tet

Description

This element was used in the past to store a single tetrahedron in a 3-dimensional triangulation. Since Regina 7.0, all top-dimensional simplices for triangulations in all dimensions are now stored using the simplex element. Moreover, Regina now supports multiple ways of encoding the gluing permutations between these top-dimensional simplices. See simplex for details.

A tet element stores a single tetrahedron in a 3-dimensional triangulation, along with its associated face gluings.

The character data of this XML element should be a whitespace-separated list of four integer pairs, representing the gluings of faces 0, 1, 2 and 3 of this tetrahedron. Note that face i is always opposite vertex i in a tetrahedron.

For each pair, the first integer represents the tetrahedron to which the face is glued (note that tetrahedra in a triangulation are numbered 0, 1, 2, etc.). The second integer represents the permutation of vertices from this tetrahedron to the other tetrahedron describing precisely how this gluing takes place. This permutation will take the current face number of this tetrahedron to the corresponding face number of the adjacent tetrahedron, and the other three vertex numbers of this tetrahedron to the corresponding three vertex numbers on the adjacent tetrahedron to which they are identified by this gluing.

A permutation is represented as a one-byte integer as follows. If the permutation maps 0, 1, 2 and 3 to a, b, c and d respectively (where a, b, c and d are 0, 1, 2 and 3 in some order), the corresponding one-byte integer is (a + 4b + 16c + 64d). For example, the identity permutation which maps (0, 1, 2, 3) to (0, 1, 2, 3) is represented by the one-byte integer (0 + 4 + 32 + 192), which is 228 (or -28 if the byte is signed).

If a face is a boundary face (i.e., it is not glued to anything), the two corresponding integers stored in the XML character data should be -1 and -1.

Attributes

Example

The following XML snippet represents tetrahedron 0 in a triangulation. Its faces 0 and 1 are both glued to tetrahedron 1 with a gluing permutation that maps (0, 1, 2, 3) to (2, 3, 0, 1); in particular, its face 0 is glued to face 2 of tetrahedron 1 and its face 1 is glued to face 3 of tetrahedron 1. Its faces 2 and 3 are each boundary faces.

<tet> 1 78 1 78 -1 -1 -1 -1 </tet>