Colourings of lattices and coincidence site lattices
Résumé
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.
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