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Girih: The Geometry in Which the Middle Ages Outran Mathematics

What looks like merely a beautiful pattern on the walls of Samarkand and Bukhara is actually a system. The stars, polygons and interlaced lines are built by exact rules — and behind them stands the idea of infinity.

A Kvazar guide · Updated 2026 · ~9 min read

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Looking at the walls of a madrasa or mosque in Uzbekistan, it's easy to see "just ornament" and walk on. But look closer and the interesting part begins: these stars and interlaced lines weren't drawn by eye. Behind them lies strict geometry, a set of rules, and an idea the whole thing was made to express. Girih isn't decoration — it's a language. And once you understand its grammar, you stop merely photographing walls and start reading them.

In short: girih (from the Persian for "knot") is Islamic geometric ornament made of interlaced straight lines forming stars and polygons. It's built with compass and straightedge from a repeating "cell" that tiles the plane with no gaps. The stars have 6, 8, 10 or 12 points. Symbolically, girih expresses infinity and the unity of creation: the pattern has neither beginning nor end.

What is girih?

Girih is Islamic decorative geometry made of angled lines forming an interlaced strapwork. The word means "knot" in Persian. A typical girih consists of stars with 6, 8, 10 or 12 points, separated by polygons and straps. The earliest examples date from around 1000 CE, and the artform flourished into the 15th century.

It helps to distinguish girih from the two other "languages" of Islamic ornament. Girih is geometry — hard straight lines and stars. Islimi is the vegetal, flowing pattern (curling stems, the image of a paradise garden). And calligraphy is text, most often quotations from the Quran. On the walls of the Registan or Bukhara, these three languages usually work together, but each has its own grammar. Of the three, girih is the most "mathematical."

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How is girih built?

The classic method is compass and straightedge. The master sets a grid of points from which "construction lines" radiate, and builds stars and polygons at their intersections. The pattern is based on a repeating cell that fills the plane with no gaps — like a mosaic or a crystal. Later came "girih tiles" — a set of shapes with lines drawn on them that sped up the work.

The logic is the same as in a crystal: there's an elementary "cell" with a given symmetry (2-, 3-, 4- or 6-fold), and it's repeated by rotations and translations to tile the surface entirely. At first masters copied a pattern from a template on a grid, drawing it with compass and straightedge. Around 1200, stars with 5- and 10-fold symmetry appear, and in the 15th century the "girih tiles": five shapes with lines that, when joined, assemble into the most complex pattern by themselves. There even survives a medieval "Topkapı Scroll" that shows the patterns together with the layout used to build them — effectively a designer's blueprint.

Brick can do girih too. Girih geometry appears not only in tilework but in brickwork — the "banna'i" technique, where the pattern is laid out in the brick itself. That's exactly how the façade of the Samanid Mausoleum in Bukhara works: there the geometry is born from the material, with no paint at all.

What does girih mean?

Girih carries spiritual meaning. The endlessly repeating pattern, with no beginning or end, is held to express the infinity of God and the unity, order and harmony of creation. Here geometry is a way of speaking about the divine without depicting living beings, in keeping with the tradition of Islamic art.

This is the key to understanding it: girih avoids figures not from a poverty of means but on principle. Where other cultures depicted gods and heroes, Islamic art chose the language of pure form — geometry that points to what cannot be depicted. A pattern that continues past the edge of the wall into an imagined infinity becomes a metaphor for what the human eye cannot take in whole. That's why girih feels at once mathematical and meditative.

Where others drew the faces of gods, here they drew infinity. And perhaps came closer to it.

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Is it true girih anticipated modern mathematics?

In part, yes. Some later girih patterns (15th century), built with "girih tiles," have a non-periodic structure that researchers link to 20th-century mathematical discoveries — Penrose's non-periodic tilings and the concept of quasicrystals. In other words, the masters arrived empirically at regularities centuries before they were formally described.

This is one of the most astonishing stories in art. In the 1970s the mathematician Roger Penrose described non-periodic tilings that can fill the plane without ever repeating regularly. Researchers later showed that certain medieval girih patterns share similar properties — what Western science reached in the 20th century, the masters of the Islamic world embodied in tile and brick five hundred years earlier. To be precise: it's not that they "proved a theorem," but that their system was powerful enough to generate structures of such complexity. And that's the best argument against seeing ornament as "mere decoration."

Where can you see girih in Uzbekistan?

Girih is everywhere in Uzbekistan's historic architecture: on the portals and walls of the Registan madrasas in Samarkand, on the tilework of Shah-i-Zinda, in the brickwork of the Samanid Mausoleum in Bukhara, on the dome of Gur-e-Amir. One early example of girih's straight lines survives on the gateway of the Ribat-i Malik caravanserai in Uzbekistan (1078).

Samarkand and Bukhara are effectively an open-air museum of girih, spanning several centuries of its development. A useful trick for the traveler: with any pattern, try to find a star "center" and trace how the grid radiates from it. The moment you see the repeating cell behind the tangle of lines, the wall "snaps into place" — and you realize you're looking not at decoration but at the layout of infinity. For the color it's all laid out in, read our piece "Why are the domes of Samarkand blue."

Ornament as a code: why this matters for brand and design

Girih is a perfect illustration of the principle Kvazar is built on: a strong visual identity is a system, not a collection of decorations. Girih has a "grammar" (rules of construction), an "alphabet" (stars and polygons) and a meaning (infinity, order). From a small set of rules, infinite variety is born — which is exactly how a good design system should work.

For us this isn't a metaphor but a method. When we work with the region's cultural code in branding, we treat ornament the way an engineer treats a system: we look for the generative rule rather than copying a picture. So girih isn't "Eastern decoration" in our palette but a reminder that beauty and logic are the same thing. For the man under whom this language reached its height, read our piece on Amir Timur.

Frequently asked questions about girih

What does the word "girih" mean?

In Persian, "girih" means "knot." It refers to Islamic geometric ornament made of interlaced straight lines forming stars and polygons — and to the art of constructing it.

How were girih patterns created?

Classically, with compass and straightedge, based on a grid of points and a repeating cell that fills the plane with no gaps. Later, "girih tiles" were used — a set of shapes with lines that assemble into a complex pattern when joined.

Why geometry rather than images in Islamic ornament?

The tradition of Islamic art avoids depicting living beings in a religious context. Geometry became a way of speaking about the divine through pure form: an infinite pattern expresses infinity and unity without resorting to figures.

Is it true girih is connected to Penrose tilings?

Yes, in part. Some 15th-century girih patterns have a non-periodic structure close to the Penrose tilings and quasicrystals discovered in the 20th century. The masters created such structures empirically, centuries before their mathematical description.

Where is the best place to see girih in Uzbekistan?

In Samarkand — on the Registan and in Shah-i-Zinda; in Bukhara — in the brickwork of the Samanid Mausoleum and on the Poi-Kalon ensemble; on the dome of Gur-e-Amir. This spans several centuries of the pattern's development.

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