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

Enrico Paolo C. Bugarin, Ma. Louise Antonette N. De Las Peñas 1 , Imogene F. Evidente 2 , Rene P. Felix 3  and Dirk Frettloeh 4
  • 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

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.

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Zeitschrift für Kristallographie – Crystalline Materials offers a place for researchers to present results of their crystallographic studies. The journal includes theoretical as well as experimental research. It publishes Original Papers, Letters and Review Articles in manifold areas of crystallography.

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