. The work reported in this paper applies group theory to  characterize local surface contact among solids, and makes such a formalization  computationally tractable. This paper serves three purposes:  (1) to report a new treatment of contacting surfaces as oriented sets and  to verify the consistency of their corresponding symmetry groups in a  group theoretical formalization framework; (2) to give a concise summary  of this group theoretical approach, from theory, to algorithms, to  applications; (3) to pinpoint some unsolved problems and possible future  directions.  