Dodecagonal antiditetragoltriate

The dodecagonal antiditetragoltriate or twadet is a convex isogonal polychoron and the tenth member of the antiditetragoltriate family. It consists of 24 dodecagonal prisms, 288 rectangular pyramids, and 288 tetragonal disphenoids of two kinds. 2 dodecagonal prisms, 4 tetragonal dispheonids, and 5 rectangular pyraids join at each vertex. However, it cannot be made scaliform.

It can be formed as the convex hull of 2 oppositely oriented semi-uniform dodecagonal duoprisms where the larger dodecagon is more than $$\sqrt6-\sqrt2$$ times the edge length of the smaller one.