prediction has been verified computationally with very high accuracy [17, 18]. On the other hand, a packing is hypostatic if it is mechanically stable (i.e., jammed) while the number of constraints is smaller than the number of degrees of freedom. For large packings, this is equivalent to the inequality Z < 2 f . It has been shown that a jammed sphere packing can be not hypostatic [17]. It is also of great practical and fundamental interest to understand the organizing prin- ciples of dense packings of nonspherical particles [19–28]. The effect of asphericity is an important feature to include on the way to characterizing more completely real dense granu- lar media as well as low-temperature states of matter. Another important application relates to supramolecular chemistry [29] of organic compounds whose molecular constituents can possess many different types of group symmetries [30]. Such systems can be approximated by nonspherical hard particles with the same group symmetries. Recently, MRJ packings of three-dimensional ellipsoids [31, 32] have been studied. In particular, it was found that the density φ and the average coordination number Z (the average number of touching neighbors per particle) increase rapidly, in a cusp-like manner, as asphericity is introduced from the sphere point. The density φ reaches a maximum at a critical aspect ratio α ∗ [33] and then begins to decrease; while Z is increasing monotonically until it attains the plateau value for all α beyond α ∗ . In addition, Z is always smaller than twice the number of degrees of freedom per particle f with its plateau value slightly below 2 f (for an ellipse f = 3 and for an ellipsoid f = 6). In other words, the packings are hypostatic [32]. The characteristics of MRJ ellipsoid packings are distinctly different from their densest crystalline counterpart [21], in which φ increases smoothly as one moves away from the sphere point, and reaches a plateau value of 0 . 7707 ... for α > √$_{3 (oblate spheroids)}$ and α < 1 $_{/}$√$_{3 (prolate spheroids).}$ In Refs. [25] and [26], we studied dense and maximally dense packings of superballs , a family of nonspherical particles with versatile shapes. In particular, a d -dimensional superball is a centrally symmetric body in R d occupying the region where x$_{i}$ ( i = 1 , . . . , d ) are Cartesian coordinates and p ≥ 0 is the deformation parameter , which indicates to what extent the particle shape has deformed from that of a d -dimensional sphere ( p = 1). Henceforth, the terms superdisk and superball will be our designations for 4 | x$_{1}$ | 2 p + | x$_{2}$ | 2 p + · · · + | x$_{d}$ | 2 p ≤ 1 , (1)