Packing of Tetrahedra Illuminates Nature of Matter

August 20, 2009 

By packing the largest number ever of tetrahedra as well as other polyhedra into a specific space, two Princeton University researchers have enriched our understanding of matter.

Packing problems concern finding arrangements of identical objects that fill a given space as efficiently as possible. To find such an arrangement for tetrahedra, Salvatore Torquato and Yang Jiao used a computer model to stuff tetrahedra into a box, shrinking the box and changing its shape to make the tetrahedra fit in the box as tightly as possible. They filled a volume to 78.2 percent of capacity with identical tetrahedra, a new record.

"From a scientific perspective, to know about the packing problem is to know something about the low-temperature phases of matter itself," Torquato observed.

The simulations also indicated that the densest packings of polyhedra are likely to be their best lattice arrangements. "This is now a strong conjecture that people can try to prove," Torquato surmised.

The findings, which can be considered a 21st-century analog of Kepler's conjecture about packing spheres, offer "compelling evidence for what happens in more complicated cases than just spheres," Henry Cohn of Microsoft Corp., in Cambridge, Mass., said.

In addition, the results may lead to improved error-detecting and error-correcting codes, information compression, and other applications requiring superefficient packing of solids.

Salvatore Torquato and Yang Jiao reported their results in the article “Dense packings of the Platonic and Archimedean solids,” published in the Aug. 13 issue of Nature.

Source: Princeton University, Aug. 12, 2009.