Girih Tiles

Line ornaments in the form of polygons and geometric patterns are the hallmark of buildings from the Islamic Middle Ages. These so-called Girih patterns (from the Persian word for "knot") adorn palaces like the Alhambra in Granada, Spain, as well as mosques and shrines of revered imams in the Middle East. How did Islamic builders manage to create the highly complex geometric decorations?

The solution to the puzzle was found by Peter Lu of Harvard University and Paul Steinhardt of Princeton University. The two physicists examined various Girih patterns on Islamic buildings from Turkey to India, as well as architectural scrolls and the decoration of medieval Quran editions. They discovered that almost all patterns can be broken down into 'Girih tiles' - a set of five simple polygons: a decagon, a hexagon, a pentagon, as well as a rhombus and a bowtie. The edges of the tiles all have the same length, and each carries a simple pattern whose lines bisect the edges. When the tiles are laid together, the line patterns connect to form a cohesive aperiodic network that extends over the entire surface. Thus, Islamic artists were already relying on a method permeated by modern mathematics, similar to the discovery of aperiodic tiling with two tiles by physicist Roger Penrose in 1973, 500 years later.

As the scientists suspect, this geometric trick brought about a veritable design breakthrough in the Islamic world by the end of the 12th century. The use of Girih tiles not only allowed for simpler, faster, and more accurate work but also enabled constructions of extreme complexity.