## Index |

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0-9 | A | B | C | D | E | F | G | H | I | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z |

### — 0-9 —

- 0-efficiency
- 1-4 move
- See: elementary moves

- 2-0 edge move
- See: elementary moves

- 2-0 vertex move
- See: elementary moves

- 2-1 move
- See: elementary moves

- 2-3 move
- See: elementary moves

- 2-manifold triangulation
- See: triangulation, 2-manifold

- 3-2 move
- See: elementary moves

- 3-ball recognition
- 3-Manifold Recogniser (Matveev)
- 3-manifold recognition
- 3-manifold triangulation
- See: triangulation, 3-manifold

- 3-sphere recognition
- 4-4 move
- See: elementary moves

- (5–15)-manifold triangulation
- See: triangulation, (5–14)-manifold

### — A —

- almost normal surfaces
- See: normal surfaces

- angle structures
- API documentation
- See: documentation

- auto-indent

### — B —

- barycentric subdivision
- bistellar flip
- See: elementary moves

- book closing move
- See: elementary moves

- book opening move
- See: elementary moves

- boundary
- boundary components
- boundary shelling move
- See: elementary moves

- boundary slopes for spun-normal surfaces
- bug reporting
- bundles, creation

### — C —

- C++ source
- See: source code

- calculation engine
- canonical retriangulation
- Casson
- See: Orb

- census
- creating a census of splitting surface signatures
- creating a census of triangulations (command-line)
- creating a census of triangulations (GUI)
- distributing census creation across several machines
- searching for a triangulation across the census databases (GUI)
- searching for a triangulation across the census databases (command line)

- central surfaces, recognising
- certifying hyperbolicity
- See: hyperbolic manifolds, certifying hyperbolicity

- character encodings
- cloning packets
- close book
- See: elementary moves

- code
- See: libraries

- collapsing an edge
- See: elementary moves

- combinatorial composition
- combining data files
- combining surface filters
- comma-separated values
- command-line tools
- compactness
- compatibility matrices
- compiling
- component decomposition
- components, viewing in a triangulation
- composition, combinatorial
- See: combinatorial composition

- configuration
- connected sum
- connectedness, testing for
- container packets
- conversion
- coordinate systems, normal surface or hypersurface
- crushing a normal surface
- crushing an edge
- See: elementary moves

- CSV
- See: comma-separated values

- cusps
- custom surfaces or hypersurfaces
- cutting along a normal surface
- CW-decomposition

### — D —

- data files
- See: files

- decomposition
- Dehn fillings
- See: fillings on cusps

- dehydrated triangulations
- deleting packets
- disjoint normal surfaces
- See: compatibility matrices for normal surfaces

- documentation
- double cover
- See: orientable double cover

- drilling edges
- See: edges, drilling out of a triangulation

- dual CW-decomposition
- See: CW-decomposition

- dual graphs
- dumping contents of a file

### — E —

- edge links
- edge weight normal coordinates
- See: coordinate systems

- edges, drilling out of a triangulation
- edges, viewing in a triangulation
- editing packets
- elementary moves on triangulations
- embeddability in homology spheres
- embedded normal surfaces or hypersurfaces, enumerating
- encodings
- See: character encodings

- enumerating
- Epstein-Penner cell decomposition
- See: canonical retriangulation

- errors, fixing
- Euler characteristic
- examples
- exhaustive simplification of triangulations
- exporting data
- extension

### — F —

- face arc normal coordinates
- See: triangle arc normal coordinates

- face gluings
- See: tetrahedron face gluings

- face pairing graphs
- See: dual graphs

- faces, viewing in a triangulation
- See: triangles (2-faces), viewing in a triangulation

- feature set
- figure eight knot complement
- files
- fillings on cusps
- filtering normal surface lists
- See: surface filters

- finite boundary
- See: boundary

- flip graph
- See: Pachner graph

- fonts, unicode symbols
- frequently asked questions
- fundamental group
- fundamental normal surfaces or hypersurfaces, enumerating

### — G —

- GAP (Groups, Algorithms and Programming)
- globally compatible normal surfaces
- See: compatibility matrices for normal surfaces

- gluing equations, hyperbolic
- gluings
- See: tetrahedron face gluings

- graphs, face pairing
- See: dual graphs

### — I —

- I-bundles, creation
- ideal vertices
- identifications
- See: tetrahedron face gluings

- identifying file types
- immersed / singular
- importing data
- incompressible surfaces, testing for
- induced homology map
- See: homology groups

- interface
- See: user interface

- internationalisation
- See: character encodings

- invalid
- See: valid

- irreducibility, testing
- isomorphism signatures
- isomorphism testing

### — L —

- labelling dual graphs
- LATIN1
- See: character encodings

- layered lens space, creation
- layered solid torus
- legacy surfaces
- legacy almost normal coordinates
- See: coordinate systems

- Legendre symbol vector
- lens space, creation
- libraries
- licence details
- links, vertex
- See: vertex links

- locally compatible normal surfaces
- See: compatibility matrices for normal surfaces

- log files, summarising (MPI)
- look up
- See: search

### — M —

- mailing lists
- matching equations
- mathematical symbols, enabling / disabling
- Matveev's 3-Manifold Recogniser
- See: 3-Manifold Recogniser

- merging data files
- moving packets in the packet tree
- MPI
- See: parallel processing

### — N —

- naming
- nice tree decomposition
- normal surfaces or hypersurfaces
- basic properties
- breakdown of total counts by properties
- central surfaces, recognising
- compatibility matrices
- coordinate systems, different systems explained
- coordinate systems, viewing in different systems
- counting different types of (hyper)surfaces
- crushing a surface
- cutting along a surface
- definition
- edge links, recognising
- enumerating vertex or fundamental normal (hyper)surfaces
- exporting to CSV files
- filtering surface lists
- homology
- matching equations
- naming (hyper)surfaces in a list
- numbering (hyper)surfaces in a list
- splitting surfaces, recognising
- triangulating a hypersurface
- vertex links, recognising

### — O —

- octagons
- octagonal almost normal surfaces
- See: normal surfaces

- one-sidedness
- See: sidedness

- open book
- See: elementary moves

- options
- See: configuration

- Orb
- orientability
- orientable double cover
- orienting tetrahedra

### — P —

- Pachner graph, searching
- Pachner moves
- packet tree
- packets
- padlock
- parallel processing
- PDF documents
- peripheral curves on cusps
- permanently fill cusps
- Poincaré homology sphere
- preferences
- See: configuration

- puncturing a triangulation
- Python scripting
- See: scripting

### — Q —

- quadrilateral normal coordinates
- See: coordinate systems

- quadrilateral-octagon almost normal coordinates
- See: coordinate systems

- questions, frequently asked

### — R —

- randomising triangulations
- rank vector
- real boundary
- See: boundary

- Recogniser, 3-Manifold (Matveev)
- See: 3-Manifold Recogniser

- recognising 3-manifolds
- recognising triangulations
- reducibility, testing
- rehydrating triangulations
- See: dehydrated triangulations

- removing
- See: deleting

- renaming
- See: naming

- reporting bugs

### — S —

- S
^{1}-bundles, creation - samples
- See: examples

- scripting
- search
- Seifert fibred space, creation
- Seifert-Weber dodecahedral space
- See: Weber-Seifert dodecahedral space

- settings
- See: configuration

- shell boundary
- See: elementary moves

- shapes of tetrahedra
- sidedness
- sigma vector
- signatures, splitting surface
- See: splitting surfaces

- simplifying group presentations
- simplifying triangulations
- singular / immersed normal surfaces
- See: immersed / singular surfaces

- skeleton
- SnapPea
- SnapPea triangulation
- canonical retriangulation
- converting from native Regina triangulations
- converting to native Regina triangulations
- cusps, viewing and filling
- examples, creating
- filling coefficients
- fundamental group
- homology
- orientability
- permanently filling cusps
- randomising
- SnapPea file contents, creating from
- SnapPea file contents, exporting to
- solution type
- tetrahedron shapes
- vertex links
- volume

- solid torus recognition
- solution type
- See: hyperbolic manifolds, solution type

- source code
- splitting surfaces
- spun-normal surfaces
- standard normal coordinates
- See: coordinate systems

- standard subcomplexes
- strict angle structures
- subcomplex
- subdivision of triangulations
- subscript / superscript symbols, enabling / disabling
- surface
- See: triangulation, 2-manifold

- surface filters
- surface, normal
- See: normal surfaces

### — T —

- tab size
- taut angle structures
- test suite
- tetrahedra
- text encodings
- See: character encodings

- text packets
- torsion linking form
- tree
- See: packet tree

- tree decomposition
- triangle arc normal coordinates
- See: coordinate systems

- triangles (2-faces), viewing in a triangulation
- triangulating
- triangulation, (2,3,4)-manifold
- 0-efficiency, testing for
- 0-efficient triangulation, conversion to
- 3-ball recognition
- 3-manifold, recognising
- 3-sphere recognition
- barycentric subdivision
- boundary components, viewing
- boundary, converting real to ideal
- boundary, testing for
- combinatorial composition
- component decomposition
- components, viewing
- connected sum, building
- connected sum, decomposition
- connectedness
- converting from a SnapPea triangulations
- converting to a SnapPea triangulation
- creation
- cusps
- dehydration string, rehydrating
- drilling edges
- dual graph
- elementary moves (3-2, 4-4, open book, etc.)
- Euler characteristic
- examples, creating
- exporting to external files
- face pairing graph
- faces, viewing shapes
- fundamental group
- homology groups
- hyperbolic solution type
- hyperbolicity, certifying
- ideal vertices, creation
- ideal vertices, testing for
- ideal vertices, truncation
- importing from external files
- isomorphism and subcomplex testing
- isomorphism signature, recreating from
- nice tree decomposition
- orientability
- orientable double cover
- puncturing
- recognising the underlying 2-manifold
- recognising the underlying 3-manifold
- searching for a triangulation across the census databases
- simplification
- skeleton, viewing details
- SnapPea triangulations
- solid torus recognition
- splitting surface, reconstructing triangulation from
- splitting surface, testing for
- tetrahedron face gluings, editing
- tree decomposition
- triangles, viewing shapes
- Turaev-Viro invariants
- unknot complement recognition
- validity
- volume

- triangulation, (5–15)-manifold
- troubleshooting
- truncation of ideal vertices
- Turaev-Viro invariants
- two-sidedness
- See: sidedness

### — U —

- unicode symbols, enabling / disabling
- unknot recognition
- user interface
- UTF-8
- See: character encodings

### — V —

- valid edges, testing for
- valid triangulation, testing for
- veering structures
- vertex angle structures, enumerating
- vertex links
- vertex normal surfaces or hypersurfaces, enumerating
- vertices, viewing in a triangulation
- viewing packets
- volume
- See: hyperbolic manifolds, volume

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