A high speed planer head. A threaded member having a frustoconical portion wedges against a knife, to clamp a knife to a hub for rotating the knife about an axis of revolution. The knife has a front and back side, two cutting edges and mirror image symmetry about a mirror plane passing through the knife. To cut both a planar face and two opposed, radiused corners, the cutting edges include respective linear face-cutting portions disposed between two concave, arcuate corner-cutting portions.