# Index

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
  making a triangulaton 0-efficient
  testing for 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)
  exporting to
3-manifold recognition
3-manifold triangulation
  See: triangulation, 3-manifold
3-sphere recognition
4-4 move
  See: elementary moves

### — A —

almost normal surfaces
  See: normal surfaces
angle structures
  definition
  enumerating vertex angle structures
  enumerating taut angle structures
  individual angles
  strict, testing for existence
  strict, type of angle structure
  taut, type of angle structure
  veering, type of angle structure
API documentation
  See: documentation
augmented triangular solid torus, creation
auto-indent

### — B —

barycentric subdivision
book closing move
  See: elementary moves
book opening move
  See: elementary moves
boundary
  extension from real to ideal
  of a normal surface
  of a triangulation
boundary components, viewing in a triangulation
boundary shelling move
  See: elementary moves
boundary slopes for spun-normal surfaces
bug reporting

### — C —

C++ source
  See: source code
calculation engine
  accessing
  documentation
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
  in imports and exports
  in Python
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
  exporting normal surface lists to CSV files
command-line tools
  scripting interface
  specialised utilities
compactness of normal surfaces
compatibility matrices for normal surfaces
  displaying
compiling
  compiling Regina into other code
  fixing compile errors when building Regina
component decomposition
components, viewing in a triangulation
composition, combinatorial
  See: combinatorial composition
configuration
  GAP (Groups, Algorithms and Programming)
  general
  Graphviz
  PDF viewing
  Python scripting
  SnapPea interaction
  tools, third-party
connected sum
  building
  decomposition
connectedness, testing for
container packets
conversion
  between file formats
  from native Regina to SnapPea triangulations
  from SnapPea to native Regina triangulations
coordinate systems, normal surface
  enumerating in a particular coordinate system
  explanation of different coordinate systems
  viewing in a different coordinate system
crushing a normal surface
crushing an edge
  See: elementary moves
CSV
  See: comma-separated values
cusps
  identifying in a native triangulation
  viewing and filling in a SnapPea triangulation
custom surfaces
cutting along a normal surface
CW-decomposition

### — D —

data files
  See: files
decomposition
  by components
  by connected sum
Dehn fillings
  See: fillings on cusps
dehydrated triangulations
  importing a list of dehydration strings
  rehydrating from a dehydration string
  viewing the dehydration string for a triangulation
deleting packets
disjoint normal surfaces
  See: compatibility matrices for normal surfaces
docking packets
documentation
  Regina objects, classes and methods
double cover
  See: orientable double cover
drilling edges
  See: edges, drilling out of a triangulation
dual 1-skeleton
  See: face pairing graphs
dual CW-decomposition
  See: CW-decomposition
dumping contents of a file

### — E —

edge linking surfaces, recognising
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, enumerating
encodings
  See: character encodings
enumerating vertex angle structures
enumerating vertex or fundamental normal surfaces
Epstein-Penner cell decomposition
  See: canonical retriangulation
errors, fixing
Euler characteristic
  of a 2-manifold
  of a 3-manifold
  of a normal surface
examples
  3-manifold triangulations
  Python scripting
  sample data files
  SnapPea triangulations
exporting data
extension
  of a triangulation boundary

### — F —

face arc normal coordinates
  See: triangle arc normal coordinates
face gluings
  See: tetrahedron face gluings
face pairing graphs
  labelling
  viewing
faces, viewing in a triangulation
  See: triangles (2-faces), viewing in a triangulation
feature set
figure eight knot complement
files
  automatic file extension
  combining data files
  comparing triangulations between data files
  conversion between file formats
  dumping contents of a file
  exporting data
  identifying file types
  importing data
  sample data files
  specification of file format
fillings on cusps
  viewing and changing filling coefficients
  permanently filling cusps
filtering normal surface lists
  See: surface filters
finite boundary
  See: boundary
floating packets in separate windows
frequently asked questions
fundamental group
fundamental normal surfaces, enumerating

### — G —

GAP (Groups, Algorithms and Programming)
  configuration
  using to simplify group presentations
globally compatible normal surfaces
  See: compatibility matrices for normal surfaces
gluing equations, hyperbolic
gluings
  See: tetrahedron face gluings
graphs, face pairing
  See: face pairing graphs
Graphviz
  configuration
  using to display face pairing graphs

### — H —

Hakenness, testing
homology groups
  all homology groups
  first homology group for native triangulations
  first homology group for SnapPea triangulations
  induced map from manifold to boundary
hyperbolic manifolds
  certifying hyperbolicity
  gluing equations, solutions to
  solution type for native triangulations
  solution type for SnapPea triangulations
  volume for native triangulations
  volume for SnapPea triangulations

### — I —

ideal vertices
  creating from real boundary components
  testing for
  truncating / converting to real boundary
  viewing
identifications
  See: tetrahedron face gluings
identifying file types
immersed / singular normal surfaces
  enumerating
  warn before enumerating
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
  importing a list of isomorphism signatures
  reconstructing triangulations from isomorphism signatures
  viewing the isomorphism signature for a triangulation
isomorphism testing
  between individual triangulations
  between sets of triangulations

### — K —

Kawauchi-Kojima invariants
  See: torsion linking form

### — L —

labelling face pairing graphs
LATIN1
  See: character encodings
layered lens space, creation
layered loop, creation
layered solid torus
  creating
  locating within a triangulation
legacy surfaces
legacy almost normal coordinates
  See: coordinate systems
Legendre symbol vector
  invariant of torsion linking form
lens space, creation
libraries
  Python
  Regina, compiling into other code
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 for normal surfaces
Matveev's 3-Manifold Recogniser
  See: 3-Manifold Recogniser
merging data files
  from the command-line
  in the graphical user interface
moving packets in the packet tree
MPI
  See: parallel processing

### — N —

naming
  packets
  surfaces in a surface list
  tetrahedra in a triangulation
normal surfaces
  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 surfaces
  crushing a surface
  cutting along a surface
  definition
  edge links, recognising
  enumerating vertex or fundamental normal surfaces
  exporting to CSV files
  filtering surface lists
  matching equations
  naming surfaces in a list
  numbering surfaces in a list
  splitting surfaces, recognising
  vertex links, recognising

### — O —

octagons
  locating within almost normal surfaces
octagonal almost normal surfaces
  See: normal surfaces
one-sidedness
  See: sidedness
open book
  See: elementary moves
options
  See: configuration
Orb
  importing from
orientability
  of a normal surface
  of a native triangulation
  of a SnapPea triangulation
orientable double cover
orienting tetrahedra
  testing for consistent orientations

### — P —

packet tree
  display large icon
  jump size
  moving packets
  overview
  refreshing a subtree
packets
  automatic docking
  available packet types
  cannot be edited
  cloning
  creating new packets
  deleting
  docking and undocking
  floating in separate windows
  moving within the tree
  viewing and editing
padlock
  in the packet tree
paper clip
  button in packet viewers
parallel processing
  census creation
PDF documents
  exporting
  importing
  PDF packets
  PDF viewer configuration
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
  invariant of torsion linking form
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 —

samples
  See: examples
scripting
  accessing Regina objects, classes and methods
  `Boost.Python.ArgumentError`, resolving
  caveats and traps
  command-line scripting interface
  configuration
  documentation of Regina objects, classes and methods
  enabling
  examples
  exporting Python scripts
  importing Python scripts
  invoking in the GUI
  ownership of objects
  Python libraries
  script packets
  `TypeError`, resolving
search
  for a triangulation across the census databases
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 of a normal surface
sigma vector
  invariant of torsion linking form
signatures, splitting surface
  See: splitting surfaces
simplifying group presentations
simplifying triangulations
singular / immersed normal surfaces
  See: immersed / singular surfaces
skeleton
  of a triangulation
  dual 1-skeleton
SnapPea
  calculations for Regina triangulations
  diagnostic messages, enabling
  exporting files to
  exporting SnapPea file contents
  importing files from
  importing SnapPea file contents
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
  combining with the Regina calculation engine
  exporting triangulations to C++
  Python scripting
splitting surfaces
  census of splitting surface signatures
  recognising in a surface list
  reconstructing a triangulation from
  testing for existence in a triangulation
spun-normal surfaces
  boundary slopes
  identifying
standard normal coordinates
  See: coordinate systems
standard subcomplexes
  creating
  testing for
strict angle structures
  testing for existence
  type of angle structure
subcomplex
  searching for standard subcomplexes
  testing between two triangulations
  testing between sets of triangulations
subdivision of triangulations
surface
  See: triangulation, 2-manifold
surface filters
  combining filters
  filtering by surface properties
  overview
surface, normal
  See: normal surfaces

### — T —

tab size
taut angle structures
  detecting
  enumerating
test suite
tetrahedra
  face gluings, editing
  orientation, testing for consistency
  shapes from hyperbolic gluing equations
text encodings
  See: character encodings
text packets
torsion linking form
  Kawauchi-Kojima invariants
tree
  See: packet tree
triangle arc normal coordinates
  See: coordinate systems
triangles (2-faces), viewing in a triangulation
triangulation, 2-manifold
  Euler characteristic
  overview
  recognising the underlying 2-manifold
triangulation, 3-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
  elementary moves (3-2, 4-4, open book, etc.)
  examples, creating
  exporting to external files
  face pairing graphs
  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
  orientability
  orientable double cover
  puncturing
  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
  triangles, viewing shapes
  Turaev-Viro invariants
  unknot complement recognition
  validity
  volume
troubleshooting
truncation of ideal vertices
Turaev-Viro invariants
two-sidedness
  See: sidedness

### — U —

undocking packets
unknot recognition
user interface
  command-line scripting interface
  graphical user interface
  specialised command-line utilities
user libraries
  See: libraries
UTF-8
  See: character encodings

### — V —

valid edges, testing for
valid triangulation, testing for
veering structures
  detecting
vertex angle structures, enumerating
vertex linking surfaces, recognising
vertex links
triangulating for native triangulations
triangulating for SnapPea triangulations
vertex normal surfaces, enumerating
vertices, viewing in a triangulation
viewing packets
volume
  See: hyperbolic manifolds, volume

### — W —

Weber-Seifert dodecahedral space
Weeks manifold

### — Z —

zero-efficiency
  See: 0-effiency