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 = 13.62032+
Found by Bhavithran Ananthan
in July 2026.
13.

s = 14.04225+
Found by Jonathan Viquerat
in May 2026. 		           14.

s = 14.23921+
Found by Aristotle Papowitz
in July 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 Bhavithran Ananthan
in July 2026. 		           18.

s = 16.40911+
Found by Joshua Wolk
in September 2026.
19.

s = 16.54447+
Found by Timo Berthold et al
in May 2026. 		           20.

s = 16.74196+
Found by Jonathan Viquerat
in August 2026. 		           21.

s = 16.78582+
Found by Bhavithran Ananthan
in July 2026.
22.

s = 17.96238+
Found by Bhavithran Ananthan
in July 2026. 		           23.

s = 18.39413+
Found by Jonathan Viquerat
in August 2026. 		           24.

s = 18.55965+
Found by Joshua Wolk
in September 2026.
25.

s = 18.92837+
Found by Joshua Wolk
in September 2026. 		           26.

s = 19.06452+
Found by Joost de Winter
in September 2026. 		           27.

s = 19.24376+
Found by Joshua Wolk
in September 2026.
28.

s = 19.28459+
Found by Joshua Wolk
in September 2026. 		           29.

s = 20.42577+
Found by Joshua Wolk
in September 2026. 		           30.

s = 20.72981+
Found by Joshua Wolk
in September 2026.
31.

s = 21.03330+
Found by Joshua Wolk
in September 2026. 		           32.

s = 21.28490+
Found by Joost de Winter
in September 2026. 		           33.

s = 21.42921+
Found by Joshua Wolk
in September 2026.
34.

s = 21.58059+
Found by Joshua Wolk
in September 2026. 		           35.

s = 21.74101+
Found by Joshua Wolk
in September 2026. 		           36.

s = 21.77463+
Found by Joshua Wolk
in September 2026.
37.

s = 22.85236+
Found by Joshua Wolk
in September 2026. 		           38.

s = 23.17430+
Found by Joshua Wolk
in September 2026. 		           39.

s = 23.41012+
Found by Joshua Wolk
in September 2026.
40.

s = 23.55971+
Found by Joshua Wolk
in September 2026. 		           41.

s = 23.77375+
Found by Joshua Wolk
in September 2026. 		           42.

s = 23.94952+
Found by Joshua Wolk
in September 2026.
43.

s = 24.09397+
Found by Joshua Wolk
in September 2026. 		           44.

s = 24.23814+
Found by Joshua Wolk
in September 2026. 		           45.

s = 24.26690+
Found by Joshua Wolk
in September 2026.
46.

s = 25.28172+
Found by Joshua Wolk
in September 2026. 		           47.

s = 25.56652+
Found by Joshua Wolk
in September 2026. 		           48.

s = 25.76702+
Found by Joshua Wolk
in September 2026.
49.

s = 26.01450+
Found by Joshua Wolk
in September 2026. 		           50.

s = 26.14249+
Found by Joshua Wolk
in September 2026.