We also observe the increase of the orientational order (measured by P$_{4}$ ) associated with the increasing p values, although the largest possible expansion rate γ has been used to suppress the formation of orders (i.e., to maintain the maximal degree of randomness) [47]. As p deviates from unity, the particle shape develops “edges” and “corners” with large curvatures, which may not be able to block rotational unjamming motions if contacts occur at significantly curved regions of the particle surface. On the other hand, low-curvature contacts are more favorable, which is associated with partial alignments of the particles. The tendency of particle alignments to form low-curvature surface contacts required by jamming becomes stronger as the particle moves further away from the sphere point. Thus, there is also a competition between orientational disorder and jamming for packings of superdisks and superballs, resulting from their unique symmetry-breaking manner, which has not been observed in random packings of ellipsoids. Due to numerical difficulties, we could not use the DTS algorithm to study the random jammed packings of particles with extreme shapes, i.e., in the limit p → 0 . 5 and p → ∞ . However, it reasonable to expect considerable orientational ordering in such packings. In this paper, we studied the maximally random jammed packings of superdisks and su- perballs. The packing densities increase dramatically and nonanalytically as one moves away from the circular-disk and sphere point ( p = 1) and the packings are hypostatic. To achieve jamming, the local arrangements of particles are necessarily non-trivially correlated and we IV. CONCLUSIONS D. Nonvanishing Orientational Order which allows the trapped particle to translate and rotate and allows all the particles to grow. Although the above analysis is for local jamming (i.e., the neighbors of the central particle are fixed), it is reasonable to expect that collective particle rearrangements further facilitate the formation of nontrivial orientational correlations and thus, enable a larger number of nongeneric jamming configurations. Indeed, the numerous hypostatic jammed packings that we found from our simulations strengthen our argument that nongeneric structures are not rare. 15