Muqarnas are ornamental features of Islamic architecture. Their 2D floor plans resemble tessellations of squares, rhombuses and kites. However, these plans often oversimplify the spatial complexity, losing key details. The underlying grid may be octagonal, hexagonal or decagonal, but in the larger muqarnas, pentagonal or heptagonal shapes are added. A mathematician can prove that it is impossible to fit these shapes into these grids, but artists and designers know how to manipulate the muqarnas units so that pentagons do fit into an octagonal plan. The idea of describing a muqarnas in terms of pre-defined units works well for the smaller muqarnas, but fails for the larger. Having become stranded in the mathematical approach, Turkish architectural books offered a way out. Parametric units fit better into the design process. I automated the drawing process and today I can 3D print muqarnas designs.