Charles Radin Orbits of Orbs: sphere packing meets Penrose tilings (338K, postscript) ABSTRACT. The venerable study of optimum density problems, such as packing spheres as efficiently as possible, has been revitalized by investigations on aperiodicity, a subject best known through the Penrose kite \& dart tilings. The result is a generalization of the basic notion of geometric symmetry for patterns in space.