When planning or describing an assembly, statements about how features should (or might) relate spatially can be expressed in terms of the symmetry groups of the features. The same is true of the interpretation of sense data. The authors show how to associate symmetry groups with features of body models created by the PADL2 system of A.A.G. Requicha and Voelcker (1982), and how to perform reasoning about spatial relationships between features of bodies occurring in an assembly in this group-theoretic context. Techniques for implementing this approach in numerical algorithms are described, with a focus on its extension to include finite rotational symmetries