Truncated cyclotruncated tetrahedral-octahedral honeycomb

The truncated bitruncated tetrahedral-octahedral honeycomb, also called the truncated cyclotruncated tetrahedral-octahedral honeycomb or tabtatoh is an isogonal honeycomb that consists of ditruncated tetrahedra, truncated tetrahedra, and triangular antiprisms. 3 ditruncated tetrahedra, 1 truncated tetrahedron, and 1 triangular antiprism join at each vertex. It can be formed by truncating the bitruncated tetrahedral-octahedral honeycomb.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the truncated tetrahedral-octahedral honeycomb with P4 symmetry, where if the truncated tetrahedral-octahedral honeycombs are of the form a3b3c3o3*a, then c = b+3a.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.02551, where a is the second largest real root of 43x6-138x4+128x2-32=0.

Optimization
Since the truncated bitruncated tetrahedral-octahedral honeycomb has one variation in its highest symmetry, optimization gives the following edge lengths as:


 * $\sqrt{3}$/3 ≈ 0.57735
 * 1