Maximum and minimum stable random packings of Platonic solids

Motivated by the relation between particle shape and packing, we measure the volume fraction phi occupied by the Platonic solids which are a class of polyhedrons with congruent sides, vertices, and dihedral angles. Tetrahedron-, cube-, octahedron-, dodecahedron-, and icosahedron-shaped plastic dice were fluidized or mechanically vibrated to find stable random loose packing phi(rlp)=0.51, 0.54, 0.52, 0.51, 0.50 and densest packing phi(rcp)=0.64, 0.67, 0.64, 0.63, 0.59, respectively, with standard deviation of similar or equal to +/- 0.01. We find that phi obtained by all protocols peak at the cube, which is the only Platonic solid that can tessellate space, and then monotonically decrease with number of sides. This overall trend is similar but systematically lower than the maximum phi reported for frictionless Platonic solids and below phi(rlp) of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower phi.