Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

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Science  23 Feb 2007:
Vol. 315, Issue 5815, pp. 1106-1110
DOI: 10.1126/science.1135491

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  • Lu and Steinhardt’s Response to Ian Cohn

    We thank Mr. Cohn for his E-Letter and for pointing us to the charming book, The Language of Pattern. We note, though, that this book is described by its authors as a study of pattern-making inspired by Islamic design, and it does not provide a natural explanation of how the Vedic square, an isolated motif, can lead to a large quasi-crystalline fragment. To be sure, the book’s purpose is aesthetic, whereas our purpose...

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    Competing Interests: None declared.
  • Lu and Steinhardt’s Reply to Cintas

    We certainly share Dr. Cintas’ admiration for the magnificent periodic and spiral patterns found at the Alhambra and other Islamic sites, which demonstrate a very high degree of aesthetic and geometric sophistication. In fact, as discussed in our paper, girih tiles were commonly used as a method to construct very complex periodic patterns, such as the Gunbad-i Kabud in Maragha, Iran. Periodic patterns, however, including the us...

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    Competing Interests: None declared.
  • Afterthoughts on Islamic Art and Crystal Symmetries

    After reading the appealing article by P. J. Lu and P. J. Steinhardt on quasi-crystalline tilings in Islamic architecture (23 Feb., p. 1106), I could not resist introducing a few considerations. The authors state that there was an important conceptual breakthrough in Islamic mathematics and hence in architecture by the 13th century—girih tiles—that evolved into more sophisticated quasi-crystal arrangements by the 15th century....

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    Competing Interests: None declared.
  • Islamic Patterns and the Vedic Square Template

    On reading P. J. Lu and P. J. Steinhardt's article "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture" (Reports, p. 1106, 23 Feb. 2007), I was immediately reminded of a Christmas gift presented to me in 1975 by my dear departed friend, the London architect Colin Dollimore, of a small book titled, The Language of Pattern by Keith Albarn, Jenny Miall Smith, Stanford Steele, and Dinah Walker (publis...

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    Competing Interests: None declared.
  • Response to H. M. K. Aboulfotouh

    In our paper, we demonstrated that a sequence of Islamic patterns ranging from simple to complex can all be obtained by taking the same set of five line-decorated polygons (girih tiles) and close-packing them in different configurations. Other constructions methods are possible, in principle; several suggestions include those in the literature referenced in our paper (refs. 3-6, 14, 18-19), and the one presented by Dr....

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    Competing Interests: None declared.
  • The Hidden Grids of the Decagonal Girih Patterns

    In their Report “Decagonal and quasi-crystalline tilings in medieval Islamic architecture” (1), Peter J. Lu et al. suggest that the decagonal girih patterns on the Darb-i Imam shrine are quasi-periodic and were constructed by tessellation, using a set of five tile types. Contrary to the approaches of the mathematicians towards understanding the process of designing and implementing these patterns, architects d...

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    Competing Interests: None declared.