Hexagonal duoprismatic tetracomb

The hexagonal duoprismatic tetracomb is a convex noble uniform tetracomb. 9 hexagonal duoprisms join at each vertex of this tessellation. It is the honeycomb product of two hexagonal tilings.

Vertex coordinates
The vertices of a hexagonal duoprismatic tetracomb of edge length 1 are given by

where i, j, k, l range over the integers.
 * $$\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2},\,3k\pm\frac12,\,\sqrt3l+\frac{\sqrt3}{2}\right),$$
 * $$\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2},\,3k\pm1,\,\sqrt3l\right),$$
 * $$\left(3i\pm1,\,\sqrt3j,\,3k\pm\frac12,\,\sqrt3l+\frac{\sqrt3}{2}\right),$$
 * $$\left(3i\pm1,\,\sqrt3j,\,3k\pm1,\,\sqrt3l\right)$$,