On Sat, Aug 15, 2009 at 6:45 PM, Stephen B. Gray <stevebg@roadrunner.com> wrote:

Packing of regular tetrahedra reaches 78.2 %. See www.sciencedaily.com/releases/2009/08/090812143943.htm .

It has now reached 100/117 ~ 0.8547 Moreover this packing by Yoav Kallus, Veit Elser and Simon Gravel is periodic with just 4 tetrahedra in the unit cell. See http://arxiv.org/abs/0910.5226 --Edwin Clark