Communication: A packing of truncated tetrahedra that nearly fills all of space and its melting properties | Zendy

Yang Jiao | Zendy; Salvatore Torquato | Zendy

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Communication: A packing of truncated tetrahedra that nearly fills all of space and its melting properties

Author(s) -

Yang Jiao,

Salvatore Torquato

Publication year - 2011

Publication title -

the journal of chemical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.071

H-Index - 357

eISSN - 1089-7690

pISSN - 0021-9606

DOI - 10.1063/1.3653938

Subject(s) - polyhedron , tetrahedron , atomic packing factor , packing problems , tessellation (computer graphics) , space (punctuation) , symmetry (geometry) , sphere packing , variety (cybernetics) , tetrahedral symmetry , mathematics , geometry , computer science , combinatorics , crystallography , chemistry , rotational symmetry , operating system , statistics

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.

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