L's in Hexagons
The following pictures show n L's with short side 1 inside the smallest known hexagon (of side s).

1.

s = 2√((11 + 6√3)/39) = 1.481+
Trivial.
  		           2.

s = 121/4 = 1.861+
Found by Maurizio Morandi
in May 2026. 		           3.

s = 1/2 + √3 = 2.232+
Found by Maurizio Morandi
in May 2026.

4.

s = 10√6/3 – 4√2 = 2.508+
Found by Maurizio Morandi
in May 2026. 		           5.

s = 5/√3 = 2.886+
Trivial.
  		           6.

s = 4/3 + √3 = 3.065+
Found by Maurizio Morandi
in May 2026.

7.

s = 4√6/3 = 3.265+ = 2.508+
Found by Maurizio Morandi
in May 2026. 		           8.

s = 2√3 = 3.464+
Trivial.
  		           9.

s = 5/2 + 2/√3 = 3.654+
Found by Maurizio Morandi
in May 2026.

10.

s = 3.94031+
Found by Jonathan Viquerat
in May 2026. 		           11.

s = 7/√3 = 4.041+
Trivial.
  		           12.

s = 5/3 + 13√3/9 = 4.168+
Found by Maurizio Morandi
in May 2026.

13.

s = 4.41460+
Found by Jonathan Viquerat
in May 2026. 		           14.

s = 4.61778+
Found by Jonathan Viquerat
in May 2026. 		           15.

s = 4.71776+
Found by Jonathan Viquerat
in May 2026.