Optimal packings of superdisks and the role of symmetry.

Almost all studies of the densest particle packings consider convex particles. Here, we provide exact constructions for the densest known two-dimensional packings of superdisks whose shapes are defined by |x{1}|{2p}+|x{2}|{2p}<or=1 and thus contain a large family of both convex (p>or=0.5) and concave (0<p<0.5) particles. Our candidate maximal packing arrangements are achieved by certain families of Bravais lattice packings, and the maximal density is nonanalytic at the "circular-disk" point (p=1) and increases dramatically as p moves away from unity. Moreover, we show that the broken rotational symmetry of superdisks influences the packing characteristics in a nontrivial way.