Multidimensional color codes for chair tilings

Research output: Contribution to journalArticlepeer-review

Abstract

Ordered aperiodic structures have been of interest to the crystallographic community for several decades, and study of them has in turn led to the study of lattice substitution systems, model sets and chair tilings. In this work a color code for chair tilings in arbitrary dimensions is presented. In two and three dimensions, it is expedient to translate the digital codes into colors. An explicit example of a three-dimensional color coding covering one octant is constructed. The tiling is then extended to the whole three-dimensional space and an indication is given of how to do this in arbitrary dimensions. Illustrations of some four-dimensional objects are also shown. The principle of color coding can be applied to other complex tilings such as brick tiling.

Original languageEnglish
Pages (from-to)359-363
Number of pages5
JournalActa Crystallographica Section A: Foundations and Advances
Volume78
DOIs
StatePublished - 1 Jul 2022

Keywords

  • aperiodic structures
  • chair tilings
  • color codes
  • digital codes
  • letter codes
  • quasicrystals

ASJC Scopus subject areas

  • Structural Biology
  • Biochemistry
  • Materials Science (all)
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry

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