Islamic geometry

The use of mathematics, especially geometry, in Islamic architecture and art is very common and quite sophisticated. My research is focused on the so called girih tiles, which are decorative geometric patterns. The goal is to explore how they are constructed and apply it in a modern context, trying to add more functions to it.


There is a tradition of aniconism in Islam to prevent idol worship, which means the absence of religious figurative depictions. That is mainly why Islamic art and architecture is characterized by rich geometric patterns and calligraphy instead.

The construction of girih patterns have baffled contemporary mathematicians for ages, and it weren’t before nine years ago that the Western world grasped them. Earlier the girih patterns were perceived as a network of intertwining lines, crafted directly with the help of a straightedge and a compass, but in 2007 the mathematicians Lu and Steinhardt discovered that they really consist of a tessellated system of polygonal tiles with decorated lines on top called girih tiles. With this technique, Islamic artists were able to create highly complex quasi-crystalline patterns 500 years earlier, which was discovered in the 1970s in the West.

By using a system consisting of five tile shapes, the Islamic artists could create geometric patterns that were highly complex yet simple to construct. These polygonal tiles each have the same side lengths, with two lines meeting in the middle of every side with angles of 108° and 72°. The word girih is Persian for the word “knot”, and describes the symmetrical lines that decorate the tilings. When placing the girih tilings side by side, this is what creates the quasicrystalline patterns.


  • A rhombus with interior angles of 72°, 108°, 72°, 108°
  • A regular pentagon with interior angles of 108°
  • A bow tie hexagon with interior angles of 72°, 72°, 216°, 72°, 72°, 216°
  • A elongated hexagon with the interior angles of 72°, 144°, 144°, 72°, 144°, 144°
  • A decagon with ten interior angles of 144°

Inspired by this old tiling system, I want to create architectural components such as tiles or bricks. By using modern techniques such as parametric design and CNC milling I want to explore the possibilities of making complex patterns or shapes that has more functions other than decorating or load-bearing.

Two projects in particular are used as references for the fabrication process: Tectonic Horizons and Digital Islam. The first one features modular components created with the use of CNC milling and a traditional method called slip casting. It “…questions the traditional mold-making process by integrating contemporary notions of mass customization with the economies of scale inherent in mold/cast systems.” source 


Allen, T. Aniconism and Figural Representation in Islamic Art. Solipsist Press. 1988 [gathered 2016-09-19]

Al-Hassani, S. New Discoveries in the Islamic Complex of Mathematics, Architecture and Art. Foundation for Science, Technology and Civilisation. [gathered 2016-09-19]

Lu, J. Peter, Steinhardt, Paul J. Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture. Science.2007 %5Bgathered 2016-09-19]

Stein, Joshua G. Tectonic Horizons. Data Clay. 2013 [gathered 2016-09-19]

Celento, D. Digital Islam – Penrose Tiling System. Data Clay. 2009.

[gathered 2016-09-19]






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