Cutting insert and a milling cutting tool

A milling cutting tool comprising:

• at least one cutting insert including two opposing side surfaces and a peripheral surface extending between said side surfaces and formed by four identical lateral surfaces, a major edge at each intersection of a lateral surface and a side surface connecting opposing said lateral surfaces and having a major cutting edge extending over at least a part of the major edge, and a minor cutting edge connected to each major cutting edge by a corner cutting edge at an intersection of adjacent lateral surfaces;
• a tool body including a front end, a rear end, between which a central rotation axis extends around which the tool is rotatable in a direction of rotation, and at least one insert pocket formed in a transition between the front end and an envelope surface extending between the front end and the rear end of the tool body, wherein said insert pocket includes adjacent side and rear walls generally transverse to a base, each said side surface of the cutting insert being provided with a first support surface configured to be supported by a first support face of the at least one pocket of the tool body providing a radial support to the insert and each lateral surface being provided with a second support surface configured to be supported by a corresponding second support face of the pocket providing an axial support to the insert in two of eight index positions of the insert and by a corresponding third support face of the pocket providing a tangential support to the insert in two other of eight index positions, wherein each lateral surface is provided with a single second support surface being concave as seen in a direction perpendicular to the side surfaces and extending diagonally across the lateral surface;
• and
• a fastening device configured to secure said insert in said pocket while pressing two said second support surfaces of the insert against said second and third support face of the pocket.