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