Packing Nonspherical Particles - Princeton University

Kepler-Like Conjecture for a Class of Polyhedra
Face-to-face contacts allow higher packing density.
Central symmetry enables maximal face-to-face contacts when
particles are aligned – consistent with the optimal lattice packing.
For any packing of nonspherical particles of volume vparticle:
upper bound
φmax ≤ φmax = min
vparticle
vsphere
π
√ ,1
18
where vsphere is the volume of the largest sphere that can be inscribed
in the nonspherical particle.
,
. – p. 11/28