Pentagons in Octagons

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

1.
           2.
           3.
s = 0.69746+
Trivial.
  		s = 1.17774+
Trivial.
  		s = 1.28954+
Found by Nicolas Campailla
in May 2026.

4.
           5.
           6.
s = 1.42986+
Trivial.
  		s = 1.61756+
Found by Nicolas Campailla
in May 2026. 		s = 1.78003+
Found by Nicolas Campailla
in May 2026.

7.
           8.
           9.
s = 1.82343+
Found by Timo Berthold et al
in May 2026. 		s = 1.95989+
Found by Nicolas Campailla
in May 2026. 		s = (√5+√(5+√5))/√(10–2√5)
s = 2.09517+
Found by Nicolas Campailla
in May 2026.

10.
           11.
           12.
s = 2.21135+
Found by Timo Berthold et al
in May 2026. 		s = 2.33111+
Found by Timo Berthold et al
in May 2026. 		s = 2.39327+
Found by Timo Berthold et al
in May 2026.

13.
           14.
           15.
s = 2.49776+
Found by Jake Loyd
in June 2026. 		s = 2.56564+
Found by Jake Loyd
in June 2026. 		s = 2.68122+
Found by Yanis Gomes
in October 2026.

16.
           17.
           18.
s = 2.75249+
Found by Jake Loyd
in June 2026. 		s = 2.81043+
Found by Jake Loyd
in June 2026. 		s = 2.89321+
Found by Jake Loyd
in June 2026.

19.
           20.
           21.
s = 2.95527+
Found by Jake Loyd
in June 2026. 		s = 3.04679+
Found by Jake Loyd
in June 2026. 		s = 3.11874+
Found by Jake Loyd
in June 2026.

22.
           23.
           24.
s = 3.19143+
Found by Aapo Lipponen
in October 2026. 		s = 3.25129+
Found by Jake Loyd
in June 2026. 		s = 3.28718+
Found by Jake Loyd
in June 2026.

25.
           26.
           27.
s = 3.36617+
Found by Jake Loyd
in June 2026. 		s = 3.42775+
Found by Jake Loyd
in June 2026. 		s = 3.49923+
Found by Joshua Wolk
in September 2026.

28.
           29.
           30.
s = 3.55850+
Found by Yanis Gomes
in October 2026. 		s = 3.61707+
Found by Joshua Wolk
in September 2026. 		s = 3.66643+
Found by Joshua Wolk
in September 2026.

31.
           32.
           33.
s = 3.73978+
Found by Joshua Wolk
in September 2026. 		s = 3.78375+
Found by Joshua Wolk
in September 2026. 		s = 3.82191+
Found by Joshua Wolk
in September 2026.

34.
           35.
           36.
s = 3.90297+
Found by Joshua Wolk
in September 2026. 		s = 3.95494+
Found by Joshua Wolk
in September 2026. 		s = 4.00891+
Found by Joshua Wolk
in September 2026.

37.
           38.
           39.
s = 4.06615+
Found by Joshua Wolk
in September 2026. 		s = 4.12156+
Found by Yanis Gomes
in October 2026. 		s = 4.16997+
Found by Joshua Wolk
in September 2026.

40.
           41.
           42.
s = 4.22001+
Found by Yanis Gomes
in October 2026. 		s = 4.27019+
Found by Joshua Wolk
in September 2026. 		s = 4.31591+
Found by Joshua Wolk
in September 2026.

43.
           44.
           45.
s = 4.36015+
Found by Joshua Wolk
in September 2026. 		s = 4.41090+
Found by Joshua Wolk
in September 2026. 		s = 4.45494+
Found by Joshua Wolk
in September 2026.

46.
           47.
           48.
s = 4.50465+
Found by Joshua Wolk
in September 2026. 		s = 4.55550+
Found by Joshua Wolk
in September 2026. 		s = 4.59735+
Found by Joshua Wolk
in September 2026.

49.
           50.
s = 4.65207+
Found by Joshua Wolk
in September 2026. 		s = 4.69827+
Found by Joshua Wolk
in September 2026.