An indexable cutting insert comprises a flank face having a generally parallelogram shape and a plurality of side faces. The flank face is bounded by a plurality of edges. Each edge joins the flank face with one of the side faces. The plurality of edges comprises a first cutting edge and a second cutting edge. The first cutting edge has a shape corresponding to a portion of a first bent curve and the second cutting edge has a shape corresponding to a portion of a second bent curve. The second bent curve is obtainable by a translation of the first bent curve along a width direction of the cutting insert. The cutting insert has a two-fold rotational symmetry with respect to an axis of symmetry that is perpendicular to the width direction, a longitudinal direction of the cutting insert being perpendicular to the width direction and the axis of symmetry.

A turning insert includes a top surface, an opposite bottom surface, side surfaces connecting the top surface and the bottom surface and two opposite nose portions. Each nose portion includes a convex nose cutting edge, a first cutting edge and a second cutting edge. The convex nose cutting edge connects the first and second cutting edges. A bisector extends equidistantly from the first and second cutting edges. In a top view the first and second cutting edges on the same nose portion form a nose angle () of 70-85 relative to each other. Each nose portion includes a third convex cutting edge adjacent to the first cutting edge and a fourth cutting edge adjacent to the third cutting edge. In a top view the fourth cutting edge forms an angle () of 0-34 relative to the bisector.

A cutting tool has an indexable cutting insert removably secured to a holding portion of an insert holder. The cutting insert has opposing first and second end surfaces with a peripheral side surface extending therebetween and a central mounting portion. The cutting insert has a plurality of cutting portions circumferentially spaced apart about a central axis, each cutting portion having a rake and relief surfaces located on the peripheral side surface. The central mounting portion has a plurality of female type or male type mounting elements having opposing first and second mounting flanks. The plurality of rake surfaces and first mounting flanks face in a first direction about the central axis, the plurality of second mounting flanks face in a second direction about the central axis opposite to the first direction, and each second mounting flank extends further from the central axis than its associated opposing first mounting flank.