Enneagonal duoexpandoprism

The enneagonal duoexpandoprism or edep is a convex isogonal polychoron and the eighth member of the duoexpandoprism family. It consists of 36 enneagonal prisms of two kinds, 81 rectangular trapezoprisms, 162 wedges, and 81 tetragonal disphenoids. 2 enneagonal prisms, 1 tetragonal disphenoid, 3 wedges, and 2 rectangular trapezoprisms join at each vertex. It can be obtained as the convex hull of two orthogonal enneagonal-octadecagonal duoprisms, or more generally enneagonal-dienneagonal duoprisms, and a subset of its variations can be obtained by expanding the cells of an enneagonal duoprism outward. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2}{1+{\tan\frac{\pi}{18}}\sqrt{3+4\cos\frac{\pi}{9}}}$$ ≈ 1:1.37136.