Maximum and minimum stable random packings of Platonic solids

Authors

Jessica Baker, Clark University
Arshad Kudrolli, Clark UniversityFollow

Document Type

Article

Abstract

Motivated by the relation between particle shape and packing, we measure the volume fraction 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 rlp =0.51,0.54,0.52,0.51,0.50 and densest packing rcp =0.64,0.67,0.64,0.63,0.59, respectively, with standard deviation of ±0.01. We find that 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 reported for frictionless Platonic solids and below rlp of spheres for the loose packings. Experiments with ceramic tetrahedron were also conducted, and higher friction was observed to lead to lower . © 2010 The American Physical Society.

Publication Title

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Publication Date

12-15-2010

Volume

82

Issue

6

ISSN

1539-3755

DOI

10.1103/PhysRevE.82.061304

Repository Citation

Baker, Jessica and Kudrolli, Arshad, "Maximum and minimum stable random packings of Platonic solids" (2010). Physics. 120.
https://commons.clarku.edu/faculty_physics/120

Cross Post Location

Student Publications