Isostaticity of constraints in amorphous jammed systems of soft frictionless Platonic solids

Abstract

The average number of constraints per particle <C(total)> in mechanically stable amorphous systems of Platonic solids approaches the isostatic limit at the jamming point (<C(total)>→12), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming, chainlike face-face clusters form with finite extent--a signature of amorphous jammed systems.