The dual of a snub quasi-regular polyhedron is face-transitive with faces shaped like irregular pentagons, hexagons, or octagons. 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 snub quasi-regular duals that are not self-intersecting, namely the Pentagonal Icositetrahedron and the Pentagonal Hexecontahedron. When self-intersection is allowed, there are 10 other snub quasi-regular duals, but only nine of these are finite. The Great Dirhombicosidodecahedron, due to its faces that pass through its center, produces a dual with vertices at infinity.