Great birhombitetrahedral honeycomb

The great birhombitetrahedral honeycomb or gabreth is an isogonal honeycomb that consists of great rhombitetratetrahedra, ditrigonal trapezoprisms and rectangular trapezoprisms obtained as a subsymmetrical faceting of the great prismated cubic honeycomb. However, it cannot be made uniform.

This honeycomb can be alternated into a snub bitetrahedral honeycomb, which is also nonuniform.

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


 * 1
 * 2