Pyritosnub cubic honeycomb

The edge-snub cubic honeycomb or esch is an isogonal honeycomb that consists of snub cubes, pyritohedral rhombicuboctahedra, square prisms, rectangular trapezoprisms and wedges obtained as a subsymmetrical faceting of the great prismated cubic honeycomb. However, it cannot be made uniform.

Optimization
Since the edge-snub cubic honeycomb has three variations in its highest symmetry, optimization gives the following edge lengths as:


 * $$1$$
 * $$root(129x^8-384x^7+68x^6+496x^5-98x^4-256x^3+4x^2+48x+9, 6) ≈ 1.5460153317338912108461019$$