² Meinecke, Michael, Die mamlukische Architektur in Ägypten und Syrien (Glückstadt, 1992), 1 89–94Google Scholar, attributes its introduction to Syrian craftsmen who in the 1340s produced a spectacularly wide range of muqarnas designs.

³ I have not succeeded in tracing the source of the first definition, but it is plainly this to which Khwāndamīr's, gunbad-i fīrūze-yi muqarnas-i gardūn (Necipoğlu, 126, n. 75) refersGoogle Scholar. For it translates not as ‘the turquoise-stalactited dome of the celestial sphere’, as Thackston, Wheeler, A century of princes (Cambridge, Mass.: MIT Press, 1989), 103 has itGoogle Scholar, but as ‘the turquoise dome of the muqarnas of the heavens’. It is also tendentious to translate the phrases saqf-i pūr muqarnas and ṭāq-i zarnigār on the porch of the tomb of Uljay/Ölçey Shadi Mulk Agha (d. 20 Jumādā II 773/29 December 1372) at the Shah-i Zinde below the muqarnas vault (Golombek, Lisa and Wilber, Donald, The Timurid architecture of Iran and Turan, Princeton, 1988, 1, 238–241) in a technical senseGoogle Scholar: the latter is plainly hyperbole; and both saqf and ṭāq appear to refer to the exterior not, as would be more consistent with a cosmological interpretation, to the inside. Shishkin's, V. A. translation (‘Nadpisi v ansamblye Shakhi-Zinda’, in Zodchestvo Uzbekistana: materialy i issledovaniya, II: Ansambl' Shakhi-Zinda, ed. Zakhidov, P. Sh., Tashkent, 1970, 7–71)Google Scholar, (21) as ‘this roof full of decorations, this gilded vault’ is more prudent. The signature on one of the alveoles, ‘amal-i ustād Shams al-Dīn [Bukhārī], must incidentally refer to a ceramic craftsman, not to the designer of the stalactite vault.

⁴ cf. Notkin, I. I., ‘Decoding sixteenth-century muqarnas drawings’, Muqarnas, 12, 1995, 148–171CrossRefGoogle Scholar. Scholars owe Professor Necipoğlu an additional debt for having established their exact location.

⁵ Some of the patterns analysed by Keane included a 13-pointed star, indicating that the craftsman must have fitted in certain elements of the design by eye. Although none of the designs in the Topkapi scroll seems to show optical corrections they must have been quite frequent.

⁶ Though not unknown, as on, for example, the mid-twelfth-century mihrab of Sayyida Nafīsa in Cairo. There is also evidence that tilework was used on Fatimid buildings, though the only published tile is part of a frieze (cf. Wiet, G., ‘Inscriptions mobilières de l'Égypte musulmane’, Journal Asiatique, CCXLVI, 1958, 237–285Google Scholar, and pl. I) dated … ‘wa khamsamī'a, hence 504, 507, 509/1110–15.

⁷ Following largely unsubstantiated assertions by Massignon, Grabar and, most recently, Tabbaa, Yasser (‘The muqarnas dome: its origin and meaning’, Muqarnas, III, 1985, 61–74).CrossRefGoogle Scholar

⁸ The Islamic philosophical positions characterized as ‘atomism’ are, however, very heterogeneous (cf. Pines, S., Beiträge zur islamischen Atomlehre, Berlin, 1936Google Scholar; ‘al-Djuz'’, EI ²) and recourse to atomism as an explanation requires, therefore, specification in much more detail. If they do have a common element it is their theories of causation, which, at their extreme, amount to occasionalism, where constant divine interference is necessary if the material world is to work; but that scarcely seems relevant.

⁹ An Arabic text of al-Buzjani's Aՙmal al-handasa (now in the library of Süleymaniye AS 2753) was among the manuscripts transcribed at Samarkand for the library of Ulugh Beg.

¹⁰ Professor Necipoğlu (p. 169 and nn. 113–15) does not appear to commit herself to a particular date for its composition, though she notes that various scholars have dated it c. 1200. The Paris copy (cf. figs. 108–14) must, however, be later, for it is written in nastaՙlīq, possibly of fifteenth-century type. Bulatov, M. S. (Geometricheskaya garmonizatsiya v arkhitekture Srednei Azii IX–XV vv., Moscow, 1978; 1988Google Scholar) has claimed that it was composed in Khwarazm, perhaps at Gurgānj/Urgench c. A.D. 1000 and that all the grid systems which appear in it occur on eleventh/twelfth-century monuments in Central Asia. Too few monuments remain to make the latter claim effective. His further claim, that the basic identity of girih and muqarnas conduces to a special harmonious unity in traditional Iranian and Central Asian architecture, remains to be demonstrated.

¹¹ cf. Golombek, L., ‘The chronology of Turbat-i Shaikh Jām’, Iran, XI, 1971, 26–44Google Scholar, especially pls. IIa and IIIa. The anonymous Persian treatise (Bibliothèque Nationale MS persan 169, 194r; cf. fig. 114 of the present volume) also illustrates two visually 3-dimensional compositions of rhombs, squares and octagons.

¹² O'Kane, Bernard. Timurid architecture in Khurasan (Costa Mesa: Mazda, 1987), 36–37Google Scholar; pls. 0.1, 0.2.

¹³ Her suggestion that the first known star-polygon frontispiece, that of the Quran attributed to Ibn al-Bawwāb in the Chester Beatty Library (391/1000–1), was probably also the work of the copyist is intriguing, though its implications are unclear.