Octahedra in Cubes
The following pictures show n unit octahedra packed inside the smallest known cube (of side s).

1.
           2.
           3.
s = .94280+
Trivial.
  		s = √2 = 1.41421+
Found by Riain Walsh in June 2026. 		s = 1.63299
Found by Riain Walsh in June 2026.

4.
           5.
           6.
s = 1.64991+
Found by Riain Walsh in June 2026. 		s = 1.75782+
Found by Riain Walsh in June 2026. 		s = 1.76776+
Found by Riain Walsh in June 2026.
7.-8.
           9.
           10.
s = 1.79133+
Found by Riain Walsh in June 2026. 		s = 1.88561+
Found by Riain Walsh in June 2026. 		s = 2.14936+
Found by Riain Walsh in June 2026.
11.
           12.
           13.
s = 2.19540+
Found by Riain Walsh in June 2026. 		s = 2.25949+
Found by Haowei Lin in July 2026. 		s = 2.33667+
Found by Haowei Lin in July 2026.
14.
           15.
           16.
s = 2.35702+
Found by Riain Walsh in June 2026. 		s = 2.41976+
Found by Riain Walsh in June 2026. 		s = 2.46211+
Found by Riain Walsh in June 2026.
17.
           18.
           19.
s = 2.47487+
Found by Haowei Lin in July 2026. 		s = 2.48257+
Found by Riain Walsh in June 2026. 		s = 2.52683+
Found by Riain Walsh in June 2026.
20.
           21.
           22.
s = 2.57792+
Found by Riain Walsh in June 2026. 		s = 2.59284+
Found by Haowei Lin in July 2026. 		s = 2.60591+
Found by Riain Walsh in June 2026.
23.
           24.
           25.
s = 2.61533+
Found by Riain Walsh in June 2026. 		s = 2.63318+
Found by Haowei Lin in July 2026. 		s = 2.63622+
Found by Riain Walsh in June 2026.
26.-27.
           28.
           29.
s = 2.63986+
Found by Riain Walsh in June 2026. 		s = 2.75738+
Found by Riain Walsh in June 2026. 		s = 2.85384+
Found by Riain Walsh in June 2026.
30.
s = 2.89186+
Found by Riain Walsh in June 2026.