Triangular prismatic honeycomb

The triangular prismatic honeycomb, or tiph, is a convex noble uniform honeycomb. 12 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the triangular tiling and the apeirogon.

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

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

Representations
A triangular prismatic honeycomb has the following Coxeter diagrams: