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Design

Geometric Design: Tenfold Star in a Rectangle

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This post is part of a series called Geometric Design for Beginners.
Geometric Design: How to Draw a Flowery Tiling Pattern
Final product image
What You'll Be Creating

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.

Tenfold Star in a Rectangle step 1

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.

Tenfold Star in a Rectangle step 2

Step 3

Join these marks to find point C on the diameter.

Tenfold Star in a Rectangle step 3

Step 4

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

Tenfold Star in a Rectangle step 4

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.

Tenfold Star in a Rectangle step 5

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.

Tenfold Star in a Rectangle step 6

Step 7

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

Tenfold Star in a Rectangle step 7

Step 8

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

Tenfold Star in a Rectangle step 8

Step 9

The circle divided in ten.

Tenfold Star in a Rectangle step 9

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.

Tenfold Star in a Rectangle step 10

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.)

Tenfold Star in a Rectangle step 11

Step 3

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

Tenfold Star in a Rectangle step 12

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.

Tenfold Star in a Rectangle step 13

Step 2

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

Tenfold Star in a Rectangle step 14

Step 3

Connect the points to draw a diamond inside the rectangle.

Tenfold Star in a Rectangle step 15

Step 4

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

Tenfold Star in a Rectangle step 16

Step 5

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

Tenfold Star in a Rectangle step 17

Step 6

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

Tenfold Star in a Rectangle step 18

Step 7

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

Tenfold Star in a Rectangle step 19

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.

Tenfold Star in a Rectangle step 20

Step 2

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

Tenfold Star in a Rectangle step 21

Step 3

Repeat step 2 with these next two lines in blue.

Tenfold Star in a Rectangle step 22

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.

Tenfold Star in a Rectangle step 23

Step 5

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

Tenfold Star in a Rectangle step 24

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.

Tenfold Star in a Rectangle step 25

Step 7

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

Tenfold Star in a Rectangle step 26

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.

Tenfold Star in a Rectangle step 27

Step 9

All lines are in place.

Tenfold Star in a Rectangle step 28

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.

Tenfold Star in a Rectangle step 29

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).

Tenfold Star in a Rectangle step 30

Step 3

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

Tenfold Star in a Rectangle step 31

Step 4

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

Tenfold Star in a Rectangle step 32

Step  5

Repeat with the following.

Tenfold Star in a Rectangle step 33

Step 6

Finally, ink these last four segments.

Tenfold Star in a Rectangle step 34

Step 7

The finished pattern.

Tenfold Star in a Rectangle finished

Step 8

Colour to taste!

Tenfold Star in a Rectangle coloured

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.

Tenfold Star in a Rectangle tiled

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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