Edited by Jane Rosemarin
A simple method for folding and one-cutting a very nearly exact regular heptagon from a square. Diagrams by Marc Kirschenbaum. See PDF diagrams.

The equilateral triangle, the square, and the regular pentagon, hexagon and octagon are by far the most popular starting shapes used in origami design.

In this article, we describe a simple method for folding and one-cutting from a square a regular heptagon that may be considered exact for most practical purposes.

The folding and cutting steps for making the heptagon are shown below.

A straightforward geometric-trigonometric analysis shows that the angles between the lines from the center to two successive vertices of the heptagon in step 17 differ at most by around a sixth of a degree.

Instructions for folding the heptagon. Step 17 is referenced in the text above.

We hope that this method will encourage more origami design efforts based on the regular heptagon.

Editor’s note: In the coming weeks, we will publish diagrams for three of Arnold Tubis’s heptagonal brooches.