Islamic Geometry: Six-Fold Hammerhead Pattern

In August, thanks to an invitation my pal, Nirja, I started learning Islamic Geometry. We’ve been taking free classes on Wednesday mornings with the Prince Foundation School of Traditional Arts and supplementing our bi-weekly classes with all the youtube lessons we can find.

I’ve spent the past week figuring out how to translate my ruler-and-compass drawings to a digital format so that I can keep track of all the designs I’ve learned. Up first: this six-fold hammerhead pattern that I learned during my first class back in August.

It shows up in Syria and again – a few years later – in Spain.

Left: El Alcázar, Sevilla, 13th-15th centuries, Right: Madrassa al-Zahiriye, Aleppo, 1217

1. Six-fold flower. Start with a horizon line and mother circle. Add a circle of the same radius at the east and west points, then four more circles of the same radius at the four intersections of the mother circle and east and west circles.

2. Intersections. Add three meridian lines that bisect the drawing vertically and diagonally. The lines all go through the larger petals formed by the circle intersections. The mother circle has now been separated into twelve equal arcs by these three lines and the tips of the smaller petals formed by the circle intersections.

3. Hexagons. Draw two overlapping hexagons – one static and one dynamic – using the 12 points that divide the circle.

4. Numbers. Number each point where the two hexagons intersect. You can also think of this as numbering the arcs. Be careful not to number the points of the hexagons.

5. Hammerheads. Connect the following points: 1-10, 2-5, 3-12, 4-7, 6-9, 8-11.

6. Star. Draw three sets of parallel lines that connect where the hammerhead lines (green) intersect with the small petal lines (gray).

Note: A circle (orange) with a radius from the corner of a hexagon to the point where the hexagons meet is the same size as a circle with a radius from the center of the mother circle to the point of the star.

7. Finish. Trace the final lines. You can might see them as a star surrounded by six hammerheads. Or as six interlocking pentagons.

Now that you’re here, the possibilities are endless. You can tile the patterns in at least two ways. I tend to think the tiling on the left is more intriguing since it creates more new polygons (triangles and diamonds) and some interesting larger kites and rectangles.

This patterns is one of those magical ones that can be filled in with just two colors. You can arrange seven tiles to make a snowflake.

If colors are more your thing, you can go wild and take advantage of the pattern’s six-foldness to make a color wheel.

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