Products of Hop an manifolds and codimension - 2 brators

A device for polishing plano-convex lenses, quartz oscillators and the like comprises a lapping dish having a concave spherical surface and mounted for oscillating and rotary movement. The material to be polished is held by a suction rotary chuck which applies the material to be polished against the lapping dish with a selected pressure. Separate motors are provided for rotating and oscillating the lapping dish and for rotating the material to be polished.