Constructing Penrose-like tilings from a single prototile and the implications for quasicrystals

Hyeong Chai Jeong, Paul J. Steinhardt

Research output: Contribution to journalArticle

84 Scopus citations

Abstract

We present two sets of rules for constructing quasiperiodic tilings that suggest a simpler structural model of quasicrystals and a more plausible explanation of why quasicrystals form. First, we show that quasiperiodic tilings can be constructed from a single prototile with matching rules which constrain the way that neighbors can overlap. Second, we show that maximizing the density of a certain cluster of fat and thin tiles can force a Penrose tiling without imposing the usual Penrose matching rules.

Original languageEnglish (US)
Pages (from-to)3520-3532
Number of pages13
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume55
Issue number6
DOIs
StatePublished - Jan 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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