A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with
\(n=2^s\) sides are unknown when
\(s \ge 4\). In this paper, we construct a family of convex small
\(s\ge 4\), and show that their perimeters and their widths are within
\(O(1/n^5)\) of the maximal perimeter and the maximal width, respectively. From this result, it follows that Mossinghoff's conjecture on the diameter graph of a convex small
\(2^s\)-gon with maximal perimeter is not true when
\(s \ge 4\).
Paru en mai 2021 , 12 pages