachner moves are used (1-5, 2-4, 3-3, 4-2, and 5-1).

The program will output each triangulation that it finds of the same size `n` (including the original input triangulation). If it ever finds a smaller triangulation (thereby proving the original to be non-minimal), it will output that smaller triangulation and then stop immediately. Otherwise it will continue outputting triangulations of size `n` until no more can be found. Although the program also finds larger triangulations as part of its exhaustive search using Pachner moves, these larger triangulations (of which there are typically many) will not be output at all.

All triangulations, both input and output, are described using isomorphism signatures. These are short text strings that identify a triangulation uniquely up to combinatorial isomorphism (i.e., up to relabellings of the tetrahedra/pentachora and their vertices). The input triangulation will be interpreted as the isomorphism signature of a 3-manifold unless you pass the option `--dim4` (in which case it will be treated as a 4-manifold instead).

From ®ina;'s graphical user interface, you can view the isomorphism signature of a triangulation by switching to the Composition tab in the triangulation viewer. From &python; you can fetch the isomorphism signature of the triangulation `x` by calling `x.isoSig()`. For a full and precise specification of isomorphism signatures for 3-manifolds, see Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations, Burton, 2011, arXiv:1110.6080.

### Options

`-h, --height=``height`

- Specifies the number of additional tetrahedra (for a 3-manifold) or pentachora (for a 4-manifold) that we allow during intermediate stages of retriangulation. That is, if the input triangulation has `n` tetrahedra (or pentachora), then this utility will exhaustively search through all triangulations that it can reach via Pachner moves that do not exceed `n` + `height` tetrahedra (or pentachora) in total.

  Note that these larger intermediate triangulations will not be written to output; however, a larger height may allow the program to access additional smaller triangulations that were otherwise inaccessible.

  The given height must be positive, and for 4-manifolds it must also be even. If not specified, this option defaults to 1 for 3-manifolds (if `--dim4` is not passed), or 2 for 4-manifolds (if `--dim4` is passed).

  In general, the running time can grow superexponentially with `height`. It is strongly suggested that you begin with `--height=1` (or 2 for 4-manifolds) and increase it one step at a time until the performance becomes unacceptable.

`-t, --threads=``threads`

- Specifies the degree to which this utility uses parallel processing. Specifically, this program will use `threads` simultaneous threads of execution as it works its way through the different retriangulations of the input manifold.

  This program is typically able to use parallelism effectively, and so running with `k` threads should approximately divide the running time by `k`.

  If not specified, this option defaults to 1 (i.e., single-threaded processing, with no parallelism).

`-4, --dim4`

- Indicates that the given isomorphism signature describes a 4-manifold triangulation. If this argument is not given, then by default the argument is assumed to describe a 3-manifold triangulation.

### Examples

The 3-manifold triangulation is non-minimal, but it requires a bit of work to see this:

        example$ retriangulate -h2 hLLAAkbdceefggdonxdjxn
        hLLAAkbdceefggdonxdjxn
        hLALPkbcbefgfghxwnxark
        Found 2 triangulation(s).
        example$ retriangulate -h3 hLLAAkbdceefggdonxdjxn
        hLLAAkbdceefggdonxdjxn
        hLALPkbcbefgfghxwnxark
        hLLMMkbcdfefgglcghtchj
        gLLPQcdcefffqsjpunw
        Triangulation is non-minimal!
        Smaller triangulation: gLLPQcdcefffqsjpunw
        example$

Although the program stopped as soon as it found a smaller triangulation, this can be simplified even further:

        example$ retriangulate gLLPQcdcefffqsjpunw
        gLLPQcdcefffqsjpunw
        fLAMcbbcdeedhwhxn
        Triangulation is non-minimal!
        Smaller triangulation: fLAMcbbcdeedhwhxn
        example$

A little more probing shows this to be the cusped hyperbolic manifold `m112`:

        example$ censuslookup fLAMcbbcdeedhwhxn
        fLAMcbbcdeedhwhxn: 1 hit
            m112 : #2 -- Cusped hyperbolic census (orientable)

        example$

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/retriangulate`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\retriangulate.exe`.

### See Also

regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

sigcensus

1

sigcensus

Form a census of splitting surface signatures

        sigcensus
        order

### Description

Forms a census of all splitting surface signatures of the given order. The order is the number of quadrilaterals in the resulting splitting surface.

The signatures will be written to standard output, one per line, followed by a count of the total number of signatures found.

Each signature will be output precisely once up to equivalence. Signatures are considered equivalent if they are related by some combination of:

- relabelling symbols;

- rotating an individual cycle;

- inverting an individual cycle (i.e., reversing the cycle and changing the case of each symbol in the cycle);

- reversing all cycles without changing the case of any symbols.

Upper-case symbols in signatures are not yet supported; this program will only output signatures whose symbols are all lower-case.

For more information on splitting surface signatures, see Burton's PhD thesis at ®manburtonthesisurl;.

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/sigcensus`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\sigcensus.exe`.

### See Also

censuslookup, tricensus, regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

tricensus

1

tricensus

Form a census of triangulations

        tricensus
        -t, --tetrahedra=tetrahedra

         -2, --dim2
         -4, --dim4

         -b, --boundary
         -i, --internal
         -B, --bdryfaces=triangles

         -o, --orientable
         -n, --nonorientable

         -f, --finite
         -d, --ideal

         -m, --minimal
         -M, --minprime
         -N, --minprimep2
         -h, --minhyp

         -s, --sigs
         -c, --subcontainers

         -p, --genpairs
         -P, --usepairs

        output-file

        tricensus
        --help

### Description

Forms a census of all 2-, 3- or 4-manifold triangulations that satisfy some set of conditions.

These conditions are specified using various command-line arguments. The only condition that you must provide is the number of top-dimensional simplices (e.g., the number of tetrahedra for 3-manifolds), but there are many other options available.

The default behaviour is to enumerate 3-manifold triangulations. If you wish to enumerate 2-manifold or 4-manifold triangulations instead, you must pass `--dim2` or `--dim4` respectively.

Each triangulation will be output precisely once up to combinatorial isomorphism. Invalid triangulations (for 3-manifolds, this means triangulations with edges identified to themselves in reverse, or vertices whose links have boundary but are not discs) will not be output at all.

As the census progresses, the state of progress will be written (slowly) to standard output. Once the census is complete, the full census will be saved to the given output file.

You can use the options `--genpairs` and `--usepairs` to split a census into smaller pieces.

A census with even a small number of top-dimensional simplices can take an incredibly long time to run, and can chew up massive amounts of memory. It is recommended that you try very small censuses to begin with (such as 3 or 4 simplices), and work upwards to establish the limits of your machine.

For very large census runs, it is highly recommended that you use the `--sigs` option, which will keep the output file small and significantly reduce the memory footprint.

### Options

`-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 ®ina; 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 ®ina; 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 ®ina; 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 ®ina; 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 ®ina; 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 ®ina; by selecting &menuimportsigs; 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 ®ina; 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, ®ina; 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.

### Examples

The following command forms a census of all 3-tetrahedron closed non-orientable 3-manifold triangulations, and puts the results in the file `results.rga`. To ensure that triangulations are closed we use the options `-i` (no boundary triangles) and `-f` (no ideal vertices).

        example$ tricensus -t 3 -nif results.rga
        Starting census generation...
        0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 2:3 2:2
        0:1 0:0 1:0 2:0 | 0:2 1:2 1:1 2:1 | 0:3 1:3 2:3 2:2
        0:1 0:0 1:0 2:0 | 0:2 2:1 2:2 2:3 | 0:3 1:1 1:2 1:3
        1:0 1:1 2:0 2:1 | 0:0 0:1 2:2 2:3 | 0:2 0:3 1:2 1:3
        Finished.
        Total triangulations: 5
        example$

The following command forms a census of 4-tetrahedron closed orientable 3-manifold triangulations, where the census creation is optimised for prime minimal triangulations. Although all prime minimal triangulations will be included, there may be some non-prime or non-minimal triangulations in the census also.

        example$ tricensus -t 4 -oifM results.rga
        Starting census generation...
        0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ...
        0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 3:0 | 1:2 2:2 2:1 3:1 | 1:3 ...
        ...
        1:0 1:1 2:0 3:0 | 0:0 0:1 2:1 3:1 | 0:2 1:2 3:2 3:3 | 0:3 ...
        Finished.
        Total triangulations: 17
        example$

The following command generates all face pairings for a 5-tetrahedron census of 3-manifold triangulation in which all triangulations have precisely two boundary triangles. The face pairings will be written to `pairings.txt`, whereupon they can be broken up and distributed for processing at a later date.

        example$ tricensus --genpairs -t 5 -B 2 pairings.txt
        Total face pairings: 118
        example$

The face pairings generated in the previous example can then be fleshed out into a full census of all 3-manifold triangulations with five tetrahedra, precisely two boundary triangles and no ideal vertices as follows. The number of tetrahedra and boundary triangles were already specified in the previous command, and cannot be supplied here. The face pairings will be read from `pairings.txt`, and the final census will be written to `results.rga`.

        example$ tricensus --usepairs -f results.rga < pairings.txt
        Trying face pairings...
        0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ...
        0:1 0:0 1:0 1:1 | 0:2 0:3 2:0 2:1 | 1:2 1:3 3:0 3:1 | 2:2 ...
        ...
        ... (running through all 118 face pairings)
        ...
        1:0 2:0 3:0 4:0 | 0:0 2:1 3:1 4:1 | 0:1 1:1 3:2 4:2 | 0:2 ...
        Total triangulations: 5817
        example$

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/tricensus`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\tricensus.exe`.

### See Also

censuslookup, sigcensus, regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;

trisetcmp

1

trisetcmp

Compare triangulations between two ®ina; data files

        trisetcmp

         -m
         -n

        -s
        file1
        file2

### Description

Compares all triangulations in the first file against all triangulations in the second file, looking for pairs of triangulations that are combinatorially isomorphic.

The two given files must be ®ina; data files. A full list of matches (or a full list of non-matches if `-n` is passed) is written to standard output. A match occurs when some triangulation from `file1` is combinatorially isomorphic to some triangulation from `file2` (i.e., identical up to a relabelling of tetrahedra and their vertices).

This utility can also do subcomplex testing instead of full isomorphism testing. See the option `-s` for details.

This utility compares both 3-manifold and 4-manifold triangulations (but no other dimensions at present). However, it will only compare triangulations of the same dimension—it will not test whether some 3-manifold triangulation appears as a subcomplex of some other 4-manifold triangulation.

### Options

`-m` (default)

- Output matches only. All isomorphic matches between triangulations in `file1` and triangulations in `file2` will be listed.

`-n`

- Output non-matches only. All triangulations from `file1` with no isomorphic match in `file2` will be listed, and vice versa.

  If `-s` is passed then non-matches are tested in one direction only, not both; see below for details.

`-s`

- Instead of testing triangulations for isomorphism, test whether one triangulation is isomorphic to a subcomplex of the other.

  In the default case of `-m` (output matches only), this program outputs all instances where a triangulation from `file1` is isomorphic to a subcomplex of a triangulation from `file2`.

  In the case of `-n` (output non-matches only), this program outputs all triangulations from `file1` that are not isomorphic to a subcomplex of any triangulation from `file2`.

&submani18n;

### &macosx; Users

If you downloaded a drag-and-drop app bundle, this utility is shipped inside it. If you dragged ®ina; to the main Applications folder, you can run it as `/Applications/Regina.app/Contents/MacOS/trisetcmp`.

### &windows; Users

The command-line utilities are installed beneath the `Program Files` directory; on some machines this directory is called `Program Files (x86)`. You can start this utility by running `c:\Program Files\Regina\Regina ®version;\bin\trisetcmp.exe`.

### See Also

censuslookup, regina-gui.

### Author

This utility was written by Benjamin Burton bab@maths.uq.edu.au. &manpageack;