Self-Intersecting Truncated Regular Duals

The dual of a truncated regular polyhedron is face-transitive with faces shaped like isosceles triangles. 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 five truncated regular duals that are not self-intersecting, namely the Triakis Tetrahedron, the Tetrakis Hexahedron, the Triakis Octahedron, the Pentakis Dodecahedron, and the Triakis Icosahedron. When self-intersection is allowed, there are five other truncated regular duals.