A family of ternary decagonal tilings

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Abstract

A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings are composed of three prototiles: an acute rhombus, a regular pentagon and a barrel shaped hexagon. In the perpendicular space, these tilings have windows with fractal boundaries, and the windows are analytically derived as the fixed sets of the conjugate maps associated with the relevant substitution rules. It is shown that the family contains an infinite number of local isomorphism classes which can be grouped into several symmetry classes (e.g., C10, D5, etc.). The member tilings are transformed into one another through collective simpleton flips, which are associated with the reorganization in the window boundaries.

Original languageEnglish
Article number012021
JournalJournal of Physics: Conference Series
Volume226
Issue number1
DOIs
Publication statusPublished - 2010
Event6th International Conference on Aperiodic Crystals, APERIODIC'09 - Liverpool, United Kingdom
Duration: 2009 Sep 132009 Sep 18

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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