Planar coincidences for N-fold symmetry

DOI10.1063/1.531424zbMath1015.11507arXivmath/0511147OpenAlexW2082231489MaRDI QIDQ5284428

Johannes Roth, Michael Baake, Peter A. B. Pleasants

Publication date: 22 January 1997

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0511147

zbMATH Keywords

algebraic number fieldsprime factorizationcoincidence problemplanar patterns\(N\)-fold symmetrycolour lattices in two dimensionscolour modules

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Other geometric groups, including crystallographic groups (20H15) Algebraic number theory: global fields (11R99) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Reflection groups, reflection geometries (51F15) Geometry of numbers (11H99)

Related Items (4)

Structure of coincidence isometry groups ⋮ Coincidence rotations of the root lattice \(A_4\) ⋮ O-LATTICES FOR RANK-DEFICIENT DISPLACEMENT FIELD MATRICES ⋮ The coincidence site lattices in 2D hexagonal lattices using Clifford algebra

Cites Work

• A classical invitation of algebraic numbers and class fields. With two appendices by Olga Taussky: ``Artin's 1932 Göttingen lectures on class field theory and ``Connections between algebraic number theory and integral matrices.
• Algebraic Solution of the Coincidence Problem in Two and Three Dimensions
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