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Abstract
This work analyzes mathematically and graphically the two methods used historically in the transitional zone between the circular base of the dome and the square top of the cube where the dome is supported. The time frame of this work is the distinguished historical buildings of Islamic Cairo built between the ninth and eighteenth centuries. Ten samples were chosen out of a total of thirty. A set of mathematical expressions has been derived to relate the different parts of the squinches/pendentives to the cube with a side of length l. The equations derived were validated twice, first by generating 3D graphical sequences for both squinches and pendentives for the selected domes using CAD software based on the values obtained from the driven equations, and second by executing physical models using a 3D printer for two examples of squinches and pendentives.[PUBLICATION ABSTRACT]