GRIDS an invisible role in Islamic geometrical design.

A grid is an arrangement of shapes (or POLYGONS). Grids play a crucial but invisible role in Islamic geometrical design. They provide the underlying structure for a composition. They allow a designer to make the first creative steps when contemplating a new composition. 

Grids allow a designer to easily alter the size of a composition without having to redesign or recalculate. Grids allow a designer to use one grid design but still create a variety of diferent geometrical compositions. 
Having the ability to discover the underlying grid in an Islamic geometric composition is one of the most useful tools for those who want to understand Islamic geometric design.

This page gives an introduction on the role and siginificance of grids 
The number of different grids that can be designed is infinite and only limited by one's imagination. However, there are only three types of grids than be created by using identical shapes (or polygons as we will call them). These grids are:

a grid of squares

a grid of hexagons

a grid of triangels
These three shapes (or polygons) are the only ones that don't need the help of other shapes to create a grid. They can fill a surface by just repeating the same single shape ( or polygon)

a grid of octagons
an octagonal grid needs a square like this

a grid of octagons
We could take any of the other polygons and demonstrate that they cannot create a grid by just repeating the only polygonal shape. Howeve, we can use the example of an octagon (an eight-sided polygon). It cannot fill a surface by just repeating the same single shape: it leaves a small square- shaped gap. Only by introducing an extra polygon (in this case the little square), can we create a grid with octagons.It is not possible to create a grid with only octagons.

The basic principle of grids in Islamic geometrical design is that each polygon can have its own small geometrical design. When combined or repeated with different or identical polygons, it creates a larger composition. We can use the example of the hexagonal grid that can be seen above in blue above. This is a very common grid in geometrical design: some of the most familiar compositions are based on this hexagonal grid.

Dish with hexagonal grid (Kubachi ware - 17th c. Iran)
The design below top is a plasterpanel from the Alhambra in Spain. The image below in the middle has red lines superimposed indicating where the grid is 'beneath' the visible composition. The small image on the right is the geomtrical star design that when repeated, creates the composition as we can see in the Alhambra. The remarkable thing about using geometrical designs in polygons is that is often not obvious what the overall composition will look like just by looking at the individual design in one polygon.



The design inside the hexagon is simply repeated as many times as is necessary, All the lines and shapes in the design join up and fit together. Every Islamic geometrical design has an underlying grid. It is a good and enlightening exercise to discover what the underlying grid is when looking at an Islamic geometrical design.

The real creativity of grids comes alive when grids of varying polygons are created. For example, by just combining a triangle and a square a range of different grids can be created. The triangles and squares can contain their own mini geometrical designs and, when combined in different ways, as seen in the grid designs below, will create different geometrical compositions.

The same principle can be applied when combining triangles, squares and hexagons, or any other combination of polygons.

1. This grid design consists of triangles, squares and hexagons arranged in a particular way. There are other ways of arranging these three polygons, but this is one of the most simple ones.

2. We can give the three different polygons their own mini geometrical design. These designs are very basic and require only a few steps to create. Seen on their own, it is almost impossible to imagine how they can work together to create a geometrical composition. It is only when the polygons on the grid are actually given their mini designs that it becomes apparent how they work together to create something new.

 a new seven-sided polygon

3. Here we see exactly the same grid design as directly above except that the single colour polygons have now been filled in with the individual mini geometrical designs. It is now visible how the individual components in the three mini-designs all contribute to create a new seven-sided polygon that makes the final geometrical composition possible.

final composition

4. This final composition has exactly the same design as has been created by the arrangement of the design-filled polygons in the grid. The only difference is that the the grid has been made invisible. What is left is just a beautiful geometrical composition.

In geometrical designs in Islamic art and architecture the grid is not immediately visible although it can be seen if know how to look

a geometrical design

When we look at a geometrical design we do not seee the grid first: we see the geometrical composition first. So, to learn to understand how a composition is constructed, it is necessary to work backwards; to deconstruct a composition.

The image on the left is a stone inlay panel in the Great Mosque of Damascus. It is almost identical to the illustrations below. The only difference is the design of the big central star. In the panel in the Great Mosque it is a 12-pointed star. In the illustration below it is a 12-pointed star that also contains a 6-pointed star.

The first step in deconstructing a composition into its constituent elements (i.e. the polgyons), is to establish how many different elements there are. In the case of this composition, there are four polygons that create the grid: a triangle, a square, an unusual hexagon and a 12-sided polygon that contains the main star design. When comparing the panel and the illustration , it becomes clear that it is possible to change one mini-design in a polygon to create a different overal composition. This principle has allowed traditional Islamic craftsmen for centuries to be innovative and create new designs. They combined polygons in certain ways to create new compositions but they also change the mini-designs in polygons to create new compositions.


The four polygons with their mini designs that create the grid and the geometrical composition

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