Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

@article{Lu2007DecagonalAQ,
  title={Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture},
  author={Peter J. Lu and Paul J. Steinhardt},
  journal={Science},
  year={2007},
  volume={315},
  pages={1106 - 1110}
}
The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (“girih tiles”) decorated with lines. These tiles enabled the creation of… Expand
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Decagonal and Quasicrystalline Tilings in Medieval Islamic Architecture by Lu, Peter J.
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Historically accurate reconstructions show that Darb-i Imam is unique, the only known example that does not repeat periodically and that displays a self-similar transformation enabling its continuation ad infinitum to a perfect quasi-crystalline pattern. Expand
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