image of a rhombus inside a hexagon made with lines representing string
A “String Design” that We Can Draw: A Rhombus Inside a Hexagon
image of a circle with radius 10 and 6 tick marks

1. Set your compass to a radius of 10 centimeters, and draw a circle. Using your compass, make six equally spaced tick marks on the circumference, one radius (10 cm.) apart.
image of the circle with a hexagon drawn in it

2. Connect adjacent tick marks and draw a regular hexagon.
image of the hexagon

3. Erase the circle.
image of the hexagon with dots

4. On the two vertical sides of the hexagon, use your ruler to make dots one centimeter apart.
image of the hexagon with the first set of lines from the top

5. Using a ruler, carefully connect the top vertex of the hexagon with each of the dots on the left side, and again on the right side.
image of the hexagon with the second set of lines from the bottom

6. Now, again using a ruler, carefully connect the bottom vertex of the hexagon with each of the dots on the left side, and again on the right side.
image of the final result, the hexagon with a rhombus in the middle formed by strings

7. Carefully erase all the dots, and that’s it!

You may color it if you want.

Can you show that the white interior area in the figure is indeed a rhombus?
image of a triangle version
image of a square version
image of a pentagon version
image of a circle in a hexagon version

8. Some other “string designs” for you to draw: in a triangle, a square, a pentagon, and (again) in a hexagon.
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