The dual of a versi-quasi-regular polyhedron is face-transitive with faces shaped like bowties. 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 seven versi-quasi-regular duals, all of which are self-intersecting. All seven have non-orientable surfaces (like that of a Klein Bottle or the Real Projective Plane except with non-zero Euler characteristics).