Islamic Geometry: Six-Fold Model

If you’ve liked diving into Islamic geometric patterns, it’s helpful to take a step back and look at the underlying armature before going further. Today, we’re going to talk about how to construct six-fold divisions of a circle. It’s called six-fold because it has six mirror lines. To put it another way, if drawn on paper, this pattern could be folded six different ways to create symmetrical halves.

Six-fold patterns will often contain triangles, hexagons, and dodecagons, since 3, 6, and 12 are divisions and multiples of 6.

1. Like any other geometric drawing, start by making a horizon line. Set your compass to any radius and keep it set at that width for the rest of the drawing. Now place your compass anywhere along the line and draw a full circle. This circle is often called the “mother circle” since it gives birth to the rest of the forms in the drawing. You’ll notice that the horizon line divides the mother circle perfectly into two halves.

2. Place your compass on the westernmost point of the mother circle – where it intersects with the horizon line – and draw another full circle. Do the same on the easternmost point. The east and west circle kiss each other right at the center of the mother circle.

3. Now place your compass at any of the four points where the east and west circles intersect with the mother circle. Draw a full circle. Do the same at the other three points. You now have a rosette pattern with arcs that divide the mother circle into six equal parts.

4. Connect the six points of the six small “petals” formed by the intersecting circles inside the mother circle. You’ve made a hexagon. This kind of hexagon is called “static” since it has a base to sit on.

5. Draw two lines connecting the opposite points of the hexagon (the horizontal line is already there). You now have three mirror lines.

6. Alternatively, draw three lines through the six large petals outside the mother circle. You’ve made one vertical and two diagonal mirror lines.

7. Together, these mirror lines form the six folds of the mother circle. We can number them like a clock for easy reference.

8. Place your compass at one of the two points where the vertical line crosses mother circle and draw a circle. Do the same at the other point. You’ll notice that these circles cross the mother circle at points you’ve already found: 2, 4, 6, and 10. This kind of multiplicity of ways to get to the same information happens all the time in Islamic geometry.

9. Draw another hexagon connecting the even points on the clock. This kind of hexagon is called “dynamic” since it looks like it could topple over at any moment. Notice that when you formed both the static and dynamic hexagons, you went around the mother circle, skipping every other point.

10. From here, the mother circle is your oyster. You can draw an equilateral triangle… or two to create a “seal of Solomon” or “star of David”… or four to make a star. These triangles are made by going around the circle and skipping every three points.

11. You can also draw a square… or three to create a different type of star. The squares are made by going around the circle and skipping every two points.

12. If you connect each of the twelve points by skipping every four points, you get a star made out of one continuous line.

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