Varieties of 12-fold rosettes and their applications in Moroccan geometric ornament

This work is devoted to the study of the 12-fold rosettes frequently encountered in Islamic art, especially in Moroccan ornamentation. Several types of 12-fold rosettes are described according to the geometric shape of their petals. They have a large number of variants and offer the possibility of building new, previously unknown rosettes, while respecting the construction method Hasba used by master craftsmen. Artisans developed a technique for combining different types of 12-fold rosettes to construct infinite periodic tiling belonging to the 17 crystallographic groups. This technique enabled them to diversify the repeated patterns based on 12-fold rosettes. An analysis of their tiling suggests a method based on elementary geometry to build new patterns with different types of 12-fold overlapped rosettes and their variants. A procedure based on combination of the distances between two overlapped rosettes is then proposed, which enables generation of new periodic and quasiperiodic patterns.