Hexagonal antiditetragoltriate

The hexagonal antiditetragoltriate or hadet is a convex isogonal polychoron and the fourth member of the antiditetragoltriate family. It consists of 12 hexagonal prisms, 72 rectangular pyramids, and 72 tetragonal disphenoids of two kinds. 2 hexagonal 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 hexagonal duoprisms where the larger hexagon is more than $$\frac{2\sqrt3}{3}$$ times the edge length of the smaller one.