Abstract
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.
Acknowledgements
M. Loquias would like to thank the Deutscher Akademischer Austausch Dienst (DAAD) for financial support during his stay in Germany. This work was supported by the German Research Council (DFG), within the CRC 701.