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Communication: A packing of truncated tetrahedra that nearly fills all of space and its melting properties
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The putative optimal packing was first briefly reported in our arXiv preprint (arXiv:1107.2300v1
) on July 12, 2011
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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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