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I have shown them because they are, perhaps, more the type of example with which we are familiar in our daily lives.
This standard and character of design is commonly found all over the Middle East.
While many of the designs illustrated here, including my attempts to deconstruct them, are based on two-dimensional designs, there are many examples of three-dimensional design work in the Islamic world.
Here to the side is the top of a fifteenth century wooden Egyptian that has been articulated with pendentives, a form of cantilever that is commonly used in masonry constructions, though here is more decorative than structural due to the inherent character of timber which has both compressive and tensile qualities which stone lacks.
These first four illustrations are of Islamic geometric patterns that have been executed on different materials, respectively silver, stone, leather and glazed mosaic, and are commonly considered representative of Islamic design.
While not demonstrating the wide variety of geometric treatments to be found in Islamic or Arab geometries, they are here to introduce something of the design character and materials that were used in decoration.
The rim of the dish is broken into nine, slightly unequal, elements inside which there are six stylised flowers hanging from the central motif which, itself, has nine points in its centre, but ten outer petals.
The first point to bear in mind is that there are three types of patterning common to the designs found in Islamic cultures: the latter of which contains the largest number of examples we are likely to come across, and is the area most commonly examined from the perspective of their mathematical bases. The first example, above, typifies the kind of design that comes to mind when thinking of Arabic geometric designs.
However, the example is not from Arabia but was made in France and is one of a pair of silver door panels, shown above on its side.
Note the strong difference in treatment and effect between the simple cursive running design on the framing and that of the main geometrically laid out panels.
There is more written about the basic geometries behind Islamic patterns on both this page and the next page which illustrate some of the constructions behind basic Islamic designs.
Incidentally, all of these first three examples are based on eight point geometry, a common and relatively easy framework to establish.