Pentagonal antiditetragoltriate

The pentagonal antiditetragoltriate or paddet is a convex isogonal polychoron and the third member of the antiditetragoltriate family. It consists of 10 pentagonal prisms, 50 rectangular pyramids, and 50 tetragonal disphenoids of two kinds. 2 pentagonal prisms, 4 tetragonal disphenoids, and 5 rectangular pyramids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform pentagonal duoprisms where the larger pentagon is more than $$\sqrt5-1$$ times the edge length of the smaller one.

The grand antiprism can be thought of as the convex hull of two inversely oriented pentagonal ditetragoltriates, with the pentagons having a ratio of 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.