Pentagons in Pentagons

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

1.-2.
           3.
           4.
Σ s = 1
Trivial.
  		Σ s = 1.38672+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 1.70075+
Found by Jonathan Viquerat
in July 2026.

5.
           6.
           7.
Σ s = 1.93875+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 9–3√5 = 2.29180+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 2.42629+
Found by Jonathan Viquerat
in July 2026.

8.
           9.
           10.
Σ s = 2.56572+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 2.70998+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 2.85146+
Found by Jonathan Viquerat
in July 2026.

11.
           12.
           13.
Σ s = 3
Found by Jonathan Viquerat
in July 2026. 		Σ s = 3.14733+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 3.30108+
Found by Jonathan Viquerat
in July 2026.

14.
           15.
           16.
Σ s = 3.45203+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 3.59224+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 3.72987+
Found by Jonathan Viquerat
in July 2026.

17.
           18.
           19.
Σ s = 3.82697+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 3.93702+
Found by Jonathan Viquerat
in July 2026. 		Σ s = 4.02422+
Found by Jonathan Viquerat
in July 2026.

20.
Σ s = 4.12565+
Found by Jonathan Viquerat
in July 2026.