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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.

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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 Peñas1 / Imogene F. Evidente2 / Rene P. Felix3 / Dirk Frettloeh4

1 Ateneo de Manila University, Mathematics Department, Quezon City, Philippinen

2 Quezon City, Philippinen

3 University of the Philippines, Institute of Mathematics, Quezon City, Philippinen

4 Bielefeld, GERMANY

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

Citation Information: Zeitschrift für Kristallographie International journal for structural, physical, and chemical aspects of crystalline materials. Volume 223, Issue 11-12, Pages 785–790, ISSN (Print) 0044-2968, DOI: 10.1524/zkri.2008.1063, September 2009

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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

Citing Articles

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Ma. Louise Antonette N. De Las Peñas, Mark L. Loyola, Antonio M. Basilio, and Eko Budi Santoso
Acta Crystallographica Section A Foundations and Advances, 2014, Volume 70, Number 1, Page 12
E. P. Bugarin, M. L. A. N. de las Peñas, and D. Frettlöh
Geometriae Dedicata, 2013, Volume 162, Number 1, Page 271
Ma. Louise Antonette N. de Las Peñas, Enrico Paolo Bugarin, and Dirk Frettlöh
Philosophical Magazine, 2011, Volume 91, Number 19-21, Page 2690

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