Islamic Geometric Girih Pattern

Islamic Geometric Girih Pattern

Islamic geometric ornament is one of the most intellectually and visually sophisticated decorative traditions in world art. The girih (Persian for 'knot' or 'grid') system -- a specific method of generating geometric tile patterns using a set of five interlocking polygon tiles -- represents the apex of this tradition, and its complexity was not fully understood by Western mathematics until Peter Lu and Paul Steinhardt published their analysis in Science in 2007, demonstrating that some 13th-century Islamic architectural surfaces contain aperiodic (quasiperiodic) patterns structurally identical to the Penrose tilings independently discovered by Roger Penrose in 1974.

Why Figural Art Was Replaced

Islamic decorative arts developed an unprecedented emphasis on geometric ornament partly due to the Hadith traditions cautioning against depiction of living forms in sacred contexts (though this interpretation varied greatly across time, region, and denomination). The prohibition directed artistic energy toward geometric pattern, calligraphy, and arabesque (vegetal scrollwork). The result was not a limitation but an explosion of geometric invention, as craftsmen and mathematician-designers pushed the logic of symmetry and infinite-plane tiling further than any other tradition.

The Five Girih Tiles

The girih system uses five shapes: a regular decagon (ten-sided polygon), an elongated hexagon, a bow-tie/chevron, a regular pentagon, and a rhombus. Each tile has lines inscribed on its face that, when tiles are assembled, produce the continuous star-polygon pattern visible on the surface. This two-level system -- a hidden scaffolding of large tiles, a visible pattern of star-polygons -- is the key insight. Major examples are found at:

• Darb-i Imam shrine, Isfahan, Iran (1453 CE) -- analyzed by Lu and Steinhardt as containing perfect quasiperiodic tiling
• Gunbad-i Qabud (Blue Tower), Maragheh, Iran (1197 CE) -- 13th-century precursor documented in the 2007 Science paper
• Alhambra Palace, Granada, Spain (1238-1358 CE) -- the most visited Islamic geometric ornament site, with the full range of 17 crystallographic symmetry groups represented across its tile and plaster work

Geometric Elements

The visual vocabulary of Islamic geometric art is built on star polygons: six-pointed stars (hexagram), eight-pointed stars, ten-pointed stars, twelve-pointed stars, and sixteen-pointed stars, generated by rotating and overlapping regular polygons. Muqarnas (stalactite vaulting) translate the two-dimensional geometry into three-dimensional carved plaster or stone. Zellige (mosaic tile work) in Morocco and Andalusia uses hand-cut terracotta tiles in the same geometric vocabulary.