Colourings of lattices and coincidence site lattices

Details Colourings of lattices and coincidence site lattices Colourings of lattices and coincidence site lattices

2010-11-03

arxiv.org/abs/1011.1001v1

Mathematics

Metric Geometry

9 pages, 6 figures

Scientific paper

10.1080/14786435.2010.524900

The relationship between the coincidence indices of a lattice $\Gamma_1$ and a sublattice $\Gamma_2$ of $\Gamma_1$ is examined via the colouring of $\Gamma_1$ that is obtained by assigning a unique colour to each coset of $\Gamma_2$. 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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