The following pictures show n dominoes (with short side 1) packed inside the smallest known hexagon (with side s).
1.
2.
3.
s = 2/√3 = 1.15470+
Trivial.
s = 1.51967+
Found by Jonathan Viquerat
in May 2026.
s = 1.86121+
Found by Jonathan Viquerat
in May 2026.
4.
5.
6.
s = 4/√3 = 2.15470+
Found by Jonathan Viquerat
in May 2026.
s = 2.30940+
Trivial.
s = 2.44337+
Found by Jonathan Viquerat
in May 2026.
7.
8.
9.
s = 2.63129+
Found by Jonathan Viquerat
in May 2026.
s = 2.85220+
Found by Jonathan Viquerat
in May 2026.
s = 2.93631+
Found by Jonathan Viquerat
in May 2026.
10.
11.
12.
s = 3.20891+
Found by Jonathan Viquerat
in May 2026.
s = 3.34790+
Found by Jonathan Viquerat
in May 2026.
s = 3.46084+
Found by Jonathan Viquerat
in May 2026.
13.
14.
15.
s = 3.52702+
Found by Jonathan Viquerat
in May 2026.
s = 3.67312+
Found by Jonathan Viquerat
in May 2026.
s = 3.74924+
Found by Jonathan Viquerat
in May 2026.
16.
17.
18.
s = 3.90286+
Found by Jonathan Viquerat
in May 2026.
s = 4.01162+
Found by Jonathan Viquerat
in May 2026.
s = 7/√3 = 4.04145+
Trivial.
19.
20.
s = 4.19677+
Found by Jonathan Viquerat
in May 2026.
s = 4.36716+
Found by Jonathan Viquerat
in May 2026.