characteristics. For both superdisks and superballs, we find that the corresponding density φ and the average contact number Z increase rapidly, in a cusp-like manner, as the particles deviate from perfect circular disks and spheres, respectively. In particular, we find that the MRJ packing density φ increases monotonically as p moves away from unity, and shows no signs of a plateau even for large p values. This is to be contrasted with the case of ellipsoids for which the packing density reaches a maximum as the aspect ratio ratio increases from its sphere-point value and then begins to decrease as the aspect ratio grows beyond that associated with the density-maximum value. Moreover, we find that Z for superdisk and superball packings reach its associated plateau value at relatively small asphericity deviations (i.e., | p − 1 | ) and the packings remain hypo- static for all values of p examined. By “hypostatic”, we mean that the Z is smaller than twice the number of degrees of freedom per particle, compared to random ellipsoid packings where the plateau value of Z is only slightly below 2 f . Therefore, to achieve jamming, the local particle arrangements are necessarily correlated in a nontrivial way. We call such correlated structures “nongeneric” [36]. We quantify the degree of “nongenericity” of the packings by determining the fraction of local coordination configurations in which the cen- tral particles have fewer contacting neighbors than average Z . We also show that such “nongeneric” configurations are not rare, which is a rather counterintuitive conclusion. In addition, we find that although the rapid increase of density is unrelated to any observable translational order, the orientational order (e.g., the cubatic order parameter [37]) increases as p moves away from unity. These packing characteristics, which are distinctly different from that of the MRJ packings of ellipsoids, are due to the unique way in which rotational symmetry is broken in superdisk and superball packings. The rest of the paper is organized as follows: In Sec. II, we briefly describe the simulation techniques and the obtained packings. In Sec. III, we provide a detailed analysis of the novel packing characteristics. In Sec. IV, we make concluding remarks. We use an event-driven molecular dynamics packing algorithm recently developed by Donev, Torquato and Stillinger [34, 35] (henceforth, referred to as the DTS algorithm) to II. MAXIMALLY RANDOM JAMMED PACKINGS VIA COMPUTER SIMULA- TION 6