The paper is concerned with the use of symmetry groups as descriptors for surfaces-such symmetry groups can be used to characterise the constraints imposed between two bodies by areal contact between their surfaces. A method is presented for combining constraints imposed by spatial relationships between features (infinite geometric entities) of bodies. It consists of an algorithm for computing the intersections of infinite symmetry groups from their characteristic invariants. It is demonstrated that invariants of symmetry groups for these combined features can be computed in an efficient and practical way