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 x1|2p+|x2|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.