Standard polygon profiles P3G and P4C (according to DIN 32711 and DIN 32712) are positive-locking shaft to hub connections. They have, compared with conventional connections like feathers or splines, many advantages. The field of research concerns basic investigations of the geometry of polygons, behavior of functions, tolerancing and manufacturing. The question of standardization, resp. new standardization is an essential point for the industrial use of this machine part. Tapered polygon profiles and the development of new, optimized non-circular-shapes for positive-locking torque transmission are some more promising fields of research.