The construction of the repeat unit (Figure 1) for this design was taken from page 79 of Geometric Concepts in Islamic Arts
by Issam El-Said & Ayse Parman
. This is an elegant method comprising of three concentric hexagonal stars (these are coloured blue for ease of identification. The red lines are for the construction and only the black lines of the unit are carried forward). The design could also be built by simply plotting the pattern on a triangular grid.
When the unit is repeatedly copied to a hexagonal grid (Figure 2) a new component emerges. This can be seen as three arrows radiating from a central point 120 degrees apart. In this form the arrows can be interpreted as the x,y and z coordinates of a spatial grid. The 3-dimensionality of this pattern can be further exposed by the addition of colour. Figure 3 is partially rendered to illustrate this.
Figure 4 shows the completed design which not only highlights the 3-D effect but displays the properties of an optical illusion - units in the pattern can be seen as building outwards or as cutting in (either way, this can be interpreted as a rudimentary stalactite ceiling).
There is a debate amongst Islamic scholars which is concerned with the 3-Dimensionality of Islamic patterns. This derives from the principle of aniconism which put simply means that religious artwork should not be representational on the grounds that this might encourage idolatry. As a consequence, Islamic art does not portray human or animal images, though stylised plants and flowers are permitted.
One line of argument in the debate goes further by saying that any representation of a solid object should be forbidden and that therefore the inherent 3-dimensionality of many patterns is denied. The use of a pattern such as is shown here is evidence to the contrary and in any case the principle is plainly not followed universally since Islamic architecture relies heavily on the 3-D interpretation of 2-D patterns as can be seen throughout the world.