Symmetry in Moorish and other ornaments

Abstract

An investigation of the Moorish ornaments from the Alhambra (in Granada, Spain) shows that their symmetry groups belong to 13 different crystallographic (wallpaper) classes; this corrects several earlier enumerations and claims. The four classes of wallpaper groups missing in Alhambra (pg, p2, pgg, p3ml) have not been found in other Moorish ornaments, either. But the classification of repeating patterns by their symmetry groups is in many cases not really appropriate—account should be taken of the coloring of the patterns, of their interlace characteristics, etc. This leads to a variety of “symmetry groups”, not all of which have been fully investigated. Moreovr, the “global” approach to repeating ornaments is only of limited applicability, since it does not correspond to the way of thinking of the artisans involved, and does not cover all the possibilities of “local” order. The proper mathematical tools for the study of such structures which are only “locally orderly” remain to be developed.