Symmetry groups of Moroccan geometric woodwork patterns

Abstract

Many works report the classification and analysis of geometric patterns, particularly those found in the Alhambra, Spain, but few authors have been interested in Moroccan motifs, especially those made on wood. Studies and analyses made on nearly a thousand Moroccan patterns constructed on wood and belonging to different periods between the 14th and 19th centuries show that, despite their great diversity, only five plane groups are present. Groups p4mm and c2mm are predominant, p6mm and p2mm are less frequent, while p4gm is rare. In this work, it is shown that it is possible to obtain the 17 plane symmetry groups by using a master craftsmen's method called Hasba. The set of patterns are generated from n‐fold rosettes, considered as the basic motif, by the Hasba method. The combination and the overlap between these basic elements generate other basic elements. By repeating these basic elements, it is possible to construct patterns having various symmetry groups. In this article, only uncoloured patterns are considered and the interlace patterns are disregarded.

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

“…Despite their great diversity, all the patterns belong to only three symmetry point groups. 4mm and 6mm are the most frequent, while 2mm are rare (Aboufadil et al, 2013a).…”

“…12-fold rosettes are among the most common in Islamic geometric ornaments in general and Moroccan ornaments in particular. These rosettes, which may be classified according to the geometric shape of their petals, allow the construction of a large number of variants as well as new rosettes, previously unknown, while respecting the Hasba construction method used by master craftsmen (Aboufadil et al, 2013a). In addition, tiling the plane with finite patterns containing 12-fold rosettes provides different periodic and non-periodic structures ( Fig.…”

Teaching periodicity and aperiodicity using 3D-printed tiles and polyhedra

“…There exist interactive tools to draw symmetry patterns with the desired plane-group symmetry (Eck, 2016). Also, decorative motifs in Moorish tiles and woodwork (Gru ¨nbaum et al, 1986;Aboufadil et al, 2013), Persian-style carpets (Bier, 1992;Atanassova & Vassileva, 2017) and particularly the beautiful artworks by Escher (Bool et al, 1992) can be used to identify equivalent lattice points, symmetry elements, the unit cell, and ultimately the point and plane symmetry (Aroyo, 2016a). All these can also be adapted to 3D-printed tiles that allow the construction of the symmetry pattern itself besides analysing the corresponding symmetry.…”

Technology and Mathematics

“…3 Irrespective of that, the method is most useful for both purposes. Moroccan carpenters still construct complex geometrical patterns with ruler-and-compass methods of ancient origin (Aboufadil et al 2013). In the Greek village Pyrgi, house façades are decorated with geometrical patterns made by craftsmen who have learned the ruler-and-compass methods by apprenticeship (Stathopoulou 2006).…”