Communication: a packing of truncated tetrahedra that nearly fills all of space and its melting properties.
Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists and mathematicians for centuries. Here, we analytically construct the densest known packing of truncated tetrahedra with a remarkably high packing fraction φ = 207/208 = 0.995192..., which is amazingly close to unity and strongly implies its optimality. This construction is based on a generalized organizing principle for polyhedra lacking central symmetry that we introduce here. The "holes" in the putative optimal packing are perfect tetrahedra, which leads to a new tessellation of space by truncated tetrahedra and tetrahedra. Its packing characteristics and equilibrium melting properties as the system undergoes decompression are discussed.
Princeton Institute of the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA.
Yang
Y
Jiao
Salvatore
S
Torquato