Point substitution processes for decagonal quasiperiodic tilings

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    Abstract

    A general construction principle for the inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of expansion and division of the tiles, where the expanded tiles can be divided arbitrarily as long as the set of prototiles is maintained. A certain kind of point decoration process turns out to be useful for the identification of possible division rules. The method is capable of generating a broad range of decagonal tilings, many of which are chiral and have atomic surfaces with fractal boundaries. Two new families of decagonal tilings are presented; one is quaternary and the other ternary. The properties of the ternary tilings with rhombic, pentagonal and hexagonal prototiles are investigated in detail.

    Original languageEnglish
    Pages (from-to)342-351
    Number of pages10
    JournalActa Crystallographica Section A: Foundations of Crystallography
    Volume65
    Issue number5
    DOIs
    Publication statusPublished - 2009 Aug 27

    Keywords

    • Decagonal tilings
    • Point decorations
    • Prototiles
    • Quasiperiodic tilings

    ASJC Scopus subject areas

    • Structural Biology

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