Abstract: An apparatus for simultaneously grinding a peripheral shape and edge surface upon a pair of ophthalmic lenses including an abrading wheel and first and second floating heads for rotatably supporting a pair of ophthalmic lenses on either side of the abrading wheel. The lenses are biased toward the wheel and are incrementally rotated about mutually parallel axes which lie parallel with a central longitudinal axis of the abrading wheel. An electronic control system is operably connected to each of the lenses and serves to control incremental rotation of each of the lenses as well as lateral engagement of the lenses with the central abrading wheel.