Elongated triangular prismatic honeycomb

The elongated triangular prismatic honeycomb, or etoph, is a convex uniform honeycomb. 4 cubes and 6 triangular prisms join at each vertex of this honeycomb. As the name suggests, it is the honeycomb product of the elongated triangular tiling and the apeirogon. It can also be thought of as a triangular prismatic honeycomb with layers of cubes inserted between adjacent layers of triangular prisms.

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

where i, j, and k range over the integers.
 * $$\left(i\frac{2+\sqrt3}{2}\pm\frac12,\,j+\frac{i}{2},\,k\right),$$