Octagons in Triangles

Octagons in Triangles

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+5√2+4√3+3√6)/4 = 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+
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 = 14.23921+
Found by Timo Berthold et al
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 = 16.06191+
Found by Timo Berthold et al
in May 2026.

18.

s = 16.41399+
Found by Timo Berthold et al
in May 2026.

19.

s = 16.54447+
Found by Timo Berthold et al
in May 2026.

20.

s = 16.74201+
Found by Timo Berthold et al
in May 2026.