A guide to lifting aperiodic structures

Baake, Michael; Écija, David and Grimm, Uwe (2016). A guide to lifting aperiodic structures. Zeitschrift für Kristallographie - Crystalline Materials, 231(9) pp. 507–515.

DOI: https://doi.org/10.1515/zkri-2016-1982

Abstract

The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a priori construction of a lattice in relation to a given symmetry group. Instead, some elementary properties of the point set in physical space are used, and explicit methods are described. This approach works particularly well for the standard symmetries encountered in the practical study of quasicrystalline phases. We also demonstrate this with a recent experimental example, taken from a sample with square-triangle tiling structure and (approximate) 12-fold symmetry.

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About

• Item ORO ID
• 48874
• Item Type
• Journal Item
• ISSN
• 2196-7105
• Keywords
• embedding and projection; planar tilings; quasicrystals; star map
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Research Group
• ?? hwpra ??
• Related URLs
• • https://arxiv.org/abs/1606.07647(Other)
• Depositing User
• Uwe Grimm