In designing architectural structures, medieval Islamic artisans hit on so-called quasicrystals, a complex pattern made famous by renowned mathematician Roger Penrose in the 1970s. After seeing hints of the pattern while traveling in Uzbekistan, Peter J. Lu, a physics graduate student at Harvard University, pored over photographs from Iran, Iraq, Turkey and Afghanistan. Some of the ornate tile work, called girih, could have only been accurately constructed using a set of five tiles—a bow tie, pentagon, diamond, elongated hexagon and large decagon—conclude Lu and co-author Paul J. Steinhardt of Princeton University. The tiling practice reached great sophistication with the Darb-i Imam shrine in Iran, which dates to 1453; it displays a symmetric pattern of pentagons and 10-sided stars. If extended indefinitely in all directions, this pattern would never repeat itself—the hallmark of a quasicrystal. The researchers describe their conclusions in the February 23 Science.