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 tetracontoctachora with F4 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.