Islamic geometric patterns often feature symmetric motifs like stars or rosettes. Historical designs include motifs with up to 96 points, but traditional construction techniques make it difficult to go higher. We present a simple polygons-in-contact method for constructing designs around a large central motif with any number of points. The method surrounds a large central polygon with conformally mapped layers of smaller tiles. The fidelity of the final design improves as the central motif grows.