February 26, 2007

Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

Peter J. Lu1* and Paul J. Steinhardt

The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns inmedieval Islamic architecture were conceived by their designers as a network of gzagging lines,where the lines were drafted directly with a straightedge and a compass. We show that by 1200C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellationsof a special set of equilateral polygons (“girih tiles”) decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, thetessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West. Read more

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