Hybrid quasiperiodic-periodic structures constructed by projection in two stages

S. I. Ben-Abraham, Alexander Quandt

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A two-stage variant of the cut-and-project method is presented, in which a periodic structure is cut and projected in a high-dimensional space onto three-dimensional physical space so that a second cut and projection onto a plane yields a quasiperiodic structure. The method is applied to the cases of octagonal, dodecagonal and pentagonal/decagonal symmetry. The focus is on the three-dimensional intermediate hybrid structures that are partly quasiperiodic and partly periodic. The method can be generalized to other symmetries as well as to include more intermediate steps.

Original languageEnglish
Article numberpz5033
Pages (from-to)177-185
Number of pages9
JournalActa Crystallographica Section A: Foundations of Crystallography
Issue number2
StatePublished - 1 Mar 2007


  • Cut-and-project method
  • Hybrid structures
  • Quasiperiodic periodic structures


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