Hexagons in Triangles

The following pictures show n unit hexagons packed inside the smallest known triangle (with side s).


1.
           2.-3.
           4.
s = 3
Trivial.
s = 5
Trivial.
s = 6
Trivial.


5.
           6.
           7.
s = 5(1+√3)/2 = 6.8301+
Found by Maurizio Morandi
in April 2015.
s = 6.89891+
Found by Jonathan Viquerat
in April 2026.
s = 8
Trivial.
 


8.
           9.-10.
           11.
s = 25/3 = 8.3333+
Found by Erich Friedman
in April 2015.
s = 5√3 = 8.6602+
Trivial.
 
s = 9.54823+
Found by Jonathan Viquerat
in April 2026.


12.
           13.-15.
           16.
s = 10
Trivial.
 
s = 6√3 = 10.3923+
Trivial.
 
s = 11.36599+
Found by Jonathan Viquerat
in April 2026.


17.
           18.-19.
           20.-21.
s = 11.63457+
Found by Jonathan Viquerat
in April 2026.
s = 12
Trivial.
 
s = 7√3 = 12.1243+
Trivial.