An insert includes four identical cutting edges disposed at the intersection of top and side surfaces surface. Each cutting edge includes a first part edge disposed tangent to a first reference circle aligned about the central mounting aperture; a second part edge extending from the first part edge, the second part edge being connected to the first part edge via a convex curved portion; a third part edge disposed tangent to a second reference circle aligned about the central mounting aperture, the second reference circle having a smaller diameter than the first reference circle, the third part edge being connected to the second part edge via a concave curved portion; and a convexly curved corner portion extending from the third part edge of one of the identical cutting edges to the first part edge of another one of the identical cutting edges.

A cutting insert includes a substrate and a cutting-edge insert. The substrate has, in a thickness direction of the substrate, a bottom surface, and a top surface opposite to the bottom surface. The top surface has a polygonal shape composed of a plurality of sides in a plan view as seen along the thickness direction. The top surface is provided with a projection projecting to a side opposite to the bottom surface along the thickness direction. The projection has a through-hole passing through the substrate along the thickness direction. The projection has a side surface contiguous to the top surface. The side surface is composed of a curved line protruding to a side opposite to the through-hole in the plan view as seen along the thickness direction.