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

1.
           2.
           3.
s = 1/√2 = .70710+
Trivial. 		s = 2√2/3 = .94280+
Trivial. 		s = 1
Found by Achille Hui in February 2016.

4.
           5.
           6.
s = 1.08648+
Found by Riain Walsh in June 2026. 		s = 1.17763+
Found by Riain Walsh in June 2026. 		s = 1.19648+
Found by Riain Walsh in June 2026.
7.
           8.
           9.
s = 1.26224+
Found by Riain Walsh in June 2026. 		s = 1.29665+
Found by Haowei Lin in July 2026. 		s = 1.33082+
Found by Riain Walsh in June 2026.
10.
           11.
           12.
s = 1.37141+
Found by Riain Walsh in June 2026. 		s = 1.39141+
Found by Riain Walsh in June 2026. 		s = 1.42615+
Found by Haowei Lin in July 2026.
13.
           14.
           15.
s = 1.46398+
Found by Haowei Lin in July 2026. 		s = 1.50588+
Found by Haowei Lin in July 2026. 		s = 1.53695+
Found by Haowei Lin in July 2026.
16.
           17.
           18.
s = 1.55391+
Found by Haowei Lin in July 2026. 		s = 1.57515+
Found by Haowei Lin in July 2026. 		s = 1.60258+
Found by Haowei Lin in July 2026.
19.
           20.
           21.
s = 1.62245+
Found by Haowei Lin in July 2026. 		s = 1.64131+
Found by Haowei Lin in July 2026. 		s = 1.67943+
Found by Riain Walsh in June 2026.
22.
           23.
           24.
s = 1.69871+
Found by Riain Walsh in June 2026. 		s = 1.71487+
Found by Riain Walsh in June 2026. 		s = 1.72649+
Found by Riain Walsh in June 2026.
25.
           26.
           27.
s = 1.74345+
Found by Riain Walsh in June 2026. 		s = 1.77297+
Found by Riain Walsh in June 2026. 		s = 1.78532+
Found by Riain Walsh in June 2026.
28.
           29.
           30.
s = 1.82224+
Found by Riain Walsh in June 2026. 		s = 1.82631+
Found by Riain Walsh in June 2026. 		s = 1.84993+
Found by Riain Walsh in June 2026.