Trihexagonal tiling

The trihexagonal tiling, or that, is one of the eleven convex uniform tilings of the Euclidean plane. 2 hexagons and 2 triangles join at each vertex of this tiling. It can be formed from the rectification of either the triangular tiling or its dual hexagonal tiling.

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


 * $$\left(\sqrt3i,\,i+2j+1\right),$$
 * $$\left(\sqrt3i+\frac{\sqrt3}{2},\,j+\frac12\right).$$

Where i and j are integers.

Representations
A trihexagonal tiling has the following Coxeter diagrams:


 * o6x3o (full symmetry)
 * x3x3o3*a (P3 symmetry, triangles of two types)
 * s6x3o (as alternated faceting)
 * s6o3x

Related polytopes
The trihexagonal tiling is the colonel of a regiment that also includes the triangular-hemiapeirogonal tiling and the hexagonal-hemiapeirogonal tiling.