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 = 2.70289+
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 = 6.35723+
Found by Joshua Wolk in September 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 = 7.32810+
Found by Joshua Wolk in September 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 = 8.14118+
Found by Joshua Wolk in September 2026.
           29.

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

s = 8.27001+
Found by Joshua Wolk in September 2026.

31.

s = 8.55448+
Found by Joshua Wolk in September 2026.
           32.

s = 8.63669+
Found by Joshua Wolk in September 2026.
           33.

s = 8.69106+
Found by Joshua Wolk in September 2026.

34.

s = 8.79338+
Found by Joshua Wolk in September 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 = 8.93472+
Found by Joshua Wolk in September 2026.
           38.

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

s = 9.50169+
Found by Joshua Wolk in September 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 = 9.85080+
Found by Joshua Wolk in September 2026.

43.

s = 9.92753+
Found by Joshua Wolk in September 2026.
           44.

s = 9.99809+
Found by Joshua Wolk in September 2026.
           45.

s = 10.18798+
Found by Joshua Wolk in September 2026.

46.

s = 10.26603+
Found by Joshua Wolk in September 2026.
           47.

s = 10.32874+
Found by Joshua Wolk in September 2026.
           48.

s = 10.35305+
Found by Joshua Wolk in September 2026.

49.

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

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