Octagons in Octagons

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

1.
           2.
           3.
s = 1
Trivial.
  		s = 2
Trivial.
  		s = 5–2√2 = 2.17157+
Found by Ignacio Vallejo
in March 2026.

4.
           5.
           6.
s = √(5+1/√2) = 2.38895+
Found by Ignacio Vallejo
in March 2026. 		s = 2+1/√2 = 2.70710+
Found by Ignacio Vallejo
in March 2026. 		s = 2.98894+
Found by Nicolas Campailla
in May 2026.

7.
           8.
           9.
s = 3
Trivial.
  		s = 3.27524+
Found by Grant Mowry
in May 2026. 		s = 2+√2 = 3.41421+
Found by Ignacio Vallejo
in March 2026.

10.
           11.
           12.
s = 3+1/√2 = 3.70710+
Found by Ignacio Vallejo
in March 2026. 		s = 3.93256+
Found by Timo Berthold et al
in May 2026. 		s = 4
Trivial.
 

13.
           14.
           15.
s = 7–2√2 = 4.17157+
Found by Ignacio Vallejo
in March 2026. 		s = 4.28135+
Found by Timo Berthold et al
in May 2026. 		s = 4.45584+
Found by Timo Berthold et al
in May 2026.

16.
           17.
           18.
s = 4.59803+
Found by Timo Berthold et al
in May 2026. 		s = 4.75688+
Found by Joshua Wolk
in September 2026. 		s = 4.85681+
Found by Timo Berthold et al
in May 2026.

19.
           20.
           21.
s = 4.93550+
Found by Timo Berthold et al
in May 2026. 		s = 5.06727+
Found by Timo Berthold et al
in May 2026. 		s = 5.19695+
Found by Timo Berthold et al
in May 2026.

22.
           23.
           24.
s = 5.35686+
Found by Bhavithran Ananthan
in July 2026. 		s = 4+√2 = 5.41421+
Found by Bhavithran Ananthan
in July 2026. 		s = 5.55414+
Found by Bhavithran Ananthan
in July 2026.

25.
           26.
           27.
s = 5.65393+
Found by Joshua Wolk
in September 2026. 		s = 5.73828+
Found by Bhavithran Ananthan
in July 2026. 		s = 5.81167+
Found by Bhavithran Ananthan
in July 2026.

28.
           29.
           30.
s = 3+2√2 = 5.82842+
Found by Ignacio Vallejo
in March 2026. 		s = 6.05648+
Found by Joshua Wolk
in September 2026. 		s = 6.15301+
Found by Joshua Wolk
in September 2026.

31.
           32.
           33.
s = 6.26490+
Found by Joshua Wolk
in September 2026. 		s = 6.36580+
Found by Joshua Wolk
in September 2026. 		s = 6.46918+
Found by Joshua Wolk
in September 2026.

34.
           35.
           36.
s = 6.56752+
Found by Joshua Wolk
in September 2026. 		s = 6.63513+
Found by Joshua Wolk
in September 2026. 		s = 6.72553+
Found by Joshua Wolk
in September 2026.

37.
           38.
           39.
s = 6.79921+
Found by Joshua Wolk
in September 2026. 		s = 6.90292+
Found by Joshua Wolk
in September 2026. 		s = 6.98405+
Found by Joshua Wolk
in September 2026.

40.
           41.
           42.
s = 7.09331+
Found by Joshua Wolk
in September 2026. 		s = 7.17346+
Found by Joshua Wolk
in September 2026. 		s = 7.26769+
Found by Joshua Wolk
in September 2026.

43.
           44.
           45.
s = 7.34966+
Found by Joshua Wolk
in September 2026. 		s = 7.41769+
Found by Joshua Wolk
in September 2026. 		s = 7.50202+
Found by Joshua Wolk
in September 2026.

46.
           47.
           48.
s = 7.56292+
Found by Joshua Wolk
in September 2026. 		s = 7.64268+
Found by Joshua Wolk
in September 2026. 		s = 7.72465+
Found by Joshua Wolk
in September 2026.

49.
           50.
s = 7.77849+
Found by Joshua Wolk
in September 2026. 		s = 7.82723+
Found by Joshua Wolk
in September 2026.