Dominoes in Hexagons

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 = 2/31/4 = 1.51967+
Found by Jonathan Viquerat
in May 2026.
s = √2(3)1/4 = 1.86120+
Found by Jonathan Viquerat
in May 2026.


4.
           5.
           6.
s = 1+2/√3 = 2.15470+
Found by Jonathan Viquerat
in May 2026.
s = 4/√3 = 2.30940+
Trivial.
 
s = 1+5√3/6 = 2.44337+
Found by Jonathan Viquerat
in May 2026.


7.
           8.
           9.
s = 2.63126+
Found by Aapo Lipponen
in July 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 = 3.20593+
Found by Aapo Lipponen
in July 2026.
s = 3.34790+
Found by Jonathan Viquerat
in May 2026.
s = 3.46078+
Found by Aapo Lipponen
in July 2026.


13.
           14.
           15.
s = 3.52702+
Found by Jonathan Viquerat
in May 2026.
s = 3.67229+
Found by Aapo Lipponen
in July 2026.
s = 2(12)1/4 = 3.72241+
Found by Maurizio Morandi
in July 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 = 2+7√3/6 = 4.02072+
Found by Maurizio Morandi
in July 2026.


19.
           20.
           21.-24.
s = 4.19677+
Found by Jonathan Viquerat
in May 2026.
s = 4.36716+
Found by Jonathan Viquerat
in May 2026.
s = 2+3√3/2 = 4.59807+
Found by Maurizio Morandi
in July 2026.


25.
           26.
           27.
s = 3+√3 = 4.73205+
Found by Maurizio Morandi
in July 2026.
s = 4+√3/2 = 4.86602+
Found by Maurizio Morandi
in July 2026.
s = 4.99031+
Found by Aapo Lipponen
in July 2026.


28.
           29.-30.
s = 5.13998+
Found by Aapo Lipponen
in July 2026.
s = 2+11√3/6 = 5.17542+
Found by Maurizio Morandi
in July 2026.