This Workshop will demonstrate the design methodology employed in the creation of particularly complex Islamic non-systematic geometric patterns with differentiated regions of compound local symmetry. This variety of Islamic geometric pattern is characterized by combinations of star forms that range from the more compatible (such as 9s and 12s) to the seemingly incompatible (such as 9s and 11s, and 11s and 13s). A series of historical pattern examples, ranging in complexity, will be used to demonstrate the non-systematic use of the Polygonal Technique of geometric pattern generation; and corroborating historical evidence will be provided that confirms that the techniques being taught in this Workshop were used by Muslim artists of the past. Along with self-similar designs, this variety of geometric pattern represents the pinnacle of Islamic geometric art; yet very little has been published on this all-but-lost design methodology. The objective of this Workshop is to assist in the rekindling of this design tradition: opening the door to working with, and teaching, the more complex aspects of this ancient design discipline.