Interrelation between grid systems and star polygons of muqarnas ground projection plans

Many muqarnas ground projection plans contain stars with unequal edge lengths in their compositions. In this study,
the geometric reasons behind the unequality of star edge lengths in muqarnas ground projection plans have been
searched. The main gates with complex-looking muqarnas belonging to the period of Suleiman the Magnifcent
(Kanuni Sultan Suleyman), designed by Architect Sinan in Istanbul, have been selected to examine. From the data
obtained by 3D laser scanning and from the verifcation made, it has been confrmed that there are stars with unequal
edge lengths in these muqarnas plans. From the geometrical examinations made according to the shape grammar
theory, it was concluded that the muqarnas plans were created using spider-web grid and square grid layouts. It was
also concluded that these grid types cause some of the star edge lengths to be unequal.