5-fold Geometry Sign My Guestbook

design composed of interlinking shape 'h' from the list of shapes below

Designs based on shapes derived from a 5-fold division of a circle are different from designs that derive from a 4-fold or 6-fold division. The main difference is that 4 or 6 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-fold shape like a hexagon. This is not the case with shapes that are generated with a 5 or 10-fold division of a circle. the series of designs that can be seen below shows  such shapes. When creating a design with 5 or 10-fold shapes, it becomes necessary to use different techniques than you would with 4 or 6 fold geometry.

Roger Penrose gave his name to a method of tiling in 5-fold geometrical design. He described two shapes, a kite and a dart, these two shapes can be combined to allow tiling in 5-fold geometry. The kite and dart shapes have appeared in islamic geometrical design for centuries. a kite shape from the Gur Emir Mausoleum in Samarkand, Uzbekistan (1404)	The kite shape corrpesponds to shape 'b' and the dart shape corresponds to shape 't' from the list of shapes below

All 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 list of images to the right of the composition and have a black border & coloured background.

a pentagram inside the circle

another pentagram inside the circle

a ten-pointed star inside the circle

the lines necessary for the creation of the below shapes

Can you recognize the shapes that have been used in this star design from Isfahan?

a b c d e f g h i j k l m n o p q r s t u

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 real expert in this field is Jay Bonner, check out his website here: www.bonner-design.com

the geometrical designs as it appears on the facades of the tomb tower	the geometrical design showing the construction grid used	Gunbad-i Qabud tomb tower in Maragha, Iran (1197)
	Three different tiles are used to make the design on the Qunbad-i Qabud tombtower. A few hundred years later the same technique is used and has been made visible in a niche of the entranceportal to the funerary complex of sultan Hasan. Instead of using a ten-pointed star design, an eight-pointed star design has been used instead.	Funerary Complex of sultan al-Nasir Hasan in Cairo, Egypt ( 1356-63)

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