An Isodiametric Problem for Equilateral Polygons

The maximal perimeter of an equilateral convex polygon with unit diameter and n = 2 m edges is not known when m ≥ 4. Using experimental methods, we construct improved polygons for m ≥ 4, and prove that the perimeters we obtain cannot be improved for large n by more than c/n 4, for a particular constant c