Biprismatotetracontoctachoron

The biprismatotetracontoctachoron or bipec is a convex isogonal polychoron that consists of 48 octahedra, 288 rectangular trapezoprisms and 192 triangular prisms. 1 octahedron, 4 triangular prisms, and 4 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite small disprismatoicositetricositetrachora (that is, variants of the small prismatotetracontoctachoron with F4 symmetry).

If the small disprismatoicositetricositetrachora have edge lengths a and b, the lacing edges between then have length $$(b-a)\sqrt{2-\sqrt2}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$1+\sqrt{\frac{2+\sqrt2}{2}}$$ ≈ 1:2.30656.