Great birhombatocubic honeycomb

The great birhombatocubic honeycomb or gabirch is an isogonal honeycomb that consists of small rhombicuboctahedra, triangular antiprisms, rectangular pyramids and tetragonal disphenoids obtained as the union of two small rhombated cubic honeycombs.

This honeycomb cannot be optimized using the ratio method, because the solution (with intended minimal ratio 1:$$\frac{\sqrt{340+136\sqrt2}}{17}$$ ≈ 1:1.35720) would yield a small birhombatocubic honeycomb instead.