Tight bounds on the maximal perimeter of convex equilateral small polygons

Abstract

A small polygon is a polygon that has diameter one. The maximal perimeter of a convex equilateral small polygon with $n=2^s$ sides is not known when $s\ge 4$. In this paper, we construct a family of convex equilateral small $n$-gons, $n=2^s$ and $s\ge 4$, and show that their perimeters are within $O(1/n^4)$ of the maximal perimeter and exceed the previously best known values from the literature. In particular, for the first open case $n=16$, our result proves that Mossinghoff's equilateral hexadecagon is suboptimal.

References in corpus (3)

• Tight bounds on the maximal perimeter and the maximal width of convex small polygons
• Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons
• The equilateral small octagon of maximal width

Cited by in corpus (2)

• Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons
• The equilateral small octagon of maximal width