# Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons

A small polygon is a polygon of unit diameter. The maximal area of a small polygon with \$n=2m\$ vertices is not known when \$m \ge 7\$. In this paper, we construct, for each \$n=2m\$ and \$m\ge 3\$, a small \$n\$-gon whose area is the maximal value of a one-variable function. We show that, for all even \$n\ge 6\$, the area obtained improves by \$O(1/n^5)\$ that of the best prior small \$n\$-gon constructed by Mossinghoff. In particular, for \$n=6\$, the small \$6\$-gon constructed has maximal area.

## Citation

Christian Bingane. Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons. Discrete & Computational Geometry, 2021.