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Similar sublattices and coincidence rotations of the root lattice A4 and its dual

Heuer, Manuela (2008). Similar sublattices and coincidence rotations of the root lattice A4 and its dual. Zeitschrift für Kristallographie, 223(11-12;) pp. 817–821.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1524/zkri.2008.1082
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Abstract

A natural way to describe the Penrose tiling employs the projection method on the basis of the root lattice A4 or its dual. Properties of these lattices are thus related to properties of the Penrose tiling. Moreover, the root lattice A4 appears in various other contexts such as sphere packings, efficient coding schemes and lattice quantizers.

Here, the lattice A4 is considered within the icosian ring, whose rich arithmetic structure leads to parametrisations of the similar sublattices and the coincidence rotations of A4 and its dual lattice. These parametrisations, both in terms of a single icosian, imply an index formula for the corresponding sublattices. The results are encapsulated in Dirichlet series generating functions. For every index, they provide the number of distinct similar sublattices as well as the number of coincidence rotations of A4 and its dual.

Item Type: Journal Article
ISSN: 0044-2968
Keywords: the root lattice A4; similar sublattices; coincidence rotations
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 15293
Depositing User: Manuela Heuer
Date Deposited: 16 Mar 2009 12:25
Last Modified: 06 Dec 2010 17:35
URI: http://oro.open.ac.uk/id/eprint/15293
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