Dominoes in Octagons

The following pictures show n dominoes (with short side 1) packed inside the smallest known octagon (with side s).

1.
2.
3.

s = 3–3/√2 = 0.87867+
Trivial.
s = √(4–2√2) = 1.08239+
Trivial.
s = √(5–√2–√(8√2–9)) = 1.43690+
Found by Maurizio Morandi
in May 2026.

4.
5.
6.

s = 1.57337+
Found by Maurizio Morandi
in May 2026. s = 1.71644+
Found by Jonathan Viquerat
in June 2026. s = √(6–√2–√(20√2–26)) = 1.75339+
Found by Maurizio Morandi
in May 2026.

7.
8.
9.

s = 2.00513+
Found by Joshua Wolk
in September 2026. s = 5(√2–1) = 2.07106+
Trivial.
s = 2.19803+
Found by Jonathan Viquerat
in June 2026.

10.
11.
12.

s = 2.32394+
Found by Jonathan Viquerat
in June 2026. s = 2.44911+
Found by Jonathan Viquerat
in June 2026. s = 6(√2–1) = 2.48528+
Trivial.

13.
14.
15.

s = 2.56542+
Found by Joshua Wolk
in September 2026. s = 2.67691+
Found by Joshua Wolk
in September 2026. s = 2.78488+
Found by Joshua Wolk
in September 2026.

16.
17.
18.

s = 2√(5–√2–√(8√2–9)) = 2.87381+
Found by Maurizio Morandi
in June 2026. s = 2.92200+
Found by Joshua Wolk
in September 2026. s = 2.98881+
Found by Joshua Wolk
in September 2026.

19.
20.
21.

s = 3.07779+
Found by Joshua Wolk
in September 2026. s = 3.16171+
Found by Joshua Wolk
in September 2026. s = 3.27191+
Found by Joshua Wolk
in September 2026.

22.
23.
24.

s = 8(√2–1) = 3.31370+
Found by Maurizio Morandi
in July 2026. s = 3.31788+
Found by Joshua Wolk
in September 2026. s = 3.38301+
Found by Joshua Wolk
in September 2026.

25.
26.
27.

s = 3.47309+
Found by Joshua Wolk
in September 2026. s = 2√(6–√2–√(20√2–26)) = 3.50679+
Found by Maurizio Morandi
in July 2026. s = 10–9/√2 = 3.63603+
Found by Maurizio Morandi
in July 2026.

28.
29
30.

s = 9(√2–1) = 3.72792+
Found by Maurizio Morandi
in July 2026. s = 3.74011+
Found by Joshua Wolk
in September 2026. s = 3.77874+
Found by Joshua Wolk
in September 2026.

31.

s = 3.80663+
Found by Aapo Lipponen
in July 2026.

1.		2.		3.
s = 3–3/√2 = 0.87867+ Trivial.		s = √(4–2√2) = 1.08239+ Trivial.		s = √(5–√2–√(8√2–9)) = 1.43690+ Found by Maurizio Morandi in May 2026.

4.		5.		6.
s = 1.57337+ Found by Maurizio Morandi in May 2026.		s = 1.71644+ Found by Jonathan Viquerat in June 2026.		s = √(6–√2–√(20√2–26)) = 1.75339+ Found by Maurizio Morandi in May 2026.

7.		8.		9.
s = 2.00513+ Found by Joshua Wolk in September 2026.		s = 5(√2–1) = 2.07106+ Trivial.		s = 2.19803+ Found by Jonathan Viquerat in June 2026.

10.		11.		12.
s = 2.32394+ Found by Jonathan Viquerat in June 2026.		s = 2.44911+ Found by Jonathan Viquerat in June 2026.		s = 6(√2–1) = 2.48528+ Trivial.

13.		14.		15.
s = 2.56542+ Found by Joshua Wolk in September 2026.		s = 2.67691+ Found by Joshua Wolk in September 2026.		s = 2.78488+ Found by Joshua Wolk in September 2026.

16.		17.		18.
s = 2√(5–√2–√(8√2–9)) = 2.87381+ Found by Maurizio Morandi in June 2026.		s = 2.92200+ Found by Joshua Wolk in September 2026.		s = 2.98881+ Found by Joshua Wolk in September 2026.

19.		20.		21.
s = 3.07779+ Found by Joshua Wolk in September 2026.		s = 3.16171+ Found by Joshua Wolk in September 2026.		s = 3.27191+ Found by Joshua Wolk in September 2026.

22.		23.		24.
s = 8(√2–1) = 3.31370+ Found by Maurizio Morandi in July 2026.		s = 3.31788+ Found by Joshua Wolk in September 2026.		s = 3.38301+ Found by Joshua Wolk in September 2026.

25.		26.		27.
s = 3.47309+ Found by Joshua Wolk in September 2026.		s = 2√(6–√2–√(20√2–26)) = 3.50679+ Found by Maurizio Morandi in July 2026.		s = 10–9/√2 = 3.63603+ Found by Maurizio Morandi in July 2026.

28.		29		30.
s = 9(√2–1) = 3.72792+ Found by Maurizio Morandi in July 2026.		s = 3.74011+ Found by Joshua Wolk in September 2026.		s = 3.77874+ Found by Joshua Wolk in September 2026.