A securing structure for an optical piece is disclosed and which comprises: a hub portion; a surrounding portion connected to the hub portion; a plurality of recess structures formed or otherwise provided in at least one of the hub portion and the surrounding portion and which are at least partially open on at least one side; and a rib structure that at least partially separates the plurality of recess structures. The structure is capable of use with an apparatus for securing and clamping optical lenses (e.g., spectacle lenses) requiring edge-machining.