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

The average number of constraints per particle in mechanically stable amorphous systems of Platonic solids approaches the isostatic limit at the jamming point (→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.