Abstract: A cutting tool for a milling, drilling or turning machine has a body with a plurality of sides and a central opening. Each side has a perimeter along which cutting planes or edges are formed. Each side has at least two such cutting planes or edges. The planes may have a straight or curved profile, or a combination of straight and curved profiles along one side. The tool may have a plurality of such cutting planes formed along each side of the tool body. The cutting planes may be located at different levels in relation to each other, entering a work piece in sequence, or may be aligned to enter the work piece simultaneously. Preferably, the cutting planes are staggered in two directions—in a feeding direction and in a cutting direction. By dividing each surface being cut into a plurality of segments, the cutting tool creates a plurality of distinct shavings, or splinters that have shorter length in comparison with conventional splinters formed by indexable tips.