Bitetrahedral honeycomb

The bitetrahedral honeycomb or bithon is an isogonal honeycomb that consists of tetrahedra and triangular antiprisms obtained as the union of two tetrahedral-octahedral honeycombs.

Optimization
Since the bitetrahedral honeycomb has no variations in its highest symmetry, the two edge lengths are always at a ratio of $\sqrt{6}$/4:1 ≈ 0.61237:1.