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 = 2.29179+
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 = 2.85147+
Found by Pedro Martins
in October 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 = 3.82787+
Found by Joost de Winter
in October 2026. 		Σ s = 3.94005+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 4.03601+
Found by Pedro Martins
in July 2026.

20.
           21.
           22.
Σ s = 4.13423+
Found by Jonathan Viquerat
in October 2026. 		Σ s = 4.23476+
Found by Joost de Winter
in October 2026. 		Σ s = 4.33704+
Found by Pedro Martins
in October 2026.

23.
           24.
           25.
Σ s = 4.44311+
Found by Pedro Martins
in October 2026. 		Σ s = 4.54060+
Found by Pedro Martins
in October 2026. 		Σ s = 4.64729+
Found by Pedro Martins
in October 2026.

26.
           27.
           28.
Σ s = 4.74665+
Found by Pedro Martins
in October 2026. 		Σ s = 4.84886+
Found by Pedro Martins
in October 2026. 		Σ s = 4.94920+
Found by Pedro Martins
in October 2026.

29.
           30.
           31.
Σ s = 5.04424+
Found by Pedro Martins
in October 2026. 		Σ s = 5.12855+
Found by Joost de Winter
in October 2026. 		Σ s = 5.21299+
Found by Pedro Martins
in October 2026.

32.
           33.
           34.
Σ s = 5.28858+
Found by Pedro Martins
in October 2026. 		Σ s = 5.36511+
Found by Pedro Martins
in October 2026. 		Σ s = 5.44057+
Found by Pedro Martins
in October 2026.

35.
           36.
           37.
Σ s = 5.52511+
Found by Pedro Martins
in October 2026. 		Σ s = 5.60148+
Found by Pedro Martins
in October 2026. 		Σ s = 5.67730+
Found by Pedro Martins
in October 2026.

38.
           39.
           40.
Σ s = 5.74943+
Found by Pedro Martins
in October 2026. 		Σ s = 5.82688+
Found by Pedro Martins
in October 2026. 		Σ s = 5.90709+
Found by Pedro Martins
in October 2026.

41.
           42.
           43.
Σ s = 5.98566+
Found by Pedro Martins
in October 2026. 		Σ s = 6.06142+
Found by Pedro Martins
in October 2026. 		Σ s = 6.14198+
Found by Pedro Martins
in October 2026.

44.
           45.
           46.
Σ s = 6.21317+
Found by Pedro Martins
in October 2026. 		Σ s = 6.29403+
Found by Pedro Martins
in October 2026. 		Σ s = 6.36504+
Found by Pedro Martins
in October 2026.

47.
           48.
           49.
Σ s = 6.43540+
Found by Pedro Martins
in October 2026. 		Σ s = 6.50530+
Found by Pedro Martins
in October 2026. 		Σ s = 6.56935+
Found by Pedro Martins
in October 2026.

50.
Σ s = 6.63069+
Found by Pedro Martins
in October 2026.