Generating Novel 6-Point Girihs (6-Point Islamic Geometric Patterns) Based on Existing Ones

6-point girihs (6-point Islamic geometric patterns) are among the earliest and most popular geometric patterns created by Muslim artists in Iran. Some of them have distinctive behavior compared to the majority of Islamic geometric patterns. This paper examines the motifs used in 6-point girihs and categorizes them into basic and secondary motifs. We propose a method for constructing 6-point girihs based on symmetry group theories. The method involves a step-by-step process starting from constructing the minimal essential information (template motif) required to generate a particular symmetry type within the fundamental region, to replicating the unit girih in a two-dimensional plane using a suitable net of 6-point girihs. Finally, we present a notation system consisting of six parameters to construct the basic motifs of p6m 6-point girihs.