Abstract
Many muqarnas contain star polygons in their ground projection plans. Such star polygons usually have equal edge lengths. In this study, the geometric background of irregular star polygons with unequal edge lengths, observed in some ground projection plans of muqarnas, was investigated. The plan of the muqarnas at the main gate of the Atik Valide Mosque was examined according to the theoretical framework of shape grammars. As a result of the case study, it was concluded that ellipse grids were used to form the layout of the ground projection plan of muqarnas. It was shown that stars placed in the areas formed by the intersections of the ellipse grid formed irregular polygons naturally. In addition, a parametric 3D geometry of muqarnas was obtained by considering a geometric decomposition of the analysed ground projection plan of muqarnas.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alacam, Sema, Orkan Z. Guzelci, Ethem Gurer, and Saadet Z. Bacinoglu. 2017. Reconnoitring computational potentials of the vault-like forms: Thinking aloud on muqarnas tectonics. International Journal of Architectural Computing 15 (4): 285–303.
Bodner, B. Lynn. 2012. From Sultaniyeh to Tashkent Scrolls: Euclidean Constructions of Two Nine- and Twelve-Pointed Interlocking Star Polygon Designs. Nexus Network Journal 14 (2): 307–332.
Bonner, Jay. 2017. Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Construction. NY: Springer.
Broug, Eric. 2008. Islamic Geometric Patterns. London: Thames and Hudson.
Bourgoin, Jules. 1879. Les Eléments de l’Art Arabe: Le Trait des Entrelacs. Paris: Firmin-Didot.
Castera, Jean-Marc. 2007. The Muqarnas Dome of the Hall of the Two Sisters in the Alhambra in Granada. In Mathematics and Culture V, ed. Michele Emmer, 101–110. Springer-Verlag Berlin Heidelberg.
Critchlow, Keith. 1983. Islamic Patterns: An Analytical and Cosmological Approach. London: Thames & Hudson.
Cromwell, Peter R. 2009. The Search for Quasi-Periodicity in Islamic 5-fold Ornament. The Mathematical Intelligencer 31: 36–56.
Dold-Samplonius, Yvonne. 1992. Practical Arabic Mathematics: Measuring the Muqarnas by al-Kashi. Centaurus 35: 193–242.
Dold-Samplonius, Yvonne, and Silvia L. Harmsen. 2005. The muqarnas plate found at Takht-i Sulayman: A new Interpretation. Muqarnas: An Annual on the Visual Culture of the Islamic World 22: 85–94.
Elkhateeb, Ahmed Ali. 2012. Domes in the Islamic Architecture of Cairo City: A Mathematical Approach. Nexus Network Journal 14 (1): 151–176.
Eris, Ihsan, Ugur Yuzeroglu, and Nuket Demir. 2013. Atik Valide Sultan Kulliyesi 2011-2013 Yillari Restorasyonu ve Uygulamalari. Vakif Restorasyon Yilligi Dergisi 6: 99–114.
Gherardini Francesco and Francesco Leali. 2016. A Framework for 3D Pattern Analysis and Reconstruction of Persian Architectural Elements. Nexus Network Journal 18:133–167.
Hankin, Ernest Hanbury. 1998. The Drawing of Geometric Patterns in Saracenic Art. New Delhi: The Director General Archaeological Survey of India.
Hamekasi, Nader, Faramarz F. Samavati, and Ahmad Nasri. 2011. Interactive Modeling of Muqarnas. Proceedings of Computational Aesthetics in Graphics, Visualization, and Imaging. 129–136.
Harb, Ulrich. 1978. Ilkhanidische Stalaktitengewolbe: Beiträge zu Entwurf und Bautechnik. Berlin: Reimer.
Harmsen, Silvia. 2006. Algorithmic Computer Reconstructions of Stalactite Vaults -Muqarnas- in Islamic Architecture. Ph.D. Thesis, Heidelberg University.
Kashef, Mohamad. 2017. Bahri Mamluk muqarnas portals in Egypt: Survey and analysis. Frontiers of Architectural Research 6: 487–503.
Kharazmi, Mahsa, and Reza Sarhangi. 2016. An Analytical Study of the Methods of Design and Geometric Constructions in Architectural Ornaments of the Friday Mosque of Forumad. Nexus Network Journal 18: 275–310
Necipoğlu, Gülru. 1995. The Topkapi Scroll: Geometry and Ornament in Islamic Architecture: Topkapi Palace Museum Library MS H. 1956. Santa Monica, CA: The Getty Center for the History of Art and the Humanities.
Özdural, Alpay. 1990. Giyaseddin Jemshid el-Kashi and stalactites. METU JFA 10: 31–49.
Özdural, Alpay. 1991. An analysis of the geometry of stalactites: Buruciye Medrese in Sivas. METU JFA 11: 57–71.
Redondo-Buitrago, Antonia, and Dirk Huylebrouck. 2015. Nonagons in the Hagia Sophia and the Selimiye Mosque. Nexus Network Journal 17 (1): 157–181.
Schneider, Gerd. 1980. Geometrische Bauornamente der Seldschuken in Kleinasien. Wiesbaden: Reichert.
Sarhangi, Reza. 2012. Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs. Nexus Network Journal 14 (2): 345–372.
Senhaji, Mohammed, and Rachid Benslimane. 2019. Automatic 3D muqarnas architectural patterns reconstruction using plane representation. Journal of Cultural Heritage 35: 25–40.
Takahashi, Shiro. 2019. Muqarnas: A Three-Dimensional Decoration of Islamic Architecture. http://www.shiro1000.jp/muqarnas/default-.htm. Accessed 19 September 2019.
Uluengin, Fatin M. 2018. Mukarnas. Istanbul: Istanbul Fetih Cemiyeti.
Acknowledgements
All images are by the author unless otherwise indicated.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Agirbas, A., Yildiz, G. Origin of Irregular Star Polygons in Ground Projection Plans of Muqarnas. Nexus Netw J 23, 507–548 (2021). https://doi.org/10.1007/s00004-020-00516-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00004-020-00516-x