Bitruncatocubic honeycomb

The bitruncatocubic honeycomb or bitach is an isogonal honeycomb that consists of octahedra, triangular antiprisms, tetragonal disphenoids, and digonal disphenoids. 1 octahedron, 4 triangular antiprisms, 4 tetragonal disphenoids, and 8 digoanl disphenoids join at each vertex. It can be obtained as the union of two truncated cubic honeycombs.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{\sqrt{5+2\sqrt2}}{2}$$ ≈ 1:1.39897.