Synopsis: Packing Polyhedra

A computational study determines the maximum packing density of 55,000 different particle shapes, with potential applications in nanotechnology and biology.
Synopsis figure
E. R. Chen et al., Phys. Rev. X (2014)

Since the 17th Century, when Johannes Kepler first studied how to pack perfect spheres into the tightest possible configuration, mathematicians have analyzed the packing properties of increasingly complex shapes. But this “packing problem” is notoriously difficult, and it is challenging to predict the packing density of one shape even if that of a similar shape is known. Elizabeth Chen at Harvard University, Daphne Klotsa at the University of Michigan, Ann Arbor, and colleagues have now expanded the study of particle packing to 55,000 shapes, enabling a more detailed investigation of how shape affects packing. Reporting in Physical Review X, the team finds that minor shape deformations can have a significant effect on packing density. The result could have applications in nanotechnology and biology, where high packing densities are often required.

Chen, Klotsa, and their colleagues generated the multitude of shapes by using computers to interpolate between symmetric solids such as cubes, tetrahedrons, octahedrons (8 faces), dodecahedrons (12 faces), and icosahedrons (20 faces). Using analytical and computational methods, they investigated the densest possible packing arrangements of each shape in an infinite, periodic three-dimensional box.

A surprising finding of the research is how sensitive the packing density is to certain small changes in shape. For example, truncating the edges of a dodecahedron results in a decreased packing density, but truncating the vertices hardly affects the packing density at all. The team concludes that rather than focus on a specific shape, future studies of packing properties should instead examine families of shapes related by small deformations. – Katherine Kornei


More Announcements »

Subject Areas

Computational PhysicsIndustrial Physics

Previous Synopsis

Biological Physics

Live Cell Imaging

Read More »

Next Synopsis

Fluid Dynamics

Droplets Caught at High Speed

Read More »

Related Articles

Synopsis: Sorting Carbon Nanotubes with Light

Synopsis: Sorting Carbon Nanotubes with Light

Laser light can be used to sort carbon nanotubes according to their chirality. Read More »

Synopsis: Light Finds Tiny Defects

Synopsis: Light Finds Tiny Defects

An optical microscopy scheme uses interference effects to reveal nanoscale defects on the surface of materials. Read More »

Synopsis: More Catalysis with Less Platinum
Materials Science

Synopsis: More Catalysis with Less Platinum

New alloys could reduce the amount of costly platinum required for catalytic converters. Read More »

More Articles