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## C. Hypostaticity and Nongeneric Local Structures 

There have been conjectures [15, 16] that frictionless random packings have just enough constraints to completely statically define the system (i.e., it is isostatic ), i.e., for large packings, one has Z = 2 f . It has been shown both experimentally and computationally that although the isostatic conjecture [15] holds for large sphere packings [40, 44], it is generally not applicable to nonspherical particles, such as ellipsoids [31, 32]. It was found that even for ellipsoids with large aspect ratios, Z is still slightly below 2 f [31]. 

Here we observe that in MRJ packings of superdisks and superballs Z is significantly smaller than 2 f for all values of p examined, i.e., the packings are significantly hypostatic . The hypostatic packings result from the competition between f$_{T}$ translational and f$_{R}$ ro- tational degrees of freedom of the particles ( f = f$_{R}$ + f$_{T}$ ) in developing the contacting networks close to the jamming point. In particular, although it is true that to constrain the translational degrees of freedom each particle needs at least 2 f$_{T}$ contacts, rotational degrees of freedom can be blocked with less than 2 f$_{R}$ additional contacts per particle if 

