Self-Intersecting Quasi-Quasi-Regular Duals

The dual of a quasi-quasi-regular polyhedron is face-transitive with faces shaped like kites or darts. Face transitivity means that for any two faces of the polyhedron, there exists a translation, rotation, and/or reflection that leaves the outward appearance of the polyhedron unchanged yet moves one face to the other. There are only two quasi-quasi-regular duals that are not self-intersecting, namely the Deltoidal Icositetrahedron and the Deltoidal Hexecontahedron. When self-intersection is allowed, there are 12 other quasi-quasi-regular duals.