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 = 4.75690+
Found by Timo Berthold et al
in May 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 = 5.35687+
Found by Timo Berthold et al
in May 2026. 		s = 5.41425+
Found by Timo Berthold et al
in May 2026. 		s = 5.55415+
Found by Timo Berthold et al
in May 2026.

25.
           26.
           27.
s = 5.65464+
Found by Timo Berthold et al
in May 2026. 		s = 5.73893+
Found by Timo Berthold et al
in May 2026. 		s = 5.81222+
Found by Timo Berthold et al
in May 2026.

28.
           29.
           30.
s = 3+2√2 = 5.82842+
Found by Ignacio Vallejo
in March 2026. 		s = 6.05746+
Found by Ignacio Vallejo
in March 2026. 		s = 6.15306+
Found by Timo Berthold et al
in May 2026.