The octahedron's symmetry group is O, of order 48, the three dimensional hyperoctahedral group. This group's subgroups include D (order 12), the symmetry group of a triangular antiprism; D (order 16), the symmetry group of a square bipyramid; and T (order 24), the symmetry group of a rectified tetrahedron. These symmetries can be emphasized by different colorings of the faces.