Geometric Links Between 2D Patterns and 3D Structures in Islamic Architectures of Andalucia

The paper intends to highlight the links between two-dimensional geometric matrices and three-dimensional structures in Andalusian architectures of Islamic origin. The deep ambivalence between plane and spatial geometries maintains a very strong evidence, for example, in the flat projections of the articulated vaulted surfaces ribs or the muquarnas cellular structures. The creative process underlying the geometric grid systems of these shapes is based on analogous proportioning systems and geometries, underlying the plane patterns. This article then analyzes in particular the geometrical principles, the transformations and the design aspects that were used to create the modules of the flat decorations and how they can be understood as structural schemes for the architectural buildings. To this end, some emblematic buildings of Islamic architectural production in Andalusia were examined, focusing on the most significant dome structures. In these it was possible to highlight how the purely ornamental aspect linked to the geometric design, constantly interacts with the architectural form.