Reinhardt's Maximum-Perimeter Polygon Problem for n=16, 32, and 64

Jizhou Guo, Yitao Luo

A convex polygon is called small if its diameter is at most one. Reinhardt proved the universal perimeter bound $\mathrm{perim}(P)\le U_n:=2n\sin (\pi /(2n))$, and the bound is a…