A double-sided reversible and indexable cutting insert has identical opposing first and second end faces and a peripheral side surface extending therebetween. A clamping through-bore extends between, and opens out to, the first and second end faces. The cutting insert has a median plane between the first and second end faces, and a through-bore axis extending perpendicularly through the median plane. The cutting insert also has a Y-fold rotational symmetry about the through-bore axis. The peripheral side surface has Y major side surfaces and Y minor side surfaces, each minor side surface interconnecting two adjacent major side surfaces. Each minor side surface is a section of a single cylindrical surface having a given radius, the given radius being greater than a minor side surface distance of each minor side surface from the through-bore axis.