The packing of congruent, convex, impenetrable bodies in 3-space has obvious practical applications. Mathematical analysis has extended the search for optimal packings to spaces of dimension n > 3. Conway and Sloane, in [6] pp. 11–12, list references for applications of sphere packings in geometry and number theory, in digital communication, in chemistry and physics, in numerical approximations, and in superstring theory in mathematical physics. Tilings are, in a sense, optimal packings, leaving no space between the bodies. Their applications range from practical tilings or tessellations of walls and areas of ground, through structure determination in crystallography [5] and the physics of crystalline matter, to aperiodic tilings [14] and to the mathematical analysis of topological manifolds [40] and their applications in cosmology [37]. In many applications, a local motif is uniquely related to a body or geometric object. The geometric arrangement then generates a pattern with this motif. In covering, one allows the overlap of the geometric objects. Any point is still covered by at least one geometric object. Therefore local motifs attached to geometric objects again generate a pattern.