Cutting insert and tool, consisting of a toolholder and cutting insert

The invention relates to a cutting insert with a supporting surface (11) and a cutting surface at a distance therefrom and at least one flank (12) positioned by a positive clearance angle, which form a circumferential round or polygonal cutting edge, as well as at least one cutting edge point (13) at a maximum distance from a plane in which the supporting surface (11) is located and at least one cutting edge point (16, 17) at a minimum distance from said plane. According to the invention, the geometric location of each cutting edge point, but at least the cutting edge point (16, 17) at a minimum distance and points adjacent thereto is teh intersection point of a vertical envelope with a plane parallel to the supporting surface (11), wherein the vertical envelope is perpendicular to the supporting surface (11) and is formed by a plurality of parallel vertical lines (18, 19) that lie in the plane parallel to the support surface (11) in which the point (13) with maximum distance from the support surface plane li