Bicubic honeycomb

The bicubic honeycomb or bichon, also known as the tetragonal disphenoidal honeycomb is a noble honeycomb that consists of tetragonal disphenoid cells. 24 cells join at each vetex, with the vertex figure being a tetrakis hexahedron. It can be constructed as the union of two dual cubic honeycombs.

The ratio between the longest and shortest edges is 1:$$\frac{2\sqrt3}{3}$$ ≈ 1:1.15470.

Vertex coordinates
The vertices of a bicubic honeycomb based on two cubic honeycombs of edge length 1 are given by: where i, j, and k are integers.
 * $$\left(i,\,j,\,k\right),$$
 * $$\left(i+\frac12,\,j+\frac12,\,k+\frac12\right).$$