The Eight and Four-Lozenge and Rhombus Knot
This article teaches how to draw an example of Iranian tilework designs using only an ungraduated straightedge and a compass. The design we intend to introduce is known the “eight and four-lozenge and rhombus” knot. (By straightedge, we mean a tool that only draws straight lines and is not used for measurement).
ُTiling
Tiling is an art that also has a practical aspect and is used to decorate walls or columns or ceilings and floors or even windows of buildings. The art of tiling has various types. The purpose of tiling is to cover a surface with geometric shapes that cover the entire surface without overlapping or leaving any empty space between them.
Of course, a real Euclidean plane is infinite, but any desired surface can be considered as part of a Euclidean plane.
One of the most important and famous types of tiling is “Gerehchini” – which means “knotting”-, which is also known as “Iranian-Islamic tiling” and has been used in post-Islamic Iranian architecture, in the decorations of mosques and houses of the great. This art reached its artistic peak during the Safavid (1501-1736 A.D.) period in Iran. There are many different types of knotting, each with its own beauty, and in this text we do not intend to introduce the exact details of this type of tiling.
One of the geometric and at the same time, entertaining aspects of the art of “Gerehchini” is drawing each of these shapes with only a ruler and compass.
Below, you can see the method of drawing one of these shapes, called the “eight-and-four-lobed and rhombus knot”:
Now, we need to draw four quarter-circles. The centers of these quarter-circles are the vertices of the large square, and their radius is equal to half the side length of the large square (Figure 9).
At this stage, we can draw the main part of the design. An eight-pointed figure is formed, with a four-lozenge at its center and four rhombuses next to the four-lozenge. You can see the main design with green lines in Figure 10.
Now, we can add fine details to this design. To do this, we again need to draw some construction lines with a pencil. First, we draw a small circle in the center of the square. The center of this circle is the square’s center of symmetry. This circle must also pass through the vertices of the rhombuses. Refer to Figure 11.
Complete the rest of the drawing based on Figure 12.
Now we can complete the rest of the design. We will again need a dark pencil or a pen. Note that by drawing the remainder of the design, we will actually create a smaller four-lozenge inside the main, large four-lozenge (Figure 13).
Now, we can expand our design (Figure 14).
