Pentagons in Hexagons

The following pictures show n unit pentagons packed inside the smallest known hexagon (with side s).

1.
           2.
           3.
s = 0.92905+
Trivial.
  		s = 1.53879+
Trivial.
  		s = 1.73240+
Trivial.
 

4.
           5.
           6.
s = 1.97666+
Found by Ethan Riddle
in May 2026. 		s = 2.21822+
Found by Nicolas Campailla
in May 2026. 		s = 2.32293+
Found by Bhavithran Ananthan
in July 2026.

7.
           8.
           9.
s = (2√5–1+√(15–6√5))/2
s = 2.36527+
Found by Nicolas Campailla
in May 2026. 		s = 2.71922+
Found by Bhavithran Ananthan
in July 2026. 		s = 2.86967+
Found by Nicolas Campailla
in May 2026.

10.
           11.
           12.
s = 2.93664+
Found by Bhavithran Ananthan
in July 2026. 		s = 3.16125+
Found by Jonathan Viquerat
in May 2026. 		s = 3.21458+
Found by Jake Loyd
in June 2026.

13.
           14.
           15.
s = 3.40902+
Found by Nicolas Campailla
in August 2026. 		s = 3.46639+
Found by Joshua Wolk
in September 2026. 		s = 3.63499+
Found by Jake Loyd
in June 2026.

16.
           17.
           18.
s = 3.69895+
Found by Nicolas Campailla
in August 2026. 		s = 3.75773+
Found by Aapo Lipponen
in October 2026. 		s = 3.84479+
Found by Jake Loyd
in June 2026.

19.
           20.
           21.
s = 3.88271+
Found by Jonathan Viquerat
in August 2026. 		s = 4.14048+
Found by Jake Loyd
in June 2026. 		s = 4.24002+
Found by Beppe Björkland
in October 2026.

22.
           23.
           24.
s = 4.32443+
Found by Jake Loyd
in June 2026. 		s = 4.39703+
Found by Jake Loyd
in June 2026. 		s = 4.46360+
Found by Jake Loyd
in June 2026.

25.
           26.
           27.
s = 4.57861+
Found by Jake Loyd
in June 2026. 		s = 4.66000+
Found by Yanis Gomes
in October 2026. 		s = 4.71691+
Found by Joshua Wolk in September 2026.

28.
           29.
           30.
s = 4.84289+
Found by Yanis Gomes
in October 2026. 		s = 4.90986+
Found by Joshua Wolk
in September 2026. 		s = 4.96247+
Found by Joshua Wolk
in September 2026.

31.
           32.
           33.
s = 5.08831+
Found by Joshua Wolk
in September 2026. 		s = 5.14524+
Found by Joshua Wolk
in September 2026. 		s = 5.18365+
Found by Yanis Gomes
in October 2026.

34.
           35.
           36.
s = 5.24898+
Found by Joshua Wolk
in September 2026. 		s = 5.28817+
Found by Joshua Wolk
in September 2026. 		s = 5.35061+
Found by Joshua Wolk
in September 2026.

37.
           38.
           39.
s = 5.37864+
Found by Joshua Wolk
in September 2026. 		s = 5.57198+
Found by Beppe Björkland
in October 2026. 		s = 5.64873+
Found by Joshua Wolk
in September 2026.

40.
           41.
           42.
s = 5.71256+
Found by Joshua Wolk
in September 2026. 		s = 5.77980+
Found by Yanis Gomes
in October 2026. 		s = 5.82725+
Found by Joshua Wolk
in September 2026.

43.
           44.
           45.
s = 5.88889+
Found by Yanis Gomes
in October 2026. 		s = 5.92846+
Found by Joshua Wolk
in September 2026. 		s = 6.03333+
Found by Joshua Wolk
in September 2026.

46.
           47.
           48.
s = 6.07857+
Found by Joshua Wolk
in September 2026. 		s = 6.12896+
Found by Joshua Wolk
in September 2026. 		s = 6.16749+
Found by Yanis Gomes
in October 2026.

49.
           50.
s = 6.29995+
Found by Yanis Gomes
in October 2026. 		s = 6.35105+
Found by Joshua Wolk
in September 2026.