Substitution tilings with dense tile orientations and n-fold rotational\n symmetry

2016/02/01 by Dirk Frettlöh, April Lynne D. Say-awen, Frettlöh, Dirk +3
Materials Science · #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1602.00518

Abstract

It is shown that there are primitive substitution tilings with dense tile\norientations invariant under n-fold rotation for n=2,3,4,5,6,8. The proof for\ndense tile orientations uses a general result about irrationality of angles in\ncertain parallelograms.\n

Citations

• Metallic Phase with Long-Range Orientational Order and No Translational Symmetry

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