Generic triangulations

Details for implementing triangulations in arbitrary dimensions. More...

Classes
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::Face< dim, dim >
	Represents a top-dimensional simplex in a dim-manifold triangulation. 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::DegreeLessThan< dim, subdim >
	Deprecated function object used for sorting faces of triangulations by increasing degree. More...
class	regina::DegreeGreaterThan< dim, subdim >
	Deprecated function object used for sorting faces of triangulations by decreasing degree. More...

Typedefs
template<int dim>
using	regina::Vertex = Face< dim, 0 >
	Refers to a vertex of a dim-dimensional triangulation. More...
template<int dim>
using	regina::Edge = Face< dim, 1 >
	Refers to an edge of a dim-dimensional triangulation. More...
template<int dim>
using	regina::Triangle = Face< dim, 2 >
	Refers to a triangular face of a dim-dimensional triangulation. More...
template<int dim>
using	regina::Tetrahedron = Face< dim, 3 >
	Refers to a tetrahedral face of a dim-dimensional triangulation. More...
template<int dim>
using	regina::Pentachoron = Face< dim, 4 >
	Refers to a pentachoron face of a dim-dimensional triangulation. More...
template<int dim>
using	regina::VertexEmbedding = FaceEmbedding< dim, 0 >
	Details how a vertex of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
template<int dim>
using	regina::EdgeEmbedding = FaceEmbedding< dim, 1 >
	Details how a edge of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
template<int dim>
using	regina::TriangleEmbedding = FaceEmbedding< dim, 2 >
	Details how a triangular face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
template<int dim>
using	regina::TetrahedronEmbedding = FaceEmbedding< dim, 3 >
	Details how a tetrahedral face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
template<int dim>
using	regina::PentachoronEmbedding = FaceEmbedding< dim, 4 >
	Details how a pentachoron face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
template<int dim>
using	regina::Simplex = Face< dim, dim >
	Refers to a top-dimensional simplex in a dim-dimensional triangulation. More...

Functions
template<int dim>
void	regina::swap (FacetPairing< dim > &a, FacetPairing< dim > &b) noexcept
	Swaps the contents of the given facet pairings. More...
template<int dim>
void	regina::swap (Isomorphism< dim > &a, Isomorphism< dim > &b) noexcept
	Swaps the contents of the given isomorphisms. More...

Detailed Description

Details for implementing triangulations in arbitrary dimensions.

Typedef Documentation

Edge

template<int dim>

using regina::Edge = typedef Face<dim, 1>

Refers to an edge of a dim-dimensional triangulation.

This is the preferred way to refer to an edge of a triangulation (as opposed to the more clumsy notation Face<dim, 1>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., Edge5).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

EdgeEmbedding

template<int dim>

using regina::EdgeEmbedding = typedef FaceEmbedding<dim, 1>

Details how a edge of a dim-dimensional triangulation appears within each top-dimensional simplex.

This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 1>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., EdgeEmbedding5).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

Pentachoron

template<int dim>

using regina::Pentachoron = typedef Face<dim, 4>

Refers to a pentachoron face of a dim-dimensional triangulation.

This alias is also valid for the case dim = 4, where it refers to a top-dimensional simplex of a 4-dimensional triangulation.

This is the preferred way to refer to a 4-face of a triangulation (as opposed to the more clumsy notation Face<dim, 4>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., Pentachoron9).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 4 and 15 inclusive.

PentachoronEmbedding

template<int dim>

using regina::PentachoronEmbedding = typedef FaceEmbedding<dim, 4>

Details how a pentachoron face of a dim-dimensional triangulation appears within each top-dimensional simplex.

This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 4>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., PentachoronEmbedding14).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 5 and 15 inclusive.

Simplex

template<int dim>

using regina::Simplex = typedef Face<dim, dim>

Refers to a top-dimensional simplex in a dim-dimensional triangulation.

This is the preferred way to refer to a top-dimensional simplex (as opposed to the more clumsy notation Face<dim, dim>).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

Tetrahedron

template<int dim>

using regina::Tetrahedron = typedef Face<dim, 3>

Refers to a tetrahedral face of a dim-dimensional triangulation.

This alias is also valid for the case dim = 3, where it refers to a top-dimensional simplex of a 3-dimensional triangulation.

This is the preferred way to refer to a 3-face of a triangulation (as opposed to the more clumsy notation Face<dim, 3>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., Tetrahedron7).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 3 and 15 inclusive.

TetrahedronEmbedding

template<int dim>

using regina::TetrahedronEmbedding = typedef FaceEmbedding<dim, 3>

Details how a tetrahedral face of a dim-dimensional triangulation appears within each top-dimensional simplex.

This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 3>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., TetrahedronEmbedding7).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 4 and 15 inclusive.

Triangle

template<int dim>

using regina::Triangle = typedef Face<dim, 2>

Refers to a triangular face of a dim-dimensional triangulation.

This alias is also valid for the case dim = 2, where it refers to a top-dimensional simplex of a 2-dimensional triangulation.

This is the preferred way to refer to a 2-face of a triangulation (as opposed to the more clumsy notation Face<dim, 2>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., Triangle4).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

TriangleEmbedding

template<int dim>

using regina::TriangleEmbedding = typedef FaceEmbedding<dim, 2>

Details how a triangular face of a dim-dimensional triangulation appears within each top-dimensional simplex.

This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 2>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., TriangleEmbedding12).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 3 and 15 inclusive.

Vertex

template<int dim>

using regina::Vertex = typedef Face<dim, 0>

Refers to a vertex of a dim-dimensional triangulation.

This is the preferred way to refer to a vertex of a triangulation (as opposed to the more clumsy notation Face<dim, 0>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., Vertex8).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

VertexEmbedding

template<int dim>

using regina::VertexEmbedding = typedef FaceEmbedding<dim, 0>

Details how a vertex of a dim-dimensional triangulation appears within each top-dimensional simplex.

This is the preferred way to refer to this class (as opposed to the more clumsy notation FaceEmbedding<dim, 0>).

Python

Python does not support templates. Instead this alias can be used by appending the dimension dim as a suffix (e.g., VertexEmbedding3).

Template Parameters

dim	the dimension of the underlying triangulation. This must be between 2 and 15 inclusive.

Function Documentation

swap() [1/2]

template<int dim>

void regina::swap ( FacetPairing< dim > &  a, FacetPairing< dim > &  b  )

noexcept

Swaps the contents of the given facet pairings.

This global routine simply calls FacetPairing<dim>::swap(); it is provided so that FacetPairing<dim> meets the C++ Swappable requirements.

Parameters

a	the first facet pairing whose contents should be swapped.
b	the second facet pairing whose contents should be swapped.

swap() [2/2]

template<int dim>

void regina::swap ( Isomorphism< dim > &  a, Isomorphism< dim > &  b  )

inlinenoexcept

Swaps the contents of the given isomorphisms.

This global routine simply calls Isomorphism<dim>::swap(); it is provided so that Isomorphism<dim> meets the C++ Swappable requirements.

Parameters

a	the first isomorphism whose contents should be swapped.
b	the second isomorphism whose contents should be swapped.