A face-gear forging die is constructed from a blank, and is cut to specification using a wire electrical discharge machining (EDM) process. The wire electrical discharge machining process is computer controlled, according to pre-specified instructions. The wire electric discharge machining process can also be used to cut the face gear tooth (47) directly, to thereby circumvent the forging procedure. The complex, curved surfaces of the face gear teeth (47) are mathematically approximated with a ruled surface, and the mathematical approximation is input to the wire electric discharge machining apparatus for subsequent execution and forming of the die.