Hexagonal prismatic honeycomb

The hexagonal prismatic honeycomb, or hiph, is a convex noble uniform honeycomb. 6 hexagonal prisms join at each vertex of this honeycomb. It is the honeycomb product of the hexagonal tiling and the apeirogon.

This honeycomb can be alternated into a gyrated tetrahedral-octahedral honeycomb, which can be made uniform.

Vertex coordinates
Coordinates for the vertices of a hexagonal prismatic honeycomb of edge length 1 are given by:


 * $$\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2},\,k\right),$$
 * $$\left(3i\pm1,\,\sqrt3j,\,k\right),$$

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

Representations
A hexagonal prismatic honeycomb has the following Coxeter diagrams: