Pentagonal quasicrystals and their linear self-similarities

Zuzana Masáková, Jan Mazáč
2020 Journal of Physics, Conference Series  
We recall the construction of a cut-and-project scheme providing planar model sets with 5-fold symmetry. The cut-and-project construction consists in projecting points of a lattice L ⊂ R 4 by two orthogonal projections π , π ⊥ to two 2-dimensional subspaces. We describe the set of all linear mappings preserving the Z-modules π (L) and π ⊥ (L) and show that the set of all such mappings is in a correspondence with a 2-dimensional cut-and-project set. Finally, we describe linear self-similarities
more » ... self-similarities of a pentagonal cut-and-project set with circular acceptance window.
doi:10.1088/1742-6596/1458/1/012010 fatcat:3g2e3772d5ddldnuxrce26a55q