Before revision:  We propose a representation called "closed symmetry loop" ' (csl) from these insights, where the angle of relevant vectors is multiplied by the symmetry order and then generalize it to 6-DOF.
After revision:  We propose a representation called "closed symmetry loop" (csl) from these insights, where the angle of relevant vectors is multiplied by the symmetry order and then generalize it to 6-DOF.