Bimesotruncatotetracontoctachoron

The bimesotruncatotetracontoctachoron or bimtec is a convex isogonal polychoron that consists of 48 truncated cubes and 144 ditetragonal trapezoprisms. 2 truncated cubes and 4 ditetragonal trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite icositetricositetrachora (that is, variants of the tetracontoctachoron with F 4 symmetry).

If the icositetricositetrachora have edge lengths a and b, the lacing edges between then have length $$(b-a)(2-\sqrt2)$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{4+\sqrt2}{2}$$ ≈ 1:2.70711.