Heptagonal ditetragoltriate

The heptagonal ditetragoltriate or hedet is a convex isogonal polychoron and the fifth member of the ditetragoltriate family. It consists of 14 heptagonal prisms and 49 rectangular trapezoprisms. 2 heptagonal prisms and 4 rectangular trapezoprisms join at each vertex. However, it cannot be made uniform. It is the first in an infinite family of isogonal heptagonal prismatic swirlchora.

It can be obtained as the convex hull of 2 similarly oriented semi-uniform heptagonal duoprisms, one with a larger xy heptagon and the other with a larger zw heptagon.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$1+{\sin\frac\pi7}\sqrt{2}$$ ≈ 1:1.61360. This value is also the ratio between the two squares of the two semi-uniform duoprisms.