Triangles in Octagons

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

1.
           2.
           3.
s = .46470+
Trivial.
  		s = √3/√(4+2√2) = .66282+
Trivial.
  		s = .73651+
Found by Ignacio Vallejo
in March 2026.

4.
           5.
           6.
s = .77731+
Found by Timo Berthold et al
in May 2026. 		s = .80366+
Found by Nicolas Campailla
in May 2026. 		s = .81574+
Found by Ignacio Vallejo
in March 2026.

7.
           8.
           9.
s = .92453+
Found by Ignacio Vallejo
in March 2026. 		s = .98777+
Found by Timo Berthold et al
in May 2026. 		s = 1.00871+
Found by Grant Mowry
in April 2026.

10.
           11.
           12.
s = 1.07515+
Found by Jake Loyd
in May 2026. 		s = 1.14562+
Found by Grant Mowry
in April 2026. 		s = 1.19914+
Found by Timo Berthold et al
in May 2026.

13.
           14.
           15.
s = 1.23726+
Found by Jake Loyd
in June 2026. 		s = 1.27629+
Found by Jake Loyd
in June 2026. 		s = 1.30240+
Found by Timo Berthold et al
in May 2026.

16.
           17.
           18.
s = 1.34566+
Found by Jake Loyd
in June 2026. 		s = 1.38854+
Found by Jake Loyd
in June 2026. 		s = 1.41763+
Found by Jake Loyd
in June 2026.

19.
           20.
           21.
s = 1.46678+
Found by Jake Loyd
in June 2026. 		s = 1.49689+
Found by Jake Loyd
in June 2026. 		s = 1.52519+
Found by Jake Loyd
in June 2026.

22.
           23.
           24.
s = 1.55435+
Found by Jake Loyd
in June 2026. 		s = 1.58348+
Found by Jake Loyd
in June 2026. 		s = 1.60180+
Found by Jake Loyd
in June 2026.

25.
           26.
           27.
s = 1.63703+
Found by Jake Loyd
in June 2026. 		s = 1.67455+
Found by Jake Loyd
in June 2026. 		s = 1.70616+
Found by Jake Loyd
in June 2026.

28.
           29.
           30.
s = 1.73796+
Found by Jake Loyd
in June 2026. 		s = 1.75285+
Found by Jake Loyd
in June 2026. 		s = 1.77911+
Found by Jake Loyd
in June 2026.

31.
           32.
s = 1.80341+
Found by Thomas Greenleaf
in June 2026. 		s = 1.83002+
Found by Thomas Greenleaf
in June 2026.