Regina Calculation Engine
Classes | Typedefs | Functions
Triangulations

Triangulations of manifolds in all supported dimensions. More...

Classes

class  regina::Example< dim >
 This class offers static routines for constructing a variety of sample dim-dimensional triangulations. More...
 
class  regina::Example< 2 >
 Offers routines for constructing a variety of sample 2-dimensional triangulations. More...
 
class  regina::Example< 3 >
 Offers routines for constructing a variety of sample 3-dimensional triangulations. More...
 
class  regina::Example< 4 >
 Offers routines for constructing a variety of sample 4-dimensional triangulations. More...
 
class  regina::FaceNumbering< dim, subdim >
 Specifies how subdim-faces are numbered within a dim-dimensional simplex. More...
 
class  regina::FacePair
 Represents a pair of tetrahedron face numbers. More...
 
class  regina::FacetPairing< 3 >
 Represents the dual graph of a 3-manifold triangulation. More...
 
struct  regina::FacetSpec< dim >
 A lightweight class used to refer to a particular facet of a particular top-dimensional simplex in a dim-dimensional triangulation. More...
 
class  regina::BoundaryComponent< dim >
 A component of the boundary of a dim-manifold triangulation. More...
 
class  regina::Component< dim >
 A connected component of a dim-manifold triangulation. More...
 
class  regina::Face< dim, subdim >
 Represents a subdim-face in the skeleton of a dim-dimensional triangulation. More...
 
class  regina::FaceEmbedding< dim, subdim >
 Details how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
 
class  regina::FacetPairing< dim >
 Represents the dual graph of a dim-manifold triangulation; that is, the pairwise matching of facets of dim-dimensional simplices. More...
 
class  regina::Isomorphism< dim >
 Represents a combinatorial isomorphism from one dim-manifold triangulation into another. More...
 
class  regina::Triangulation< dim >
 A dim-dimensional triangulation, built by gluing together dim-dimensional simplices along their (dim-1)-dimensional facets. More...
 
class  regina::HomologicalData
 Data type that deals with all the detailed homological information in a manifold. More...
 
class  regina::XMLTriangulationReader< dim >
 An XML packet reader that reads a single dim-dimensional triangulation. More...
 
class  regina::XMLTriangulationReader< 2 >
 An XML packet reader that reads a single 2-dimensional triangulation. More...
 
class  regina::XMLTriangulationReader< 3 >
 An XML packet reader that reads a single 3-dimensional triangulation. More...
 
class  regina::XMLTriangulationReader< 4 >
 An XML packet reader that reads a single 4-dimensional triangulation. More...
 

Typedefs

typedef Example< 2 > regina::Dim2ExampleTriangulation
 Deprecated typedef for backward compatibility. More...
 
typedef Example< 3 > regina::NExampleTriangulation
 Deprecated typedef for backward compatibility. More...
 
typedef Example< 4 > regina::Dim4ExampleTriangulation
 Deprecated typedef for backward compatibility. More...
 
typedef FacePair regina::NFacePair
 Deprecated typedef for backward compatibility. More...
 
typedef FacetPairing< 3 > regina::NFacePairing
 Deprecated typedef for backward compatibility. More...
 
typedef FacetSpec< 2 > regina::Dim2TriangleEdge
 Deprecated typedef for backward compatibility. More...
 
typedef FacetSpec< 3 > regina::NTetFace
 Deprecated typedef for backward compatibility. More...
 
typedef FacetSpec< 4 > regina::Dim4PentFacet
 Deprecated typedef for backward compatibility. More...
 
typedef HomologicalData regina::NHomologicalData
 Deprecated typedef for backward compatibility. More...
 

Functions

int regina::binomSmall (int n, int k)
 Returns the binomial coefficient
choose k for small arguments n and k. More...
 
template<int dim>
int regina::faceOppositeEdge (int i, int j)
 Returns the (dim-2)-face number that is opposite the edge joining vertices i and j in a dim-dimensional simplex. More...
 

Closed Triangulations

static Triangulation< 3 > * regina::Example< 3 >::s2xs1 ()
 Returns a two-tetrahedron triangulation of the product space S^2 x S^1. More...
 

Detailed Description

Triangulations of manifolds in all supported dimensions.

Typedef Documentation

◆ Dim2ExampleTriangulation

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef Dim2ExampleTriangulation, you should use the full class name Example<2>.

◆ Dim2TriangleEdge

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef Dim2TriangleEdge, you should use the real class name FacetSpec<2>.

◆ Dim4ExampleTriangulation

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef Dim4ExampleTriangulation, you should use the full class name Example<4>.

◆ Dim4PentFacet

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef Dim4PentFacet, you should use the real class name FacetSpec<4>.

◆ NExampleTriangulation

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef NExampleTriangulation, you should use the full class name Example<3>.

◆ NFacePair

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
The class NFacePair has now been renamed to FacePair.

◆ NFacePairing

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef NFacePairing, you should use the full class name FacetPairing<3>.

◆ NHomologicalData

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
The class NHomologicalData has now been renamed to HomologicalData.

◆ NTetFace

Deprecated typedef for backward compatibility.

This typedef will be removed in a future release of Regina.

Deprecated:
Instead of the old typedef NTetFace, you should use the real class name FacetSpec<3>.

Function Documentation

◆ binomSmall()

int regina::binomSmall ( int  n,
int  k 
)
inline

Returns the binomial coefficient
choose k for small arguments n and k.

This routine is very fast, since it uses a constant-time lookup. The trade-off is that it can only be used for n ≤ 16.

If you need a compile-time constant, you should use the constant FaceNumbering<n-1, k-1>::nFaces instead. This function is provided for situations where n and/or k are not known until runtime.

Note
The constraint n ≤ 16 is large enough for working with triangulations in Regina, since Regina restricts its triangulations to dimension ≤ 15 (where each simplex has 16 vertices).
Parameters
nthe parameter n in (n choose k); this must be between 0 and 16 inclusive.
kthe parameter k in (n choose k); this must be between 0 and n inclusive.
Returns
the binomial coefficient n choose k.

◆ faceOppositeEdge()

template<int dim>
int regina::faceOppositeEdge ( int  i,
int  j 
)
inline

Returns the (dim-2)-face number that is opposite the edge joining vertices i and j in a dim-dimensional simplex.

This function is offered because its implementation is faster than working through the FaceNumbering class.

The arguments i and j do not need to appear in ascending order.

Parameters
ithe first vertex of an edge in a dim-dimensional simplex. This must be between 0 and dim inclusive.
jthe second vertex of an edge in a dim-dimensional simplex. This must be between 0 and dim inclusive, and must be different from i.
Returns
the number of the (dim-2)-face opposite the given edge.

◆ s2xs1()

Triangulation< 3 > * regina::Example< 3 >::s2xs1 ( )
inlinestatic

Returns a two-tetrahedron triangulation of the product space S^2 x S^1.

This is identical to calling the generic routine sphereBundle().

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

Copyright © 1999-2016, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).