Islamic · 9th century CE · Girih & Arabesque

Islamic
Geometry

Fold symmetry. Interlocking stars. A mathematics that tiles the infinite plane without repetition — discovered in Baghdad nine hundred years before Western science named it.

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Zone I — Origin & meaning

The Alhambra, Baghdad, Cairo. One mathematics.

Islamic geometric art emerged in the 9th century CE as a response to a theological and aesthetic challenge: how to create visual art of transcendent beauty without depicting the human form. The answer was mathematics — the most abstract, universal, and eternal of languages.

The girih tiles — five specific polygon shapes that tile the plane — were used by Islamic architects centuries before Roger Penrose described similar non-repeating tilings in 1974. The geometry was known. Only the name was missing.

"The craftsman who designed the Alhambra's tile patterns understood, intuitively and practically, mathematics that Western science would not formalise for five hundred years. The geometry is the theology."

The girih system uses five polygons: a regular decagon, pentagon, hexagon, bowtie, and rhombus. Decorated with internal lines, these five shapes tile the plane in infinitely many ways without ever exactly repeating.

Islamic · 9th century CEGirih tilesAlhambra · Isfahan · CairoQuasi-crystallinePenrose tiling — 500 years earlier
Zone II — The mathematics

Infinite patterns from five shapes

The key mathematical property is fold symmetry — the number of times you can rotate the pattern and have it look identical. Five-fold and ten-fold symmetry cannot tile the plane periodically. Islamic geometers found quasi-periodic solutions that Western mathematics wouldn't discover until the 1970s.

// Girih star polygon
Points: P_k = (R·cos(k·2π/n), R·sin(k·2π/n))
Star: connect every s-th point, s = floor(n/3)
// Quasi-crystalline: 5-fold, 10-fold aperiodic
Girih shapes
5
infinite combinations
Fold symmetry
5–12
selectable
Penrose tiling
1974
500 yrs after Isfahan
Repetition
never exactly
Zone III — Your sandbox

Enter the tile

A unique Islamic geometry computed now. Change fold symmetry between 5-fold and 12-fold. Zoom in to watch the sub-pattern emerge inside the tile.

Level 1 — The Tile
One complete girih unit. Perfect fold symmetry.
At zoom levels 2–4: drag to explore · PDF captures your exact view
Custom colours
Palette presets
Seed: IG-0000-xxxx
Current design — seed: IG-0000-xxxx
This pattern exists nowhere else

Your Islamic geometry was generated at this moment. The A3 PDF embeds the formula, fold symmetry, seed, and your name.

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