The Projection Strategies of Gireh on the Iranian Historical Domes

The Gireh is an Islamic geometric pattern which is governed by mathematical rules and conforms to Euclidean surfaces with fixed densities. Since dome-shaped surfaces do not have a fixed density, it is difficult to make use of a structure like Gireh on these surfaces. There are, however, multiple domes which have been covered using Gireh, which can certainly be thought of a remarkable achievement by past architects. The aim of this paper is to discover and classify the strategies employed to spread the Gireh over dome surfaces found in Iran. The result of this research can provide new insights into how Iranian architects of the past were able to extend the use of the Gireh from flat surfaces to dome-shaped elements. The result of this paper reveal that the projection of Gireh on dome surface is based on the following six strategies: 1- Spherical solids, 2- radial gore segments, 3- articulation, 4- changing Gireh without articulating, 5- changing the number of Points in the Gireh based on numerical sequences, and 6- hybrid. Except for the first method, all of the other strategies have been discovered in this study. The radial gore segments strategy is different from the previously-developed methods.