Enneagonal ditetragoltriate

The enneagonal ditetragoltriate or edet is a convex isogonal polychoron and the seventh member of the ditetragoltriate family. It consists of 18 enneagonal prisms and 81 rectangular trapezoprisms. 2 enneagonal 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 enneagonal prismatic swirlchora.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$1+{\sin\frac\pi9}\sqrt{2}$$ ≈ 1:1.48369. This value is also the ratio between the two squares of the two semi-uniform duoprisms.