In the last decade polygon joints and their manufacturing equipment were introduced. The finishing of external polygon surfaces has been solved, as well as that of internal surfaces of materials of low hardness (HRC < 45). Finishing of hardened bores shows well-known difficulties. The author presents the results of his research performed in this field, the development of a new machining process and a tool family, which is protected by a patent. (C) 2001 Published by Elsevier Science B.V.