Nonagon

The unconstructible regular Polygon with nine sides and Schläfli Symbol $\{9\}$. It is sometimes called an Enneagon.

Although the regular nonagon is not a Constructible Polygon, Dixon (1991) gives several close approximations. While the Angle subtended by a side is $360^\circ/9=40^\circ$, Dixon gives constructions containing angles of $\tan^{-1}(5/6)\approx 39.805571^\circ$ and $2\tan^{-1}((\sqrt{3}-1)/2)\approx 40.207819^\circ$.

Madachy (1979) illustrates how to construct a nonagon by folding and knotting a strip of paper.

See also Nonagram, Trigonometry Values Pi/9

References

Dixon, R. Mathographics. New York: Dover, pp. 40-44, 1991.

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 60-61, 1979.