Abstract: A rhombic cutting insert includes cutting edges merging with each other at a nose part disposed at a diagonal acute-angle corner of an upper face of the insert. The cutting edges each form convex-curved shapes and are each inclined with respect to a mounting face of the insert. The cutting edges each include linear sub-cutting-edges, disposed in the vicinity of the nose part, forming a substantially right angle therebetween. Rake faces are formed on the upper face of the insert and each have positive rake angles and twisted-inclined surfaces. The insert is mounted on a tool part. One cutting edge serves as a peripheral cutting edge having a sub-cutting-edge disposed substantially parallel to an axis of the tool part, and the other cutting edge serves as a facing cutting edge having a sub-cutting-edge disposed substantially perpendicular to the axis of the tool part.

Abstract: A rhombic cutting insert includes a pair of cutting edges merging with each other at a nose part disposed at one of diagonal acute-angle corners of an upper face of the insert. The pair of cutting edges are individually formed in convex-curved shapes and are inclined to a mounting face of the insert from the nose part toward portions away from the nose part of the respective cutting edges. The pair of cutting edges individually include linear sub-cutting-edges disposed in the vicinity of the nose part, the sub-cutting-edges forming a substantially right angle therebetween. Rake faces formed on the upper face individually have positive rake angles and have twisted-inclined surfaces so that the rake faces become closer to the mounting face along the respective cutting edges from the nose part toward a region disposed along a diagonal line between obtuse-angle corners. The insert is mounted to a tool part so as to dispose the nose part at the periphery of an end of the tool part.