FIVE FOLD GEOMETRY

 A ceramic tile panel for the Gur Emir.

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
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 pentagram inside a circle

the lines necessary for the creation of the below shapes. 
a variety of designs
the Qunbad-i Qabus tombtower in Iran

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

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


Islamic Architecture Series:
5. Islamic geometric designs
6. Geeks Rule: Quasicrystalline Patterns in Mediaeval Islamic Architecture


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