Abstract: Method for producing workpieces having polygonal outer and/or inner contours, preferably by machining, wherein the workpiece to be machined rotates at a constant speed about a stationary axis, while the tool is guided on a closed, curved path, with the rate of rotation of the workpiece and the speed at which the tool revolves on its curved path being dependent upon one another and wherein further the tool engages at the workpiece during the entire revolution. The traveling speed of the tool during one revolution is varied according to a law of motion which is defined by the stationary rotation of the workpiece, the path of movement of the tool and the desired polygonal contour. The tool is guided, preferably translatorily, on a circularly cylindrical path.