Abstract: Power operated sharpener for nonconic rectangular pencils has single, orbital, weight-balanced cylindrical milling cutter which follows orbital path set by the track of an eliptical internal gear. The cylindrical milling cutter is carried loosely upstanding within an elliptic conic space rising from the track, so as to accommodate the rectangular shape of the workpiece. In operation the sharpener puts a taper on each of the four sides of the end of a rectangular pencil.