Snub rectified cubic honeycomb

The snub rectified cubic honeycomb or serch is an isogonal honeycomb that consists of snub cubes, pyritohedral icosahedra, tetragonal disphenoids and sphenoids obtained through the process of alternating the great rhombated cubic honeycomb. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.02551, where a is the second largest real root of 43x6-1384+1282-32.

Optimization
Since the snub rectified cubic honeycomb has two degrees of variations in its highest symmetry, optimization gives the following edge lengths as:


 * $$root(32x^6-128x^4+138x^2-43, 5) ≈ 0.9751208138297195564947756$$
 * $$1$$