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The LEARN section of this website has a number of sections that each deal with different aspects islamic geometrical design. 

INTRODUCTION: What are the principles of islamic geometrical design?

GRIDS: The hidden structure of Islamic geometric design, grids allow for creativity and innovation and make complex designs less complex.

Designs based on the division of a circle into five equal parts has characteristics that are different than all other kinds of geometrical design. Find out why.

Learn how to design one of the most common geometric designs in Islamic art and architecture. All you need is a pencil, a piece of paper and a compass and a ruler.

Learn how to design another common geometric design from Islamic art and architecture.

The building blocks of geometric designs. Polygons work together to make grids

The three- dimensional manifestation of two dimensional Islamic geometric design. They are Islamic architecture's a truly unique contribution to world architecture.

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Learn: Five Fold Geometry

Designs based on a fivefold division of a circle hold a unique place in geometry in general, and in Islamic geometrical design in particular. You can recognise fivefold geometrical design by counting the number of  'points' on a central geometrical star design or by counting the petals around the central star design.  The image  on the left is a ceramic tile panel for the Gur Emir. the central star has ten points and around the stars there are ten shapes like this. 

Designs based on a five-fold division of a circle are different from
 designs that derive from, for example, a 4-fold or 6-fold division.  The main difference is that 4-fold or 6-fold fold shapes can be repeated infintely.
A square will always fit next to a square and can be repeated to cover a big surface, the same is true for a 6-sided shape like a hexagon. This is not the case with five-sided or ten-sided  shapes. 

When creating an Islamic geometric design with 5 or 10-fold shapes, it becomes necessary to use different techniques than with 4 or 6 fold geometry.

All the shapes that are used in 5 or 10-fold geometrical compositions can be found inside a circle that has two pentagrams and a 10-pointed star placed inside it, as can be seen here on the right.

The design below is a classical 10-pointed design. It contains 11 different shapes. The shapes that have been used in the composition can be seen in the small video  to the right of the composition.
a pentagram inside
a circle
another pentagram inside a circle a ten-pointed star
inside a circle
the lines necessary for the creation of the below shapes. These shapes also appear in the short video

Islamic craftsmen created methods to make it easier for them to create designs based on 5-fold geometry. It would have been impractical to the design with a compass and a ruler because of the risk of inaccuracies.
Instead they discovered a number of shapes that could contain certain parts of the design and could be arranged in different ways to create a variety of designs. The design that is shown here is from the Qunbad-i Qabus tombtower in Iran and has intricate 5-fold geometrical designs on all its facades.

The geometrical compostion on one of the facades of the Gunbad-i Qabus in Iran. The same composition showing the invisible grid of polygons that lie underneath the composition   The three polygons that are used to create the composition on one of the facades on the Qunbad-i Qabus