A Construction Site

The original pattern for this design (figure 1) came from page 112 of Geometric Concepts in Islamic Art by Issam El-Said and Ayse Parman. It is one of very few in the book which appear as a whole unit rather than part of a continuous space filling design.
The pattern is a complex piece, the construction for which is not easy to represent, but for readers with the determination to understand it, I have shown the method of building the master grid in Figures 2 - 5.
In Figure 2 I have shown the containing circle divided into 12 equal segments. The diameters cut the circumference at vertices. Connect vertices 1-4-7-10, 2-5-8-11 and 3-6-9-12 such that 3 (red)squares are produced. Use the vertices of the 12 sided polygon created by the lines of the red squares to repeat the process to generate 3 more (purple) squares. Repeat the process once again to generate the 3 (blue) squares.
In Figure 3 I have extended the edges of the squares to the circumference of the outer circle and drawn in a further 12 diagonals such that each bisects two of the adjacent diagonals in Figure 2. The new lines are in purple.
The lines introduced in Figure 4 are drawn through the points where the extensions to the blue squares in Figure 1 intersect with the purple squares to produce parallel pairs of lines either side of each digonal in Figure 1. The last set of construction lines defines the position of the inner and outer perimeter to the final hexagonal pattern. They are the lines drawn through the points where the extensions to the purple squares intersect one of the newly drawn parallel pairs.
It is then simply a matter of picking out the pattern from this maze of lines as shown in Figure 5

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