Trihexagonal prismatic honeycomb

The trihexagonal prismatic honeycomb, or thiph, is a convex uniform honeycomb. 4 triangular prisms and 4 hexagonal prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the trihexagonal tiling and the apeirogon.

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


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

Where i, j, and k range over the integers.

Representations
A trihexagonal prismatic honeycomb has the following Coxeter diagrams:


 * x∞o o6x3o
 * x∞x o6x3o
 * x∞o x3x3o3*a
 * x∞x x3x3o3*a