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class | regina::detail::ComponentBase< dim > |
| Helper class that provides core functionality for a connected component of a dim-manifold triangulation. More...
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class | regina::detail::FaceEmbeddingBase< dim, subdim > |
| Helper class that provides core functionality for describing how a subdim-face of a dim-dimensional triangulation appears within each top-dimensional simplex. More...
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class | regina::detail::FaceStorage< dim, codim > |
| Helper class for storing all the ways in which a given face of codimension codim in a dim-dimensional triangulation appears within the various top-dimensional simplices. More...
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class | regina::detail::FaceValidity< allowsInvalid, testLinks > |
| Helper class that stores whether a face is valid. More...
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class | regina::detail::FaceValidity< false, testLinks > |
| Helper class that stores whether a face is valid. More...
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class | regina::detail::FaceValidity< true, false > |
| Helper class that stores whether a face is valid. More...
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class | regina::detail::FaceOrientability< allowsNonorientable > |
| Helper class that stores whether the link of a face is orientable. More...
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class | regina::detail::FaceOrientability< false > |
| Helper class that stores whether the link of a face is orientable. More...
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struct | regina::detail::FaceListHolder< class, int > |
| Helper class that indicates what data type Base uses to store its list of subdim-faces. More...
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class | regina::detail::FaceBase< dim, subdim > |
| Helper class that provides core functionality for a subdim-face in the skeleton of a dim-dimensional triangulation. More...
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class | regina::detail::FaceNumberingAPI< dim, subdim > |
| Placeholder class that outlines the functions provided by FaceNumbering<dim, subdim>. More...
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class | regina::detail::FaceNumberingImpl< dim, subdim, lex > |
| Implementation details for numbering subdim-faces of a dim-dimensional simplex. More...
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class | regina::detail::FaceNumberingImpl< dim, subdim, false > |
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class | regina::detail::FaceNumberingImpl< dim, 0, true > |
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class | regina::detail::FaceNumberingImpl< 1, 0, true > |
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class | regina::detail::FaceNumberingImpl< 2, 0, true > |
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class | regina::detail::FaceNumberingImpl< 2, 1, false > |
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class | regina::detail::FaceNumberingImpl< 3, 0, true > |
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class | regina::detail::FaceNumberingImpl< 3, 1, true > |
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class | regina::detail::FaceNumberingImpl< 3, 2, false > |
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class | regina::detail::FaceNumberingImpl< 4, 0, true > |
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class | regina::detail::FaceNumberingImpl< 4, 1, true > |
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class | regina::detail::FaceNumberingImpl< 4, 2, false > |
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class | regina::detail::FaceNumberingImpl< 4, 3, false > |
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class | regina::detail::FacetPairingBase< dim > |
| Provides core functionality for facet pairings (that is, dual graphs) of dim-dimensional triangulations. More...
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class | regina::detail::IsomorphismBase< dim > |
| Provides core functionality for combinatorial isomorphisms between dim-manifold triangulations. More...
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class | regina::detail::SimplexFaces< dim, subdim > |
| Helper class for storing which subdim-faces of a dim-dimensional triangulation appear within each top-dimensional simplex. More...
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class | regina::detail::SimplexFacesSuite< dim, subdim > |
| Internal class that helps a simplex store the details of its lower-dimensional faces. More...
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class | regina::detail::SimplexBase< dim > |
| Helper class that provides core functionality for a top-dimensional simplex in a dim-manifold triangulation. More...
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class | regina::detail::FaceListSuite< dim, subdim > |
| Internal class that helps a triangulation store its lists of faces. More...
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struct | regina::detail::FaceListHolder< detail::TriangulationBase< dim >, subdim > |
| Helper class that indicates what data type is used by a triangulation class to store a list of subdim-faces. More...
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struct | regina::detail::FaceCalculator< dim, subdim, codim > |
| Internal class used to calculate lower-dimensional faces in a triangulation. More...
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class | regina::detail::TriangulationBase< dim > |
| Provides core functionality for dim-dimensional triangulations. More...
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struct | regina::detail::XMLTriangulationTags< dim > |
| Internal class that indicates the XML tags and attributes used to describe top-dimensional simplices in a dim-dimensional triangulation. More...
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class | regina::detail::XMLSimplexReader< dim > |
| Helper class that reads the XML element for a single top-dimensional simplex in a dim-dimensional triangulation. More...
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class | regina::detail::XMLSimplicesReader< dim > |
| Helper class that reads the XML element for the set of all top-dimensional simplices in a dim-dimensional triangulation. More...
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class | regina::detail::XMLTriangulationReaderBase< dim > |
| Helper class that provides core functionality for the XML packet reader that reads a single dim-dimensional triangulation. More...
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REGINA_API const int *const | regina::detail::binomSmall_ [17] |
| A lookup table that stores (n choose k) for all n ≤ 16. More...
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static constexpr int | regina::detail::FaceNumberingImpl< dim, subdim, lex >::nFaces |
| The total number of subdim-dimensional faces in each dim-dimensional simplex. More...
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static constexpr int | regina::detail::FaceNumberingImpl< dim, subdim, false >::nFaces |
| The total number of subdim-dimensional faces in each dim-dimensional simplex. More...
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static constexpr int | regina::detail::FaceNumberingImpl< dim, 0, true >::nFaces = dim + 1 |
| The total number of vertices in each dim-dimensional simplex. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 1, 0, true >::nFaces = 2 |
| The total number of vertices in each edge. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 2, 0, true >::nFaces = 3 |
| The total number of vertices in each triangle. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 2, 1, false >::nFaces = 3 |
| The total number of edges in each triangle. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 3, 0, true >::nFaces = 4 |
| The total number of vertices in each tetrahedron. More...
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static const int | regina::detail::FaceNumberingImpl< 3, 1, true >::edgeNumber [4][4] |
| A table that maps vertices of a tetrahedron to edge numbers. More...
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static const int | regina::detail::FaceNumberingImpl< 3, 1, true >::edgeVertex [6][2] |
| A table that maps edges of a tetrahedron to vertex numbers. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 3, 1, true >::nFaces = 6 |
| The total number of edges in each tetrahedron. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 3, 2, false >::nFaces = 4 |
| The total number of triangles in each tetrahedron. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 4, 0, true >::nFaces = 5 |
| The total number of vertices in each pentachoron. More...
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static const int | regina::detail::FaceNumberingImpl< 4, 1, true >::edgeNumber [5][5] |
| A table that maps vertices of a pentachoron to edge numbers. More...
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static const int | regina::detail::FaceNumberingImpl< 4, 1, true >::edgeVertex [10][2] |
| A table that maps edges of a pentachoron to vertex numbers. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 4, 1, true >::nFaces = 10 |
| The total number of edges in each pentachoron. More...
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static const int | regina::detail::FaceNumberingImpl< 4, 2, false >::triangleNumber [5][5][5] |
| A table that maps vertices of a pentachoron to triangle numbers. More...
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static const int | regina::detail::FaceNumberingImpl< 4, 2, false >::triangleVertex [10][3] |
| A table that maps triangles of a pentachoron to vertex numbers. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 4, 2, false >::nFaces = 10 |
| The total number of triangles in each pentachoron. More...
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static constexpr int | regina::detail::FaceNumberingImpl< 4, 3, false >::nFaces = 5 |
| The total number of tetrahedra in each pentachoron. More...
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Implementation details that end users should not need to reference directly.
template<int dim, int subdim>
Given a subdim-face number within a dim-dimensional simplex, returns the corresponding canonical ordering of the simplex vertices.
If this canonical ordering is c, then c[0,...,subdim] will be the vertices of the given face in increasing numerical order. That is, c[0] < ... < c[subdim]. The remaining images c[(subdim + 1),...,dim] will be ordered arbitrarily.
Note that this is not the same permutation as returned by Simplex<dim>::faceMapping<subdim>():
- ordering() is a static function, which returns the same permutation for the same face number, regardless of which dim-simplex we are looking at. The images of 0,...,subdim will always appear in increasing order, and the images of (subdim + 1),...,dim will be arbitrary.
- faceMapping() examines the underlying face F of the triangulation and, across all appearances of F in different dim-simplices: (i) chooses the images of 0,...,subdim to map to the same respective vertices of F; and (ii) chooses the images of (subdim + 1),...,dim to maintain a "consistent
orientation" constraint.
- Parameters
-
face | identifies which subdim-face of a dim-dimensional simplex to query. This must be between 0 and (dim+1 choose subdim+1)-1 inclusive. |
- Returns
- the corresponding canonical ordering of the simplex vertices.
A table that maps triangles of a pentachoron to vertex numbers.
Triangles in a pentachoron are numbered 0,...,9. This table converts triangle numbers to vertices; in particular, triangle i in a pentachoron is spanned by vertices triangleVertex[i][0]
, triangleVertex[i][1]
and triangleVertex[i][2]
. Here i must be between 0 and 9 inclusive; the resulting vertex numbers will be between 0 and 4 inclusive.
It is guaranteed that triangleVertex[i][0]
will always be smaller than triangleVertex[i][1]
, which in turn will always be smaller than triangleVertex[i][2]
.
- Note
- Accessing
triangleVertex[i][j]
is equivalent to calling ordering(i)[j]
.