The average number of constraints per particle in
mechanically stable systems of Platonic solids (except cubes) 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 chain-like
face-face clusters with finite extent form in these systems.Comment: 4 pages, 3 figures, 4 tabl