Triangles in Circles

The following pictures show n equilateral triangles packed inside a unit circle, so that the total sum of the sides of the triangles is as large as possible.

1.
           2.
           3.
Σ s = √3 = 1.73205+
Trivial.
  		Σ s = 4/√3 = 2.30940+
Trivial.
A continuum of solutions. 		Σ s = 3.18767+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 4.15470+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5
Trivial.
  		Σ s = 6
Trivial.
 

7.
           8.
           9.
Σ s = 6.15471+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 6.62452+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.00630+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 7.39853+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 7.77426+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 8.09500+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 8.53190+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 8.83315+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 9.25219+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 9.57822+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 9.93206+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 10.23592+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
Σ s = 10.53835+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 10.86683+
Found by Jonathan Viquerat
in June 2026.