Thomas Fernique ; Carole Porrier - Ammann Bars for Octagonal Tilings

dmtcs:10764 - Discrete Mathematics & Theoretical Computer Science, November 4, 2024, vol. 26:3 - https://doi.org/10.46298/dmtcs.10764
Ammann Bars for Octagonal TilingsArticle

Authors: Thomas Fernique ; Carole Porrier

    Ammann bars are formed by segments (decorations) on the tiles of a tiling such that forming straight lines with them while tiling forces non-periodicity. Only a few cases are known, starting with Robert Ammann's observations on Penrose tiles, but there is no general explanation or construction. In this article we propose a general method for cut and project tilings based on the notion of subperiods and we illustrate it with an aperiodic set of 36 decorated prototiles related to what we called Cyrenaic tilings.


    Volume: vol. 26:3
    Section: Combinatorics
    Published on: November 4, 2024
    Accepted on: October 4, 2024
    Submitted on: January 3, 2023
    Keywords: Computer Science - Discrete Mathematics,Mathematics - Dynamical Systems,37B52, 52C23

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