Abstract

This work introduces the idea of symmetry order, which describes the rotational symmetry types of tilings in the hull of a given substitution. Definitions are given of the substitutions σ6 and σ7 which give rise to aperiodic primitive substitution tilings with dense tile orientations and which are invariant under six-and sevenfold rotations, respectively; the derivation of the symmetry orders of their hulls is also presented.

Original languageAmerican English
Pages (from-to)388-398
Number of pages11
JournalMathematics Faculty Publications
Volume74
Issue number4
StatePublished - Jul 1 2018

ASJC Scopus Subject Areas

  • Structural Biology
  • Biochemistry
  • General Materials Science
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry
  • Inorganic Chemistry

Keywords

  • symmetry order
  • aperiodic tilings
  • substitution tilings
  • rotation-invariant tilings
  • dense tile orientations

Disciplines

  • Geometry and Topology
  • Mathematics

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