The 4-dimensional analog of the icosahedral symmetry group "I"h is the symmetry group of the 600-cell (also that of its dual, the 120-cell). Just as the former is the Coxeter group of type "H"3, the latter is the Coxeter group of type "H"4, also denoted [3,3,5]. Its rotational subgroup, denoted is a group of order 7200 living in SO(4). SO(4) has a double cover called Spin(4) in much the same way that Spin(3) is the double cover of SO(3). Similar to the isomorphism Spin(3) = Sp(1), the group Spin(4) is isomorphic to Sp(1) × Sp(1).