PURPOSE: To enhance a productivity of the work for polyhedral cutting of jewels, plane cutting of dial glasses, etc., by rotating both of the work and the cutting tool, and simultaneously performing both of the adjustments for its rotational speed ratio and the cutting tool radius.

CONSTITUTION: A distance, from center of the polygon required to be cut to each face, is assumed R, and a distance (cutter radius), from center of a cutter 2 to the point end of its edge, assumed R', and in accordance with a value of R/R', the gear ratio of a gear 3, 4 is adjusted. Subsequently in accordance with the gear ratio, the radius R' is adjusted. The above adjustment is performed according to the following formula 1 of relationship between R/R' and rotational speed ratio K. R/R'K(K-2)...1 where: K=Z/Z', Z shows a mumber of teeth of the gear 3 and Z' shows that of the gear 4. A locus of the point end of edge of the cutter 2 for a work 1, even without making R' unreasonably big, can be approximated fully practically to a plane.