Octagons in Hexagons

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

1.

s = cos(7.5°)/√3/sin(22.5°) = 1.49578+
Trivial.
  		           2.

s = 1 + √2 + √3/6 = 2.70288+
Trivial.
  		           3.

s = 2.88958+
Found by Mohamed Metwalli
in June 2026.

4.

s = 11+8√2–16/√3–4√6 = 3.27814+
Found by Mohamed Metwalli
in June 2026. 		           5.

s = 3.71848+
Found by Jonathan Viquerat
in June 2026. 		           6.

s = 3.94730+
Found by Aristotle Papowitz
in July 2026.
7.

s = 3.97716+
Found by Jonathan Viquerat
in June 2026. 		           8.

s = 4.56653+
Found by Jonathan Viquerat
in June 2026. 		           9.

s = 4.93304+
Found by Jonathan Viquerat
in June 2026.
10.

s = 5.06929+
Found by Jonathan Viquerat
in June 2026. 		           11.

s = 5.34796+
Found by Bhavithran Ananthan
in July 2026. 		           12.

s = 5.38669+
Found by Jonathan Viquerat
in June 2026.
13.

s = 5.75470+
Found by Jonathan Viquerat
in June 2026. 		           14.

s = 5.77752+
Found by Jonathan Viquerat
in June 2026. 		           15.

s = 6.13744+
Found by Bhavithran Ananthan
in June 2026.
16.

s = 6.21438+
Found by Jonathan Viquerat
in June 2026. 		           17.

s = 6.35722+
Found by Yanis Gomes
in October 2026. 		           18.

s = 6.42774+
Found by Bhavithran Ananthan
in July 2026.
19.

s = 6.44696+
Found by Bhavithran Ananthan
in July 2026. 		           20.

s = 6.99419+
Found by Leo Strijbos
in August 2026. 		           21.

s = 7.06795+
Found by Joshua Wolk in September 2026.
22.

s = 7.32809+
Found by Yanis Gomes
in October 2026. 		           23.

s = 7.43164+
Found by Joshua Wolk in September 2026. 		           24.

s = 7.53131+
Found by Joshua Wolk in September 2026.
25.

s = 7.74422+
Found by Joshua Wolk in September 2026. 		           26.

s = 7.84079+
Found by Joshua Wolk in September 2026. 		           27.

s = 7.86114+
Found by Joshua Wolk in September 2026.
28.

s = 8.14117+
Found by Beppe Björkland
in October 2026. 		           29.

s = 8.24943+
Found by Joshua Wolk in September 2026. 		           30.

s = 8.27000+
Found by Yanis Gomes
in October 2026.
31.

s = 8.55447+
Found by Beppe Björkland
in October 2026. 		           32.

s = 8.63668+
Found by Beppe Björkland
in October 2026. 		           33.

s = 8.69103+
Found by Beppe Björkland
in October 2026.
34.

s = 8.79337+
Found by Beppe Björkland
in October 2026. 		           35.

s = 8.86335+
Found by Joshua Wolk in September 2026. 		           36.

s = 8.92001+
Found by Joshua Wolk in September 2026.
37.

s = 8.93471+
Found by Beppe Björkland
in October 2026. 		           38.

s = 9.36761+
Found by Joshua Wolk in September 2026. 		           39.

s = 9.50159+
Found by Beppe Björkland
in October 2026.
40.

s = 9.55404+
Found by Joshua Wolk in September 2026. 		           41.

s = 9.77460+
Found by Joshua Wolk in September 2026. 		           42.

s = 9.85064+
Found by Beppe Björkland
in October 2026.
43.

s = 9.92752+
Found by Beppe Björkland
in October 2026. 		           44.

s = 9.99692+
Found by Yanis Gomes
in October 2026. 		           45.

s = 10.18730+
Found by Beppe Björkland
in October 2026.
46.

s = 10.26593+
Found by Beppe Björkland
in October 2026. 		           47.

s = 10.32723+
Found by Beppe Björkland
in October 2026. 		           48.

s = 10.35244+
Found by Beppe Björkland
in October 2026.
49.

s = 10.58403+
Found by Joshua Wolk in September 2026. 		           50.

s = 10.66657+
Found by Joshua Wolk in September 2026.