In this collection, I have chosen a number of images that feature patterns and compositions that are based on a sixfold division of a circle. What this means in practical design terms is that these patterns can be considered to have same source of origin: a circle divided into six equal sections. Dividing a circle in this way yields intersections that can be used to create hundreds of different patterns and compositions.

The vast majority of patterns and compositions that can be found in Islamic art and architecture, fall into one of three categories:

1. Fourfold: these are patterns that can be based on the division of a circle into four equal sections.
   
2. Fivefold: these are patterns that can be based on the division of a circle into five equal sections.
   
3. Sixfold: these are patterns that can be based on the division of a circle into four equal sections.
   

Craftsmen across the centuries in the Islamic world made geometric designs with a pair of compasses and a ruler. By drawing circles and lines they made their patterns. The essential design choice that determined which pattern was created begins with: which intersections of lines and circles to connect with a straight line. Which lines the craftsmen chose and, after that, which segment of this line would remain visible in the final chapter, determined the visual end result. 

This design method explains:

• the enormous diversity of Islamic geometric patterns
  
• why certain patterns can be found in different parts of the Islamic world, often with a period of many centuries between appearances of the pattern.
  

What is so special about sixfold Islamic geometric design is that there is such a great variety of patterns. Of the main three ‘geometric families,’ the sixfold geometric design probably encompasses the greatest number of different patterns. I hope that this collection shows some of that variety. Sixfold Islamic geometric design is also the most rewarding for those who come new to this design tradition, either 500 years ago or now. Sixfold geometric design allows for quite fast proficiency. In this context, it is interesting to note that when geometric patterns are used in miniature painting or Islamic metalwork, they are almost invariably always sixfold patterns.

All sixfold patterns can be tessellated in a grid of hexagons to make larger compositions. Often these patterns in hexagons would be combined with patterns in squares and patterns in triangles to create more complex and new compositions. 

An interesting feature of sixfold geometric patterns are those that feature twelve pointed star patterns. Quite a few of these can be found in these images. These star patterns can be designed by placing: 

• Four triangles inside a circle (4 x 3=12) or
  
• Three squares inside a circle (3x4=12) or
  
• Two hexagons inside a circle (2x6=12) 
  

For this reason, many twelve pointed star patterns can also be tessellated in a grid of squares. Over the centuries, craftsmen have exploited this versatility of twelve pointed star patterns to create a very wide range of compositions. It is an interesting exercise to try and identify how craftsmen have used these specific characteristics of twelve pointed star patterns to create their compositions.

Identifying and recognizing patterns and being able to see to which geometric category they belong, is a useful skill. It enables us to better understand what similarities they have, how patterns are sometimes related or have ‘evolved’ from another pattern. A good habit to develop is that of counting the number of ‘petal shapes’ or other identical shapes around a star. If it has 6 shapes, or 12 shapes, or 24 shapes, we can be sure it belongs to the category of sixfold geometric patterns. If, on the other hand, it has ten petal shapes around a star, we can be sure it belongs to the category of fivefold geometric patterns.  

The collection of images presented here is just a start. More will be added.