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Volumn 315, Issue 5815, 2007, Pages 1106-1110

Decagonal and quasi-crystalline tilings in medieval Islamic architecture

Author keywords

[No Author keywords available]

Indexed keywords

ARCHITECTURE; MEDIEVAL; POLYGON;

EID: 33847263544     PISSN: 00368075     EISSN: 10959203     Source Type: Journal    
DOI: 10.1126/science.1135491     Document Type: Article
Times cited : (192)

References (32)
  • 3
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    • I. El-Said, A. Parman, in Geometric Concepts in Islamic Art (World of Islam Festival, London, 1976), pp. 85-87.
    • I. El-Said, A. Parman, in Geometric Concepts in Islamic Art (World of Islam Festival, London, 1976), pp. 85-87.
  • 7
    • 33847265763 scopus 로고    scopus 로고
    • Abu'l-Wafa al-Buzjani's (940-998 C.E.) treatise On the Geometric Constructions Necessary for the Artisan, and an anonymous manuscript appended to a Persian translation of al-Buzjani and likely dating from the 13th century, On Interlocks of Similar or Corresponding Figures (2), document specific techniques for architecturally related mathematical constructions (2, 25). The mathematical tools needed to construct the girih tiles are entirely contained in these two manuscripts-specifically, bisection, division of a circle into five equal parts, and cutting and rearrangement of paper tiles to create geometric patterns.
    • Abu'l-Wafa al-Buzjani's (940-998 C.E.) treatise On the Geometric Constructions Necessary for the Artisan, and an anonymous manuscript appended to a Persian translation of al-Buzjani and likely dating from the 13th century, On Interlocks of Similar or Corresponding Figures (2), document specific techniques for architecturally related mathematical constructions (2, 25). The mathematical tools needed to construct the girih tiles are entirely contained in these two manuscripts-specifically, bisection, division of a circle into five equal parts, and cutting and rearrangement of paper tiles to create geometric patterns.
  • 9
    • 0005175183 scopus 로고
    • Princeton Univ. Press, Princeton, NJ, color plates IV, IXb, plates 46, 374
    • L. Golombek, D. Wilber, in The Timurid Architecture of Iran and Turan (Princeton Univ. Press, Princeton, NJ, 1988), pp. 246-250, 308-309, 384-386, 389, color plates IV, IXb, plates 46, 374.
    • (1988) The Timurid Architecture of Iran and Turan
    • Golombek, L.1    Wilber, D.2
  • 10
    • 33847316035 scopus 로고    scopus 로고
    • Additional examples of this particular 10/3 decagonal pattern, shown in fig. S1: the Seljuk Congregational Mosque in Ardistan, Iran (∼1160 C.E.) (16); the Timurid Tuman Aqa Mausoleum in the Shah-i Zinda complex in Samarkand, Uzbekistan (1405 C.E.) (9, 16); the Darb-i Kushk shrine in Isfahan, Iran (1496 C.E.) (2, 9, 17); and the Mughal l'timad al-Daula Mausoleum in Agra, India (∼1622 CE.) (25).
    • Additional examples of this particular 10/3 decagonal pattern, shown in fig. S1: the Seljuk Congregational Mosque in Ardistan, Iran (∼1160 C.E.) (16); the Timurid Tuman Aqa Mausoleum in the Shah-i Zinda complex in Samarkand, Uzbekistan (1405 C.E.) (9, 16); the Darb-i Kushk shrine in Isfahan, Iran (1496 C.E.) (2, 9, 17); and the Mughal l'timad al-Daula Mausoleum in Agra, India (∼1622 CE.) (25).
  • 12
    • 33847253891 scopus 로고    scopus 로고
    • Additional architectural examples of patterns that can be reconstructed with girih tiles, shown in fig. S3: the Abbasid Al-Mustansiriyya Madrasa in Baghdad, Iraq (1227 to 1234 C.E, 26, the Ilkhanid Uljaytu Mausoleum in Sultaniya, Iran (1304 C.E, 17, the Ottoman Green Mosque in Bursa, Turkey (1424 C.E, 27, and the Mughal I'timad al-Daula Mausoleum in Agra, India (∼1622 C.E, 28, Similar patterns also appear in the Mamluk Qurans of Sandal (1306 to 1315 C.E, and of Aydughdi ibn Abdallah al-Badri (1313 C.E, 29, Note that the girih-tile paradigm can make pattern design structure more clear. For example, all of the spandrels with decagonal girih patterns we have thus far examined (including Fig. 3C and figs. 52 and 53A) follow the same prescription to place decagons: Partial decagons are centered at the four external corners and on the top edge directly above the apex of the arch
    • Additional architectural examples of patterns that can be reconstructed with girih tiles, shown in fig. S3: the Abbasid Al-Mustansiriyya Madrasa in Baghdad, Iraq (1227 to 1234 C.E.) (26); the Ilkhanid Uljaytu Mausoleum in Sultaniya, Iran (1304 C.E.) (17); the Ottoman Green Mosque in Bursa, Turkey (1424 C.E.) (27); and the Mughal I'timad al-Daula Mausoleum in Agra, India (∼1622 C.E.) (28). Similar patterns also appear in the Mamluk Qurans of Sandal (1306 to 1315 C.E.) and of Aydughdi ibn Abdallah al-Badri (1313 C.E.) (29). Note that the girih-tile paradigm can make pattern design structure more clear. For example, all of the spandrels with decagonal girih patterns we have thus far examined (including Fig. 3C and figs. 52 and 53A) follow the same prescription to place decagons: Partial decagons are centered at the four external corners and on the top edge directly above the apex of the arch.
  • 13
    • 33847277826 scopus 로고    scopus 로고
    • A similar convention was used to mark the same girih tiles in other panels (e.g., 28, 50, 52, and 62) in the Topkapi scroll (fig. 54) (2).
    • A similar convention was used to mark the same girih tiles in other panels (e.g., 28, 50, 52, and 62) in the Topkapi scroll (fig. 54) (2).
  • 15
    • 33847275100 scopus 로고    scopus 로고
    • This pattern type also occurs on the Great Mosque in Malatya, Turkey (∼1200 C.E, 6, and the madrasa in Zuzan, Iran (1219 C.E, 30, fig. 55, as well as on a carved wooden double door from a Seljuk building in Konya (∼13th century C.E, in the Museum of Islamic Art in Berlin Inv. Nr. 1.2672
    • This pattern type also occurs on the Great Mosque in Malatya, Turkey (∼1200 C.E.) (6), and the madrasa in Zuzan, Iran (1219 C.E.) (30) (fig. 55), as well as on a carved wooden double door from a Seljuk building in Konya (∼13th century C.E.), in the Museum of Islamic Art in Berlin (Inv. Nr. 1.2672).
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    • D. Hill, O. Grabar, in Islamic Architecture and Its Decoration, A.D. 800-1500 (Univ. of Chicago Press, Chicago, 1964), pp. 53, 62, 65, plates 38, 276, 346, 348.
    • D. Hill, O. Grabar, in Islamic Architecture and Its Decoration, A.D. 800-1500 (Univ. of Chicago Press, Chicago, 1964), pp. 53, 62, 65, plates 38, 276, 346, 348.
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    • Smithsonian Institution, Washington, DC, plates 34-36
    • S. P. Seherr-Thoss, Design and Color in Islamic Architecture (Smithsonian Institution, Washington, DC, 1968), plates 34-36, 40, 84, 90.
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    • Seherr-Thoss, S.P.1
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    • (2003) ISAMA/Bridges Conference Proceedings , pp. 1-12
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    • A single figure, part of a geometric proof from On Interlocks of Similar or Corresponding Figures, has been related to the outlines of individual Penrose tiles, but there is no evidence whatsoever for tessellation (31). Makovicky has connected the Maragha Gunbad-i Kabud pattern in Fig. 2 with the Penrose tiling (18), but explicitly states (as we show in fig. 56) that the pattern is periodic, so by definition it cannot be a properly quasi-periodic Penrose tiling.
    • A single figure, part of a geometric proof from On Interlocks of Similar or Corresponding Figures, has been related to the outlines of individual Penrose tiles, but there is no evidence whatsoever for tessellation (31). Makovicky has connected the Maragha Gunbad-i Kabud pattern in Fig. 2 with the Penrose tiling (18), but explicitly states (as we show in fig. 56) that the pattern is periodic, so by definition it cannot be a properly quasi-periodic Penrose tiling.
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    • Shinshindo, Kyoto, plates 378
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    • We thank G. Nedpoglu and J. Spurr, without whose multifaceted assistance this paper would not have been possible. We also thank R. Holod and K. Dudley/M. Eniff for permission to reproduce their photographs in Figs. 2C and 3A, respectively; C. Tam and E. Simon-Brown for logistical assistance in Uzbekistan; S. Siavoshi and A. Tafvizi for motivating the exploration of Isfahan's sights; and S. Blair, J. Bloom, C. Eisenmann, T. Lentz, and I. Winter for manuscript comments. Photographs in Fig. 2, A and B, and in the online figures courtesy of the Fine Arts Library, Harvard College Library. Supported by C. and F. Lu and by the Aga Khan Program for Islamic Architecture at Harvard University.
    • We thank G. Nedpoglu and J. Spurr, without whose multifaceted assistance this paper would not have been possible. We also thank R. Holod and K. Dudley/M. Eniff for permission to reproduce their photographs in Figs. 2C and 3A, respectively; C. Tam and E. Simon-Brown for logistical assistance in Uzbekistan; S. Siavoshi and A. Tafvizi for motivating the exploration of Isfahan's sights; and S. Blair, J. Bloom, C. Eisenmann, T. Lentz, and I. Winter for manuscript comments. Photographs in Fig. 2, A and B, and in the online figures courtesy of the Fine Arts Library, Harvard College Library. Supported by C. and F. Lu and by the Aga Khan Program for Islamic Architecture at Harvard University.


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