Turning tool

The invention relates to an indexable cutting insert for a cutting tool for material processing machines, which has a first axis of symmetry (A), a fastening bore (16) passing through the indexable cutting insert parallel or coaxially with the first axis of symmetry (A), wherein two groups of main cutting edges, secondary cutting edges and cutting corners are rotationally symmetrically opposite one another about a second axis of symmetry (B). At least the main cutting edges enclose an acute cutting angle ([gamma]) with a plane (E) oriented orthogonally to the first axis of symmetry (A). The invention also relates to a cutting insert holder (17) that holds and fixes the indexable cutting insert (1). A recess (9) for receiving the indexable cutting insert (1) is on an elongated base body (37) with polygonal cross-section. A support surface (38) for supporting the indexable cutting insert (1) is rotated about thelongitudinal axis (L) of the base body (37) and tilted about a second axis, aline of intersection bet