Pentagons in Triangles

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


1.
           2.
           3.
s = 2.71618+
Trivial.
 
s = 4.01079+
Found by Ethan Riddle
in May 2026.
s = 4.12157+
Trivial.
 


4.
           5.
           6.
s = 5.21983+
Found by Jonathan Viquerat
in May 2026.
s = 5.55809+
Found by Jonathan Viquerat
in May 2026.
s = 5.63540+
Found by Jonathan Viquerat
in May 2026.


7.
           8.
           9.
s = 6.50034+
Found by Jonathan Viquerat
in May 2026.
s = 6.81134+
Found by Jonathan Viquerat
in May 2026.
s = 7.08971+
Found by Jonathan Viquerat
in May 2026.


10.
           11.
           12.
s = 7.17240+
Found by Jonathan Viquerat
in May 2026.
s = 7.93748+
Found by Jonathan Viquerat
in May 2026.
s = 8.19117+
Found by Jonathan Viquerat
in May 2026.


13.
           14.
           15.
s = 8.37807+
Found by Jonathan Viquerat
in May 2026.
s = 8.58923+
Found by Jonathan Viquerat
in May 2026.
s = 8.69300+
Found by Jonathan Viquerat
in May 2026.


16.
           17.
           18.
s = 9.29702+
Found by Jonathan Viquerat
in May 2026.
s = 9.57846+
Found by Jonathan Viquerat
in May 2026.
s = 9.78480+
Found by Jonathan Viquerat
in May 2026.


19.
           20.
           21.
s = 9.93813+
Found by Jonathan Viquerat
in May 2026.
s = 10.10536+
Found by Jonathan Viquerat
in May 2026.
s = 10.19935+
Found by Ethan Riddle
in May 2026.


22.
           23.
           24.
s = 10.76669+
Found by Ethan Riddle
in May 2026.
s = 11.00309+
Found by Ethan Riddle
in May 2026.
s = 11.205987+
Found by Ethan Riddle
in May 2026.


25.
           26.
s = 11.33243+
Found by Ethan Riddle
in May 2026.
s = 11.47365+
Found by Ethan Riddle
in May 2026.