Bimesotruncatotetrahedral honeycomb

The bimesotruncatotetrahedral honeycomb or bimteth is an isogonal honeycomb that consists of truncated tetrahedra, tetrahedra, and ditrigonal trapezoprisms. 1 tetrahedron, 3 truncated tetrahedra, and 6 ditrigonal trapezoprisms join at each vertex. It can be obtained as the union of two bitruncated tetrahedral-octahedral honeycombs with P4 symmetry.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+2\sqrt6}{3}$$ ≈ 1:2.63299.