triangle

Description

This element was used in the past to store a single triangle in a 2-manifold 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 triangle element stores a single triangle in a 2-manifold triangulation, along with its associated edge gluings.

The character data of this XML element should be a whitespace-separated list of three integer pairs, representing the gluings of edges 0, 1 and 2 of this triangle. Note that edge i is always opposite vertex i in a triangle.

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

A permutation is represented as an integer between 0 and 5 inclusive, representing the index of the permutation into Regina's internal array Perm3::S3. Specifically, the integers 0, 1, 2, 3, 4 and 5 represent the permutations (0,1,2), (0,2,1), (1,2,0), (1,0,2), (2,0,1) and (2,1,0) respectively.

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