Papers › The equilateral small octagon of maximal width
The equilateral small octagon of maximal width
Christian Bingane, Charles Audet
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A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with n=2ˢ 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=2ˢ with s≥4, whose widths are within O(1/n⁴) of the maximal width.
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