Octagons in Dominoes

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

1-2.

s = 1 + √2 = 2.41421+
Trivial.
  		           3.

s = 3.51366+
Found by Aapo Lipponen
in July 2026. 		           4.

s = 2 + 7√2/5 = 3.97989+
Found by Aapo Lipponen
in July 2026.

5.

s = 13/6 + 3/√2 = 4.28798+
Found by Jonathan Viquerat
in May 2026. 		           6.

s = (16 + 11√2)/7 = 4.50804+
Found by Jonathan Viquerat
in May 2026. 		           7.-8.

s = 2 + 2√2 = 4.82842+
Trivial.
 
9.

s = 8/3 + 2√2 = 5.49509+
Found by Jonathan Viquerat
in May 2026. 		           10.

s = 3 + 2√2 = 5.82842+
Found by Jonathan Viquerat
in May 2026. 		           11.

s = 16/5 + 2√2 = 6.02842+
Found by Jonathan Viquerat
in May 2026.
12.

s = 6.31126+
Found by Jonathan Viquerat
in May 2026. 		           13.

s = 6.51127+
Found by Joshua Wolk
in September 2026. 		           14.

s = (21 + 13√2)/6 = 6.56412+
Found by Jonathan Viquerat
in May 2026.
15.

s = (47 + 29√2)/13 = 6.77016+
Found by Jonathan Viquerat
in May 2026. 		           16.

s = 7.10456+
Found by Jonathan Viquerat
in May 2026. 		           17.-18.

s = 3 + 3√2 = 7.24264+
Trivial.
 
19.

s = 7.77123+
Found by Jonathan Viquerat
in May 2026. 		           20.

s = 8.03947+
Found by Jonathan Viquerat
in May 2026. 		           21.

s = 8.21837+
Found by Bhavithran Ananthan
in July 2026.
22.

s = 8.34004+
Found by Thomas Greenleaf
in June 2026. 		           23.

s = 8.48865+
Found by Joshua Wolk
in September 2026. 		           24.

s = 8.61577+
Found by Joshua Wolk
in September 2026.
25.

s = 8.74630+
Found by Joshua Wolk
in September 2026. 		           26.

s = 8.84027+
Found by Joshua Wolk
in September 2026. 		           27.

s = 9.02232+
Found by Joshua Wolk
in September 2026.
28.

s = 9.05076+
Found by Joshua Wolk
in September 2026. 		           29.

s = 9.35715+
Found by Joshua Wolk
in September 2026. 		           30.

s = 9.53259+
Found by Joshua Wolk
in September 2026.
31.-32.

s = 4 + 4√2 = 9.65685+
Trivial. 		           33.

s = 10.04653+
Found by Joshua Wolk
in September 2026. 		           34.

s = 10.19975+
Found by Joshua Wolk
in September 2026.
35.

s = 10.40742+
Found by Joshua Wolk
in September 2026. 		           36.

s = 10.44975+
Found by Joshua Wolk
in September 2026. 		           37.

s = 10.60461+
Found by Joshua Wolk
in September 2026.
38.

s = 10.66599+
Found by Joshua Wolk
in September 2026. 		           39.

s = 10.81844+
Found by Joshua Wolk
in September 2026. 		           40.

s = 10.90099+
Found by Joshua Wolk
in September 2026.
41.

s = 11.02660+
Found by Joshua Wolk
in September 2026. 		           42.

s = 11.08248+
Found by Joshua Wolk
in September 2026. 		           43.

s = 11.11641+
Found by Joshua Wolk
in September 2026.
44.

s = 11.40858+
Found by Joshua Wolk
in September 2026. 		           45.

s = 11.44253+
Found by Joshua Wolk
in September 2026. 		           46.

s = 11.68038+
Found by Joshua Wolk
in September 2026.
47.

s = 11.80335+
Found by Joshua Wolk
in September 2026. 		           48.

s = 11.95272+
Found by Joshua Wolk
in September 2026. 		           49.-50.

s = 5 + 5√2 = 12.07107+
Found by Joshua Wolk
in September 2026.