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 Joanthan Viquerat
in June 2026.
s = √(6–√2–√(20√2–26)) = 1.75339+
Found by Maurizio Morandi
in May 2026.
7.
8.
9.
s = 2.00516+
Found by Joanthan Viquerat
in June 2026.
s = 5(√2–1) = 2.07106+
Trivial.
s = 2.19803+
Found by Joanthan Viquerat
in June 2026.
10.
11.-12.
13.
s = 2.32394+
Found by Joanthan Viquerat
in June 2026.
s = 6(√2–1) = 2.48528+
Trivial.
s = 2.56556+
Found by Joanthan Viquerat
in June 2026.
14.
15.
16.
s = 2.67740+
Found by Joanthan Viquerat
in June 2026.
s = 2.80446+
Found by Joanthan Viquerat
in June 2026.
s = 7(√2–1) = 2.89949+
Found by Maurizio Morandi
in May 2026.
17.
18.
s = 5(2–√2) = 2.92893+
Found by Maurizio Morandi
in May 2026.
s = 37–24√2 = 3.05887+
Found by Maurizio Morandi
in May 2026.