The Dual of an Augmented Tetrahedron

If someone had showed me the polyhedron above, a week ago, and asked me to explain how it was constructed, I would have had a hard time coming up with the answer. I made it using Stella 4d (which you can try for free here). It’s the dual of the polyhedron shown below, which was made by augmenting the four faces of a tetrahedron with identical tetrahedra.