Triangular tiling

The triangular tiling, or trat, is one of the three regular tilings of the Euclidean plane. 6 triangles join at each vertex of this tiling. It is also the 2-dimensional simplectic honeycomb. It is also the alternation of the hexagonal tiling.

Vertex coordinates
The vertices of a triangular tiling of edge length 1 are given by

where i and j range over the integers.
 * $$\left(i\frac{\sqrt3}{2},\,j+\frac{i}{2}\right),$$

Representations
A triangular tiling has the following Coxeter diagrams:


 * o6o3x (full symmetry)
 * x3o3o3*a (P3 symmetry, triangles considered of two types)
 * s6o3o (alternated hexagonal tilling)
 * o6s3s
 * s3s3s3*a
 * xdoo3xodo3xood&#zx (as hull of hexagonal tiling and three larger triangular tilings)

Related polytopes
The triangular tiling is te colonel of a two-member that also includes the ditrigonary triangular-hemiapeirogonal tiling. Also in this regiment is a compound of three hexagonal tilings.