Biprismatocubic honeycomb

The biprismatocubic honeycomb or bipach is an isogonal honeycomb that consists of cubes, square prisms and rectangular trapezoprisms obtained as the union of two small prismated cubic honeycombs.

This honeycomb can be alternated into a biruncicubic honeycomb, although it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:(3+2$\sqrt{3}$)/2 ≈ 1:2.15470.

Optimization
Since the biprismatocubic honeycomb has one variation in its highest symmetry, optimization gives the following edge lengths as:


 * 1
 * (3+2$\sqrt{3}$)/3 ≈ 2.1547005383792515290182976