In 4D space, the Hopf angles parameterize the 3-sphere. For fixed they describe a torus parameterized by and , with being the special case of the Clifford torus in the - and -planes. These tori are not the usual tori found in 3D-space. While they are still 2D surfaces, they are embedded in the 3-sphere. The 3-sphere can be stereographically projected onto the whole Euclidean 3D-space, and these tori are then seen as the usual tori of revolution. It can be seen that a point specified by undergoing a rotation with the - and -planes invariant will remain on the torus specified by . The trajectory of a point can be written as a function of time as and stereographically projected onto its associated torus, as in the figures below. In these figures, the initial point is taken to be , i.e. on the Clifford torus. In Fig. 1, two simple rotation trajectories are shown in black, while a left and a right isoclinic trajectory is shown in red and blue respectively. In Fig. 2, a general rotation in which and is shown, while in Fig. 3, a general rotation in which and is shown.