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 approximatively 3.24 % larger than the width of the regular octagon:
\(\cos(\pi/8)\). In addition, the paper proposes a family of equilateral small
\(s\ge 4\), whose widths are within
\(O(1/n^4)\) of the maximal width.
Paru en août 2021 , 14 pages