SYMMETRY IN MOORISH AND OTHER ORNAMENTS††The research reported in this paper has been supported by National Science Foundation grants MCS 8001570 and MCS 8301971, and by a Fellowship from the John Simon Guggenheim Memorial Foundation. One version of this material was presented in an address to the Pacific Northwest Section meeting of the Mathematical Association of America in Moscow, Idaho, on June 18, 1983.
Branko Grünbaum, Zdenka Grünbaum, Geoffrey C. Shephard · Symmetry · 1986
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. Moreover, 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.