Brian Hayes reviews Symmetry Comes of Age: The Role of Pattern in Culture, edited by Dorothy K. Washburn and Donald W. Crowe, and Embedded Symmetries, Natural and Cultural, edited by Dorothy K. Washburn, at American Scientist:
On a visit to the Alhambra some years ago, I toted along a copy of Symmetry in Science and Art, a weighty text by A. V. Shubnikov and V. A. Koptsik, as a field guide to the carvings and tilings that decorate that extravagant palace overlooking Granada. The two books under review here would probably serve as better field guides—Symmetry Comes of Age even includes a useful flowchart for classifying the symmetry groups of patterns—but I suspect that the authors and editors would not entirely approve of this use of their work. The tourist who stalks the halls of the Alhambra trying to complete a checklist of the 17 two-dimensional symmetry groups is not their ideal student of “the role of pattern in culture.” When one is looking at an artifact such as a tiled floor or a woven fabric or a beadwork ornament, identifying crystallographic groups is at best the beginning of understanding the object. The classification might tell you something about the meaning of the work in the context of Western mathematics, but it is unlikely to reveal much about the object’s meaning within the culture that created it.
This point is made emphatically by Branko Grünbaum—a mathematician who certainly knows his symmetry groups—in a previously published article on ancient Peruvian textiles that is reprinted in Symmetry Comes of Age.
More here.