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Learn: Five Fold Geometry
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.
 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.
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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 geometri
cal
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. 
a pentagram inside 
another pentagram
inside a circle
a ten-pointed star 
the lines necessary
for
the creation of the below shapes. These shapes also
appear in the short video
