In future work, Roggen and his colleagues plan to examine how factors including humidity, combustion source and packing density influence a joint’s architecture and effects.

She said that a method that generally gives an upper bound on the packing density turns out to be the exact solution in these cases.

Her best packing easily eclipsed what Dr. Conway and Dr. Torquato had found, with a packing density of almost 78 percent, surpassing spheres.

A few days before Christmas, Dr. Torquato and Yang Jiao, a graduate student, reported that they had tweaked the Cornell structure to bump up the packing density by a fraction, to 85.55 percent.

The new world record for packing density of tetrahedrons: 85.63 percent.