Heptagonal antiditetragoltriate

The heptagonal antiditetragoltriate or headet is a convex isogonal polychoron and the fifth member of the antiditetragoltriate family. It consists of 14 heptagonal prisms, 98 rectangular pyramids, and 98 tetragonal disphenoids of two kinds. 2 heptagonal 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 heptagonal duoprisms where the larger heptagon is more than $$\frac{1}{\cos\frac\pi7}$$ times the edge length of the smaller one.