Here’s an octagonal antiprism.

Next, the dual of this antiprism: a trapezohedron. Its faces are sixteen kites.

If you stellate this trapezohedron twice, you get a two-part compound.

Now, the compound of the octagonal antiprism and its dual.

The next thing I did was to form the convex hull of this compound.

The next thing I did was to examine this convex hull’s dual.

Lastly, I stellated this dual once.

I did all of this using Stella 4d: Polyhedron Navigator. You can try this software for free at http://www.software3d.com/Stella.php.