Abstract
We study the structural transformations induced, via the cut-and-project method, in quasicrystals and tilings by lattice transitions in higher dimensions, with a focus on transition paths preserving at least some symmetry in intermediate lattices. We discuss the effect of such transformations on planar aperiodic Penrose tilings, and on three-dimensional aperiodic Ammann tilings with icosahedral symmetry. We find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting, tile flipping and tile merger, and we investigate the origin of these local transformation mechanisms within the projection framework.
Original language | English |
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Pages (from-to) | 1452-1471 |
Number of pages | 20 |
Journal | Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences |
Volume | 468 |
Issue number | 2141 |
Early online date | 8 Feb 2012 |
DOIs | |
Publication status | Published - 8 May 2012 |