For each rotation of 4-space (fixing the origin), there is at least one pair of orthogonal 2-planes and each of which is invariant and whose direct sum is all of 4-space. Hence operating on either of these planes produces an ordinary rotation of that plane. For almost all (all of the 6-dimensional set of rotations except for a 3-dimensional subset), the rotation angles in plane and in plane – both assumed to be nonzero – are different. The unequal rotation angles and satisfying , are almost uniquely determined by . Assuming that 4-space is oriented, then the orientations of the 2-planes and can be chosen consistent with this orientation in two ways. If the rotation angles are unequal (), is sometimes termed a "double rotation".