The equilateral small octagon of maximal width

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 ≥ 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( π/ 8) . In addition, the paper proposes a family of equilateral small n -gons, for n = 2 s with s ≥ 4 , whose widths are within O (1 /n 4 ) of the maximal width.

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