New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals - e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.

Original languageEnglish (US)
Pages (from-to)14267-14270
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number25
StatePublished - Dec 10 1996
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General


  • crystallography
  • icosahedral alloys
  • quasiperiodicity

Cite this