The following pictures show n unit octagons packed inside the smallest known equilateral triangle (of side s).
1. 
s = 4.38541+
Found by Jonathan Viquerat
in May 2026.
2. 
s = 6.79962+
Found by Jonathan Viquerat
in May 2026.
3. 
s = 6.83693+
Found by Jonathan Viquerat
in May 2026.
4. 
s = 8.65211+
Found by Jonathan Viquerat
in May 2026.
5. 
s = 9.28498+
Found by Jonathan Viquerat
in May 2026.
6. 
s = 9.31576+
Found by Jonathan Viquerat
in May 2026.
7. 
s = 11.06632+
Trivial.
Found by Jonathan Viquerat
in May 2026.
8. 
s = 11.51025+
Found by Jonathan Viquerat
in May 2026.
9. 
s = 11.72998+
Trivial.
10. 
s = 11.80642+
Found by Jonathan Viquerat
in May 2026.
11. 
s = 13.24689+
Found by Jonathan Viquerat
in May 2026.
12. 
s = 13.62033+
Found by Jonathan Viquerat
in May 2026.
13. 
s = 14.04225+
Found by Jonathan Viquerat
in May 2026.
14. 
s = 14.24006+
Found by Jonathan Viquerat
in May 2026.
15. 
s = 14.28169+
Found by Jonathan Viquerat
in May 2026.
16. 
s = 15.66136+
Found by Jonathan Viquerat
in May 2026.
17. 
s = 16.06209+
Found by Jonathan Viquerat
in May 2026.
18. 
s = 16.43378+
Found by Jonathan Viquerat
in May 2026.
19. 
s = 16.55207+
Found by Jonathan Viquerat
in May 2026.
20. 
s = 16.74308+
Found by Jonathan Viquerat
in May 2026.