A double-sided cutting insert having a plurality of convex cutting edges (411a,411c,421a,421c), said double-sided cutting insert comprising: a) a top face and a bottom face separated by a virtual middle plane; b) at least three convex cutting edges (411a,411c,421a,421c) on each of said top and bottom faces (401,402); c) at least three nose corners (405-408,436,437) on each of said top and bottom faces (401,402), each nose corner (405-408,436,437) connecting two of said convex cutting edges (411a,411c,421a,421c); and d) at least three peripheral side surfaces extending from the top face to the bottom face; characterized in that each convex cutting edge (411a,411c,421a,421c) comprises a substantially straight cutting edge region (411b,421b) located between two curved convex cutting edge regions (411a,411c,421a,421c); and wherein each peripheral side surface comprises: i. a first primary conical peripheral surface extending from a primary curved convex cutting edge region at said top face toward a twisted secondary curved convex cutting edge region at said bottom face, and a second primary conical peripheral surface extending from a secondary curved convex cutting edge region at said top face toward a twisted primary curved convex cutting edge region at said bottom face; ii. a first primary planar surface extending from a primary substantially straight cutting edge region at said top face toward a virtual middle plane, and a second primary planar surface extending from a primary substantially straight cutting edge region at said bottom face toward a virtual middle plane, wherein both said first and second primary planar surfaces (433,434) are truncated by at least a lateral face; and iii. a secondary peripheral surface extending from a nose corner at the top face to a nose corner at the bottom face. a) a top face and a bottom face separated by a virtual middle plane; b) at least three convex cutting edges (411a,411c,421a,421c) on each of said top and bottom faces (401,402); c) at least three nose corners (405-408,436,437) on each of said top and bottom faces (401,402), each nose corner (405-408,436,437) connecting two of said convex cutting edges (411a,411c,421a,421c); and d) at least three peripheral side surfaces extending from the top face to the bottom face; i. a first primary conical peripheral surface extending from a primary curved convex cutting edge region at said top face toward a twisted secondary curved convex cutting edge region at said bottom face, and a second primary conical peripheral surface extending from a secondary curved convex cutting edge region at said top face toward a twisted primary curved convex cutting edge region at said bottom face; ii. a first primary planar surface extending from a primary substantially straight cutting edge region at said top face toward a virtual middle plane, and a second primary planar surface extending from a primary substantially straight cutting edge region at said bottom face toward a virtual middle plane, wherein both said first and second primary planar surfaces (433,434) are truncated by at least a lateral face; and iii. a secondary peripheral surface extending from a nose corner at the top face to a nose corner at the bottom face.