Great birhombitetrahedral honeycomb

The great birhombitetratetrahedral honeycomb is an isogonal honeycomb that consists of pyritohedral rhombicuboctahedra, square prisms and rectangular trapezoprisms obtained as a subsymmetrical faceting of the omnitruncated cubic honeycomb. However, it cannot be made uniform.

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


 * 1
 * (3+$\sqrt{6}$)/3 ≈ 1.8164965809277260327324280