Islamic Art - Introduction to Sixfold Symmetry Shapes

Hi friends!

Having seen the four-fold symmetry shapes, let's now look at six-fold symmetry as
a starting point for drawing a pattern.

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Let's start by drawing a circle with the compass.

Then, with the same compass opening, place the compass needle anywhere on the circumference and draw a semicircle inwards...

...to obtain two intersection points on the main circle as shown below.

Now increase the compass opening until it reaches the distance between those intersection points.

Then rotate it until it intersects the main circle on the opposite side, thus marking a third crossing point.

As you can see, we could draw segments that join these three points and we would obtain the shape of an equilateral triangle, but we will leave that for later.
At this stage, we have divided the circle into three equal parts.

By drawing a segment that starts from one of the three intersection points, crossing the central point of the circle until cutting the circumference on the opposite side, we obtain a new intersection point between the other two.

Repeating this process for the other points we obtain the division of the circle into six equal parts.

By joining the points we can draw a regular polygon with six sides called a hexagon.

Or, by joining three opposite points we get an equilateral triangle, and then repeating this with the intermediate points we get another triangle in the opposite direction. Or... if you want, we could say that we have a hexagon surrounded by six triangles.

So far we have divided the circle into six equal parts, now we are going to divide it into twelve equal parts. To do this we'll draw a segment that passes through the intersection points between the triangles drawn, with the condition that this segment passes through the central point of the circle as shown below.

Repeating this process the necessary three times we will obtain the division in twelve.

By drawing the corresponding triangles we obtain this first pattern.

By joining the twelve externe points to draw a regular polygon of twelve faces we make the pattern a bit more interesting.

Even more so when dividing the central shape.

Outlining the pattern, using all these helplines...

We finished by colouring the pattern.

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I wish you a very nice day!

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