On Color Groups of Bravais Colorings of Planar Modules with Quasicrystallographic Symmetries

• Main Authors: Bugarin, Enrico Paolo, De Las Peñas, Ma. Louise Antonette N, Evidente, Imogene F, Felix, Rene P, Frettlöh, Dirk
• Format: text
• Published: Archīum Ateneo 2008
• Subjects: Color groups; Lattices; Planar modules; Quasicrystals; Cyclotomic fields; Mathematics
• Online Access: https://archium.ateneo.edu/mathematics-faculty-pubs/104; https://www.degruyter.com/view/journals/zkri/223/11-12/article-p785.xml?tab_body=abstract
• Institution: Ateneo De Manila University

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.