Abstract: A triangular threading insert has a mount portion (60) with three sides forming locating faces (50, 52, 54) that lie on the three sides of an imaginary triangle (96) and has three cutting arms (21-23) with outer edges (80) for cutting threads. The outer edge of each arm projects sidewardly beyond the sides of the imaginary triangle, to leave locating faces of long length. The top face (110) of the mount portion forms a hexagon with the cutting arms projecting radially from three of the sides (71-73) of the hexagon, and with the other three sides of the hexagon extending parallel to the locating faces of the mount portion. Each locating face has a smaller height (H) than the thickness (T) of the insert, with concave border regions merging the top and bottom (124, 126) of each locating face to the top and bottom faces of the insert, and merging horizontally-spaced ends (134, 136) of each locating face to a cutting arm.