Medial birhombatocubic honeycomb

The medial birhombatocubic honeycomb or mabirch is an isogonal honeycomb that consists of cuboctahedra, square prisms, 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.