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 vertical bar x(1)vertical bar(2p) + vertical bar x(2)vertical bar(2p) <= 1 and thus contain a large family of both convex (p >= 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.