# Geometric Design: Tenfold Star in a Rectangle

For our 15th and last lesson in this series, I chose a motif with a complex construction that requires you to pay close attention to join the correct points. The central "star" crops up often in Islamic geometry, but the number of its arms varies constantly, from six to more than 90 in some Moroccan designs. This one has ten arms, and will require us to divide the circle into 20.

## 1. Divide the Circle in Ten

### Step 1

Draw a circle on a horizontal line, and bisect it. Work big, as the final result will be entirely contained in the circle.

### Step 2

Returning the compass opening to the circle radius, move it to one of the side points and make two marks on the circle.

### Step 3

Join these marks to find point C on the diameter.

### Step 4

From C, set the compass to distance CA and find point D on the same diameter.

### Step 5

From A, set the compass to distance AD and mark two points on the circle. These are two of the ten points we're looking for, with A being the third.

### Step 6

Set the compass opening to OD, but place the point on B to mark two more points on the circle. We now have five of the ten points.

### Step 7

Without changing the compass opening, place the point on A to mark two more points.

### Step 8

Set the compass to the distance BD and mark two more points. B itself is the tenth point.

### Step 9

The circle divided in ten.

## 2. Divide the Circle in 20

### Step 1

We could repeat all of the above on the horizontal axis to find the next ten points, but there is a simpler way. Set the compass opening to the distance between A and the next point, and place the compass point as shown to mark two points.

### Step 2

From each of these two points, walk this distance around the circle. Just be careful not to mistakenly place the compass on one of the first ten points (although if you do, all that will happen is that you'll find you're marking over an existing point.)

### Step 3

The circle is now divided in 20, including all four cardinal points.

## 3. Prepare the Grid

### Step 1

Draw all the lines connecting diametrically opposite points. Careful: if the line doesn't go through the centre, you're joining the wrong pair of points.

### Step 2

Connect the following points to create a rectangle. This will contain the final pattern.

### Step 3

Connect the points to draw a diamond inside the rectangle.

### Step 4

Place your ruler between the points indicated to make the mark shown below. Double-check that your result matches the figure.

### Step 5

With the compass point in the centre and the opening set to the mark just made, draw a circle.

### Step 6

With the same compass opening, draw four more circles, on each of the rectangle's corners.

### Step 7

Back to the centre, with the opening set to the point on the diamond shown here, draw a larger circle.

## 4. Place the Lines

### Step 1

We now have several sets of line to add, so I'm zooming in. We are working on the smallest central circle. Start by adding two vertical lines: they join the points that are directly on either side of the top and bottom points, these being already joined by a vertical.

### Step 2

In the same way, join points to draw lines on either side of the diagonals highlighted in blue.

### Step 3

Repeat step 2 with these next two lines in blue.

### Step 4

Now draw the lines that connect the points circled in blue. The lines should go on until they hit the sides of the rectangle.

### Step 5

Draw verticals between the following points, but this time do extend the lines beyond the rectangle, as they will be needed later.

### Step 6

Add the following lines, bounded by the rectangle's sides. Note that their inward end is the point where the circle cuts the rectangle.

### Step 7

Add four more line segments. Again note their inward end.

### Step 8

Draw the following lines, which connect on the central axis of the rectangle; you only need to draw the parts that are inside it.

### Step 9

All lines are in place.

## 5. Finish Off

### Step 1

We'll start by inking the central, ten-fold shape. Start with the following lines. Note that they end at the straight sides of the decagon inscribed in the circle, *not* at the circle itself.

### Step 2

Ink the crossing lines that define the ends of six of the *safts* (for a refresher on what a *saft* is, see Eight-fold Rosette Pattern, step 11).

### Step 3

Ink the last four, which meet at a point that's on the rectangle.

### Step 4

Now ink the following sets of lines, which are continuous from one* saft*-end to its opposite.

### Step 5

Repeat with the following.

### Step 6

Finally, ink these last four segments.

### Step 7

The finished pattern.

### Step 8

Colour to taste!

## Awesome Work, You're Done!

A complex tiling pattern is achieved by drawing several of the above side by side. Or if you really feel up to a challenge, you can turn it into a weave, as we learned to do in Knots and Weaves.

This completes our tutorial series on geometric designs! I hope you enjoyed rediscovering this age-old, universal art that requires nothing more complex than a compass, and that you felt a taste of the tranquility that is brought about by unhurried constructions on paper.

Geometric patterns such as we have learned to make are today used as a therapeutic activity, and have the ability to keep children still and focused as they get completely absorbed in the magic of it. And, above all, they are beautiful in a timeless way, with infinite applications for the creative mind.

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