Take five flat shapes with every edge cut to the same length, the largest of them ten-sided. Draw a few straight lines across each one, then lay them side by side. The tiles drop out of sight. What's left is a net of ten-pointed stars and crossing bands that looks as if someone drew it in one sitting. That's girih. You don't see the tiles. You see the lines.
What You See
Start with the biggest piece, the decagon. Inside it, the lines form a ten-pointed star, the kind made by joining every third point of the ten. Around it sit the smaller pieces: a pentagon holding a five-pointed star, an elongated hexagon whose lines bend into a bat-like shape, a bowtie whose lines read as two quadrilaterals facing away from each other, and a rhombus that carries its own small bowtie.
Now look at any seam between two tiles. Every edge has the same length, and the decorating lines cross the midpoint of every edge at 72° and 108°. Because every tile follows that same rule, a line leaving one piece always has a partner waiting in the next. The seams vanish and the bands run on.
Count the angles and you'll keep landing on multiples of 36°, a tenth of a full turn. That's why girih feels like it counts in tens. If the eight-pointed star of zellige is the geometric star you know, girih is its ten-pointed counterpart.
What is girih?
Girih is a style of geometric ornament in Islamic architecture, found on buildings in Iran, Turkey and Herat. Its star-and-polygon line patterns can be built from five equal-edged tiles (a decagon, pentagon, elongated hexagon, bowtie and rhombus), each decorated with lines. By around 1200 CE, designers had begun to treat these patterns as tilings of exactly those shapes.
The One Thing to Know
Girih is a drawing system before it is a surface. The pattern lives in the lines; the five tiles are the scaffolding underneath.
Scholars Peter Lu and Paul Steinhardt describe a turning point: by 1200 CE, girih patterns had been reconceived as tessellations of those five decorated tiles, a shift that allowed "simpler, faster, and more accurate execution by artisans unfamiliar with their mathematical properties." In other words, the hard part was built into the tiles. An artisan didn't need to work out the mathematics behind the tiles: place one shape against another, follow the lines, and a crisp ten-fold star arrives.
The tiles also carry different kinds of symmetry. The decagon has ten-fold symmetry, the pentagon five-fold, and the elongated hexagon, bowtie and rhombus two-fold. Mix them, and you get a field where big ten-pointed stars anchor the eye while the smaller pieces fill the spaces between with steady, mirrored motion.
That's also what sets girih apart from its neighbors. Zellige is a cutting craft; girih is a drafting system. And where the arabesque follows a growing stem, girih follows straight lines held to fixed angles.
How It Traveled
The surviving buildings give you a set of dated stops. They show the method at work on buildings from the Seljuk era to the Timurid era and beyond, from Maragha to Herat; the sources here mark where it appears, not who carried it between them.
Maragha, Iran, 1197. On the Gunbad-i Kabud, an octagonal tomb tower, seven of the eight exterior wall panels are filled with decagons, elongated hexagons, bowties and rhombuses. Walk around it and almost every side tells you the same thing: the system was already working at full scale. It is one of the clearest early places to see the five-tile logic working across a whole facade.
Tercan, Turkey, 1200. Three years later and far to the west, the Mama Hatun Mausoleum shows the same family of patterns. Lu and Steinhardt place it among the Seljuk buildings where patterns of this type appear around 1200. Two sites, three years apart, already a long way from each other on the map.
Herat, 1425 to 1429. At Gazargah, in Herat, the shrine of Khwaja Abdullah Ansari carries girih more than two centuries after Maragha. By now the method is not an experiment. It is a working vocabulary.
The Topkapi Scroll, 15th century. This is the stop where you get to look over a designer's shoulder. Made in the Timurid-Turkmen world and now held in the Topkapi Palace Museum in Istanbul, the scroll shows patterns with the outlines of the five girih tiles drawn in ink beneath them. The scaffolding that buildings hide is out in the open here. Lu and Steinhardt call the scroll direct documentation that the tiles were used.
Isfahan, the Darb-i Imam. The oldest part of this shrine was built in 1453, in the Timurid era, and the 2007 study gave the shrine that date. The girih panel the 2007 study analyzed, though, may be much later: researcher Lauwers argues it dates to the end of the Safavid period, 1715 to 1717. It is easy to merge the two dates, but if Lauwers is right, they are more than 260 years apart, and this panel sits at the center of the debate in the next section.
Between these stops are gaps the record doesn't fill. What's clear is that from the late 12th century to the 15th, and beyond, the same five shapes and the same 72°/108° rule kept producing new stars on new walls.
Why It's Still Alive
In 2007, girih walked into a physics debate. In a paper in Science, Peter Lu and Paul Steinhardt argued that by the 15th century, girih tilings had reached "nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West." The claim put Isfahan's tilework next to modern mathematics.
The authors set their own limits. They reported no evidence that artisans used the matching rules a true Penrose tiling needs, and they counted 11 mismatches among about 3,700 Penrose tiles in the pattern they analyzed.
Others pushed back. Lauwers, writing in 2018, describes the claim as "disputed (and refuted) by several authors." He reports Makovicky's view that the pattern is periodic, built from one large repeating unit, and Cromwell finds no quasiperiodic pattern among the medieval designs in his catalog. And as noted above, the panel at the heart of the claim may date to the early 1700s, not 1453.
So the question is still argued over, and that's its own kind of life. A five-tile system drawn by artisans can still send mathematicians back to the wall, measuring angles and arguing over what the makers knew.
Your Pattern
You can try the rule yourself. Draw a regular pentagon and mark the midpoint of each edge. From every midpoint, draw two short lines pointing inward, one leaning left and one leaning right, each meeting its own edge at 72°. Stop each line where it meets a line from the next midpoint. Watch a five-pointed star appear where you never drew one.
If that kind of order is what draws you in, two Flowbam designs play with line in their own way: the Open Crossing Tote loops broad bands that cross and run on, and the Gridline Weekender Bag breaks a grid into short, straight segments. They aren't girih; they're simply made for people who like to follow a line across a surface.
For the eight-pointed side of the family, read the zellige story. For the curving counterpart, find the arabesque. Or browse more Pattern Stories.