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Juan E. Iglesias

Enumeration of closest-packings by the space group: a simple approach

Keywords: Sphere packing, Enumeration of closest packing, Möbius inversion

The problem of enumerating the possible closest-packings of equal spheres having a period P for each of the possible space groups is solved by systematic exploitation of the properties of the two-color symmetry group of the cyclotomic representation of the Zhdanov symbol. No sophisticated combinatorial or group-theoretical techniques are required, and for some space groups, non-recursive, simple analytical expressions are obtained through the use of Möbius Inversion Formula. A corollary to Möbius theorem, used in the derivation, has been proved.

Zeitschrift für Kristallographie, Oldenbourg Wissenschaftsverlag

Print ISSN: 0044-2968
Volume: 221, 04/2006
Pages: 237 - 245

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