Circles in Pentagons

The following pictures show n circles packed inside a unit pentagon, so that the total sum of the radii of the circles is as large as possible.

1.
           2.
           3.
Σ s = cot(π/5)/2 = .68819+
Trivial.
  		Σ s = .76085+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.03457+
Found by Jonathan Viquerat
in June 2026.

4.
           5.
           6.
Σ s = 1.25099+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 5/(2tan(π/5)+2) = 1.44799+
Found by Jonathan Viquerat
in June 2026. 		Σ s = (4+csc(π/5))/(2tan(π/5)+2) = 1.65107+
Found by Jonathan Viquerat
in June 2026.

7.
           8.
           9.
Σ s = 1.74099+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.85250+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 1.95668+
Found by Jonathan Viquerat
in June 2026.

10.
           11.
           12.
Σ s = 2.06920+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.20261+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.29901+
Found by Jonathan Viquerat
in June 2026.

13.
           14.
           15.
Σ s = 2.40969+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.51439+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.61251+
Found by Jonathan Viquerat
in June 2026.

16.
           17.
           18.
Σ s = 2.72429+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.78356+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 2.85730+
Found by Jonathan Viquerat
in June 2026.

19.
           20.
Σ s = 2.93757+
Found by Jonathan Viquerat
in June 2026. 		Σ s = 3.01869+
Found by Jonathan Viquerat
in June 2026.