# Fold Heptagons from a Strip of Paper

You can create this regular heptagon and seven-pointed stars by folding one long strip of paper. The iterative process of folding creates the precise angles you need to make these figures without measurement. You start with a fold that is approximately right. As you continue folding, any error you had in the initial fold is quickly diminished.

## Materials

- A long strip of paper. You can use any width, but the paper should be about 40 times as long as it is wide to make all models. You can use paper from a roll of adding machine paper or cut strips of wrapping paper or newspaper and tape them together.

## Steps

- Start by making one crease near the end of your paper that is about 77° from the top edge of your paper. You do not need to measure this angle because, after performing steps 2 - 4 a few times, the angles will converge to the proper angles.

- Fold the top edge so it lies along this crease. Make a crease and open the paper.

- Fold the top edge a second time along the most recent crease. Open.

- Switch to the bottom edge. Fold it up along the latest crease. Open.

- Continue by repeating steps 2 - 4, alternating two folds from the top edge and one fold from the bottom edge. With each iteration, your angles will get closer to their appropriate values. So even if your first fold was inaccurate, subsequent folds will be better. Tear off a few of the first sets of triangles and work with the more accurate part of the strip to fold your models.

- To make the heptagon shown here, fold the strip of paper at longest crease first and then the next longer crease. Move to the next set of creases and repeat.

- To make a seven pointed star, fold the strip of paper at the long crease then the short one. Skip a set of creases then repeat. When you are done folding this sequence, you can fold the points of the star.

- To form another star, fold the strip of paper at the middle crease then the short one. Skip a set of creases and then repeat.

## Notes

- You can make an 11-gon and an 11-pointed star (both a {11/3} and {11,4}) by folding a strip of paper in the following order: Down from the top edge once, Up from the bottom edge 3 times, Down once, Up once, Down three times, and Up once. D-U3 D-U-D3-U. Another way to remember this is alternate folding down and folding up in a 1-3-1 sequence.

## References