particles by a finite small amount such that the sizes of inter-particle gaps increase from 10 − 6 to 10 − 4 of the particle diameter. 

[40] A. Donev, S. Torquato and F. H. Stillinger, J. Appl. Phys. 95 , 989 (2004). 

[41] A. Donev, F. H. Stillinger and S. Torquato, Phys. Rev. Lett. 96 , 225502 (2006); A. Donev, F. H. Stillinger and S. Torquato, J. Chem. Phys. 127 , 124509 (2007). 

[42] The numerically computed right and left slope of φ ( p ) for binary superdisks at p = 1 are a$_{+}$ ≈ 0 . 135 and a$_{−}$ ≈ − 0 . 083, respectively. 

[43] The numerically computed right and left slope of φ ( p ) for monodispersed superballs at p = 1 are a$_{+}$ ≈ 0 . 229 and a$_{−}$ ≈ − 0 . 113, respectively. 

[44] J. D. Bernal and J. Mason, Nature (London) 385 , 910 (1990). 

[45] The fact that the superdisks and superballs can significantly explore their configurational space associated with the rotational degrees of freedom, i.e., they can rotate significantly, near the jamming point is manifested as long-period oscillations of the pressure of the system, which is also observed for ellipsoid systems. 

[46] In this sense, it is similar to the ellipse packings in two dimensions, i.e., the isostatic packing requires six contacts per particles, which can only be realized with translational crystallization. 

[47] Expansion rates γ within the range 0 . 1 − 0 . 5 were employed to suppress the formation of order in the superdisk and superball packings; larger γ would cause numerical instability of the DTS algorithm. Note that for ellipsoids, γ ∼ 0 . 05 is sufficient to produce random packings with vanishing orientational order [31, 32]. 

