Pentagonal quasicrystals and their linear self-similarities

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 ⊂ ℝ4 by two orthogonal projections π||, π⊥ to two 2-dimensional subspaces. We describe the set of all linear mappings...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 1458; no. 1; pp. 12010 - 12014
Main Authors Masáková, Zuzana, Mazáč, Jan
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.01.2020
Subjects
Physics
Quasicrystals
Similarity
Subspaces
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Summary: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 ⊂ ℝ4 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 of a pentagonal cut-and-project set with circular acceptance window.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1458/1/012010