Origin of Irregular Star Polygons in Ground Projection Plans of Muqarnas

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.