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Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Boldyreva, Elena V. / Huppertz, Hubert / Petrícek, Václav / Tiekink, E. R. T.

12 Issues per year


IMPACT FACTOR 2016: 3.179

CiteScore 2016: 3.30

SCImago Journal Rank (SJR) 2016: 1.097
Source Normalized Impact per Paper (SNIP) 2016: 2.592

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2196-7105
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Volume 223, Issue 11-12 (Dec 2008)

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On color groups of Bravais colorings of planar modules with quasicrystallographic symmetries

Enrico Paolo C. Bugarin / Ma. Louise Antonette N. De Las Peñas / Imogene F. Evidente / Rene P. Felix / Dirk Frettloeh
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/zkri.2008.1063

Abstract

In this work we study the color symmetries pertaining to colorings of Mn = Z[ξ], where ξ = exp (2πi/n) for n ∈ {5,8,12} which yield standard symmetries of quasicrystals. The first part of the paper treats Mn as a four dimensional lattice Λ with symmetry group G and a result is provided on sublattices of Λ which are invariant under the point group of G. The second part of the paper characterizes the color symmetry groups and color fixing groups corresponding to Bravais colorings of Mn using an approach involving ideals.

Keywords: Color groups; Lattices; Planar modules; Quasicrystals; Cyclotomic fields

About the article

* Correspondence address: Katipunan Avenue, Loyola Heights, 1108 Quezon,


Published Online: 2009-09-25

Published in Print: 2008-12-01


Citation Information: Zeitschrift für Kristallographie International journal for structural, physical, and chemical aspects of crystalline materials, ISSN (Print) 0044-2968, DOI: https://doi.org/10.1524/zkri.2008.1063.

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© by Oldenbourg Wissenschaftsverlag, Quezon, Germany. Copyright Clearance Center

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[1]
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Acta Crystallographica Section A Foundations and Advances, 2014, Volume 70, Number 1, Page 12
[2]
E. P. Bugarin, M. L. A. N. de las Peñas, and D. Frettlöh
Geometriae Dedicata, 2013, Volume 162, Number 1, Page 271
[3]
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