Quasiperiodic-periodic structures by projection in two stages: An illustrative example

Alexander Quandt, Shelomo I. Ben-Abraham

Research output: Contribution to journalArticlepeer-review


Recently we have modified a two-stage variant of the cut-and-project method used to generate layered 8-fold (Ben-Abraham, 2004) and 12-fold (Ben-Abraham et al., 2004) quasiperiodic structures in three dimensions, and obtained 8-fold, 10-fold and 12-fold quasiperiodic structures via cut-and-project from various four dimensional lattices (Ben-Abraham and Quandt, 2006). However four dimensions are certainly not the most suitable playground to illustrate the basics of our general two-stage projection method. To this end we cut and project a periodic structure in three dimensions onto two-dimensional physical space, such that a second cut and projection onto a line yields a quasiperiodic structure. This simple example contains all of the basic elements of our two-stage projection method, but now the essential steps may directly be visualized.

Original languageEnglish
Pages (from-to)759-761
Number of pages3
JournalZeitschfrift fur Kristallographie
Issue number12
StatePublished - 27 Dec 2006


  • Cut-and-project method
  • Fibonacci chain
  • Quasiperiodic structures

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Inorganic Chemistry


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