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

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.