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Coordination sequences for lattices

โœ Scribed by O'Keeffe, M.

Book ID
120343894
Publisher
Oldenbourg Wissenschaftsverlag
Year
1995
Tongue
English
Weight
552 KB
Volume
210
Category
Article
ISSN
2194-4946

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โœฆ Synopsis

Abstract

Coordination sequences for five 3-dimensional, ten 4-dimensional and eleven higher-dimensional lattices have been determined and all but one can be expressed as simple polynomials. Some regularities in these polynomials are observed. The correlation between topological and geometric density is demonstrated for 4-dimensional lattices. It is conjectured that hexagonal closest packing is topologically the densest packing in three dimensions.

๐Ÿ“œ SIMILAR VOLUMES

Coordination sequences for hyperbolic ti
Coordination sequences for hyperbolic tilings
โœ O'Keeffe, M. ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Oldenbourg Wissenschaftsverlag ๐ŸŒ English โš– 815 KB

## Abstract Coordination sequences have been determined for tilings {__p__,__q__} of the hyperbolic plane in which__q p__-gons meet at each vertex. The number of vertices in successive shells is related by a recurrence to the numbers in earlier shells and grows exponentially. General expressions fo