A Parametric Design Method for the Wooden Turkish Triangle Plated Structure (Barkat) Model

Abstract Mimar Sinan’s mosques are celebrated as masterpieces of central-plan mosque design, showcasing exceptional spatial composition and structural form. A previous study designed a novel model by adapting these forms using a catenary curve, folded plates, and Turkish triangles. However, that model established only a static topology. Distinguishing itself by advancing this topology into a dynamic computational framework, this research introduces a novel parametric algorithm that mathematically defines the Turkish triangle. This method allows for both the analytical classification of historical transition zones and the generation of the contemporary ‘Barkat’ mosque model. Using Grasshopper and Python, geometries are defined via wall segmentation/folding (n) and hoop (ring) edge (k) parameters. The analysis confirms that combinations of (n = 1–3) and (k = 4–8) yield the most balanced forms. The resulting framework offers a dual contribution: a digital reconstruction tool for architectural history and a fabrication-ready design method for folded plate structures.