Colourings of lattices and coincidence site lattices
Abstract
The relationship between the coincidence indices of a lattice 1 and a sublattice 2 of 1 is examined via the colouring of 1 that is obtained by assigning a unique colour to each coset of 2. 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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