Given n unit length edges that cannot intersect except at endpoints, what configuration will maximize the product of the area of the polygons produced? The best known configurations (with area A) are shown.

3 A = √3/4 A = .43301+ Trivial.

4 A = 1 Trivial.

5 A = 5√(1+2/√5)/4 A = 1.72047+ Trivial.

6 A = 3√3/2 A = 2.59807+ Trivial.

7 A = 7cot(π/7)/4 A = 3.63391+ Trivial.

8 A = 2+2√2 A = 4.82842+ Trivial.

9 A = 9cot(π/9)/4 A = 6.18182+ Trivial.

10 A = 5√(5+2√5)/2 A = 7.69420+ Trivial.

11 A = 11cot(π/11)/4 A = 9.36563+ Trivial.

12 A = (89+26√13)/16 = 11.42152+ Found by Erich Friedman in July 2026.

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13 A = 15.64315+ Found by Maurizio Morandi in July 2026.

14 A = 21.27924+ Found by Maurizio Morandi in July 2026.

15 A = 28.57572+ Found by Maurizio Morandi in July 2026.

16 A = 37.47861+ Found by Maurizio Morandi in July 2026.

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17 A = 48.59712+ Found by Maurizio Morandi in August 2026.

18 A = 60.99397+ Found by Maurizio Morandi in August 2026.

19 A = 82.40152+ Found by Maurizio Morandi in August 2026.

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20 A = 121.12562+ Found by Maurizio Morandi in August 2026.

21 A = 171.57295+ Found by Maurizio Morandi in August 2026.

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