The equilateral small octagon of maximal width

Abstract

A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with $n=2^s$ vertices is not known when $s\ge 3$. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximately $3.24\%$ larger than the width of the regular octagon: $\cos (\pi /8)$. In addition, the paper proposes a family of equilateral small $n$-gons, for $n=2^s$ with $s\ge 4$, whose widths are within $O(1/n^4)$ of the maximal width.

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
• Tight bounds on the maximal perimeter of convex equilateral small polygons

Cited by in corpus (2)

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