Geodesic
Ammann Bars for Octagonal Tilings
Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3.

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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. 
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     author = {Fernique, Thomas and Porrier, Carole},
     title = {Ammann {Bars} for {Octagonal} {Tilings}},
     journal = {Discrete mathematics & theoretical computer science},
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     doi = {10.46298/dmtcs.10764},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.10764/}
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Fernique, Thomas; Porrier, Carole. Ammann Bars for Octagonal Tilings. Discrete mathematics & theoretical computer science, Tome 26 (2024) no. 3. doi : 10.46298/dmtcs.10764. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.10764/

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