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/content/aip/journal/jcp/135/15/10.1063/1.3653938
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/content/aip/journal/jcp/135/15/10.1063/1.3653938
2011-10-17
2016-09-27

Abstract

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 meltingproperties as the system undergoes decompression are discussed.

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