1 1.5 2 2.5 3 p 0.625 0.65 0.675 0.7 0.725 0.75 1 1.5 2 2.5 3 p 6 6.5 7 7.5 8 Z FIG. 6: The density of MRJ packings of superballs as a function of p . Insert: the average contact number Z as a function of p . B. MRJ Packings of Monodisperse Superballs In three dimensions, monodispersed superballs can be easily compressed into a jammed random packing due to geometrical frustration (i.e., the densest local particle arrangement cannot tile space). Typical jammed packing configurations are shown in Fig. 5. The quan- tities φ and Z as a function of p are shown in Fig. 6, respectively. As in two dimensions, φ and Z increase rapidly, in a cusp-like manner [43], as the particles deviate from perfect sphere. φ increases monotonically as p moves away from unity, quickly goes beyond the optimal sphere packing density and shows no signs of plateau, even for relatively large p values. The contact number per particle Z reaches its plateau value Z ∗ ≈ 8 . 15 at p ≈ 1 . 4, which is significantly smaller than 2 f = 12, indicating that the packings are hypostatic. The measured cubatic order parameter is P$_{4}$ ≈ 0 . 03 to 0 . 21, which increases with | p − 1 | . III. PACKING CHARACTERISTICS A. Rattlers MRJ packings generated in both two and three dimensions contain a small fraction of rattlers, i.e., particles that can wander freely within cages formed by their jammed non- 10