Colourings of lattices and coincidence site lattices

Manuel Joseph Cruz Loquias (1, 2) , Peter Zeiner (3)

1 Mathematics
2 Mathematics
3 Universität Bielefeld = Bielefeld University

The relationship between the coincidence indices of a lattice Γ₁ and a sublattice Γ₂ of Γ₁ is examined via the colouring of Γ₁ that is obtained by assigning a unique colour to each coset of Γ₂. In addition, the idea of colour symmetry, originally defined for symmetries of lattices, is extended to coincidence isometries of lattices. An example involving the Ammann-Beenker tiling is provided to illustrate the results in the quasicrystal setting.

Keywords: Physical Sciences

Manuel Joseph Cruz Loquias, Peter Zeiner. Colourings of lattices and coincidence site lattices. Philosophical Magazine, 2010, pp.1. ⟨10.1080/14786435.2010.524900⟩. ⟨hal-00643462⟩