Bimesotruncatodecachoron

The bimesotruncatodecachoron or bimted is a convex isogonal polychoron that consists of 10 truncated tetrahedra and 20 ditrigonal trapezoprisms. 2 truncated tetrahedra an 4 ditrigonal trapezoprisms join at each vertex. It can be obtained as the convex hull of two opposite pentapentachora (that is, variants of the decachoron with A4 symmetry).

If the pentapentachora have edge lengths a and b, the lacing edges between then have length $$(b-a)\frac{\sqrt{10}}{5}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt{10}}{2}$$ ≈ 1:2.58114.