Maximum and minimum stable random packings of Platonic solids

Jessica Baker and Arshad Kudrolli
Phys. Rev. E 82, 061304 – Published 15 December 2010

Abstract

Motivated by the relation between particle shape and packing, we measure the volume fraction ϕ 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 ϕrlp=0.51,0.54,0.52,0.51,0.50 and densest packing ϕrcp=0.64,0.67,0.64,0.63,0.59, respectively, with standard deviation of ±0.01. We find that ϕ 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 ϕ reported for frictionless Platonic solids and below ϕrlp of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower ϕ.

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  • Received 10 August 2010

DOI:https://doi.org/10.1103/PhysRevE.82.061304

©2010 The American Physical Society

Authors & Affiliations

Jessica Baker and Arshad Kudrolli

  • Department of Physics, Clark University, Worcester, Massachusetts 01610, USA

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Issue

Vol. 82, Iss. 6 — December 2010

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