Most optics exhibit rotational symmetry. They are used in the vast majority of existing applications. Yet optics exhibiting non-rotational symmetries often possess numerous advantages over their more traditional, rotationally symmetric counterparts.
Examples include biconic lenses and mirrors, which combine two surface radii on a single substrate; faceted lenses and mirrors, which combine multiple plano surfaces onto a single substrate; and optical arrays -- both reflective and transmissive -- which combine multiple curved surfaces onto a single substrate. Additional non-rotationally symmetric optics include long working distance off-axis parabolas, ring-focus parabolas, and rooftop beamsplitters.