Triangulations

Triangulations of 3-manifolds. More...

Classes
class	regina::Dim2ExampleTriangulation
	This class offers routines for constructing sample 2-manifold triangulations of various types. More...
class	regina::NSnapPeaTriangulation
	Offers direct access to the SnapPea kernel from within Regina. More...
class	regina::NBoundaryComponent
	Represents a component of the boundary of a triangulation. More...
class	regina::NComponent
	Represents a component of a triangulation. More...
class	regina::NEdgeEmbedding
	Details how an edge in the skeleton forms part of an individual tetrahedron. More...
class	regina::NEdge
	Represents an edge in the skeleton of a triangulation. More...
class	regina::NExampleTriangulation
	This class offers routines for constructing sample 3-manifold triangulations of various types. More...
class	regina::NFacePair
	Represents a pair of tetrahedron face numbers. More...
class	regina::NIsomorphism
	Represents a combinatorial isomorphism from one triangulation into another. More...
class	regina::NIsomorphismDirect
	A deprecated synonym for NIsomorphism, provided for backward compatibility only. More...
class	regina::NPermItS4
	An iterator class that runs through all 24 permutations of four elements. More...
class	regina::NTetrahedron
	Represents a tetrahedron in a triangulation. More...
class	regina::NTriangleEmbedding
	Details how a triangle in the skeleton forms part of an individual tetrahedron. More...
class	regina::NTriangle
	Represents a triangle in the skeleton of a triangulation. More...
struct	regina::PacketInfo< PACKET_TRIANGULATION >
	Stores information about the 3-manifold triangulation packet. More...
class	regina::NTriangulation
	Stores the triangulation of a 3-manifold along with its various cellular structures and other information. More...
class	regina::NVertexEmbedding
	Details how a vertex in the skeleton forms part of an individual tetrahedron. More...
class	regina::NVertex
	Represents a vertex in the skeleton of a triangulation. More...
class	regina::NXMLTriangulationReader
	An XML packet reader that reads a single triangulation. More...

Typedefs
typedef NPerm4	regina::NPerm
	A legacy typedef provided for backward compatibility only. More...

Variables
REGINA_API const int	regina::edgeNumber [4][4]
	edgeNumber[i][j] is the number of the edge linking vertices i and j in a tetrahedron. More...
REGINA_API const int	regina::edgeStart [6]
	edgeStart[k] is the vertex of a tetrahedron at which edge k of the tetrahedron begins. More...
REGINA_API const int	regina::edgeEnd [6]
	edgeEnd[k] is the vertex of a tetrahedron at which edge k of the tetrahedron ends. More...

Detailed Description

Triangulations of 3-manifolds.

Typedef Documentation

typedef NPerm4 regina::NPerm

A legacy typedef provided for backward compatibility only.

Deprecated:

As of Regina 4.6.1, the class NPerm has been renamed as NPerm4 (which has identical functionality). This NPerm typedef is provided for backward compatibility, and will be removed in some future version of Regina.

Variable Documentation

REGINA_API const int regina::edgeEnd[6]

edgeEnd[k] is the vertex of a tetrahedron at which edge k of the tetrahedron ends.

k must be between 0 and 5 inclusive. The resulting vertex number will be between 0 and 3 inclusive.

Note that edge numbers of opposite edges will always add to 5. You are guaranteed that edgeStart[e] will always be smaller than edgeEnd[e].

Deprecated:

This array has been superceded by NEdge::edgeVertex (where edgeEnd[i] is now NEdge::edgeVertex[i][1]). Users are advised to switch to NEdge::edgeVertex instead, since the old regina::edgeStart and regina::edgeEnd will eventually be removed in some future version of Regina.

REGINA_API const int regina::edgeNumber[4][4]

edgeNumber[i][j] is the number of the edge linking vertices i and j in a tetrahedron.

i and j must be between 0 and 3 inclusive and may be given in any order. The resulting edge number will be between 0 and 5 inclusive.

Note that edge numbers of opposite edges will always add to 5.

Deprecated:

This array has been replaced with the identical array NEdge::edgeNumber. Users are advised to switch to NEdge::edgeNumber instead, since the old regina::edgeNumber will eventually be removed in some future version of Regina.

REGINA_API const int regina::edgeStart[6]

edgeStart[k] is the vertex of a tetrahedron at which edge k of the tetrahedron begins.

k must be between 0 and 5 inclusive. The resulting vertex number will be between 0 and 3 inclusive.

Note that edge numbers of opposite edges will always add to 5. You are guaranteed that edgeStart[e] will always be smaller than edgeEnd[e].

Deprecated:

This array has been superceded by NEdge::edgeVertex (where edgeStart[i] is now NEdge::edgeVertex[i][0]). Users are advised to switch to NEdge::edgeVertex instead, since the old regina::edgeStart and regina::edgeEnd will eventually be removed in some future version of Regina.