A cutting insert for retention in a rotating cutting tool having an axis of rotation has two opposing end surfaces and a peripheral surface extending therebetween, each end surface having a mutual first axis of symmetry passing through the end surfaces about which each end surface has N-fold rotational symmetry for some value of N where N is chosen from the group consisting of 2, 3 and 4. A peripheral cutting edge is formed at the junction between each end surface and the peripheral surface, the peripheral cutting edge having N curved cutting edges merging with N straight cutting edges which extend between the curved cutting edges at extremities thereof. The curved cutting edges of the two end surfaces are not aligned in an end view of the cutting insert along the first axis of symmetry.