Biprismatodecachoron

The biprismatodecachoron or biped is a convex isogonal polychoron that consists of 10 tetrahedra, 30 rectangular trapezoprisms and 20 triangular prisms. 1 tetrahedron, 3 triangular prisms, and 6 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite small disprismatopentachora (that is, variants of the small prismatodecachoron with A4 symmetry).

If the small disprismatopentapentachora have edge lengths a and b, the lacing edges between then have length $$(b-a)\frac{\sqrt{15}}{5}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+\sqrt{15}}{3}$$ ≈ 1:2.29099.