Hexagons in Pentagons

The following pictures show n regular hexagons with side 1 packed inside the smallest known regular pentagon (of side length s).

1.

s = 1.39538+
Trivial.
  		2.

s = 2.46585+
Found by Jonathan Viquerat
in May 2026. 		3.

s = 2.74282+
Found by Ethan Riddle
in May 2026.

4.

s = 3.01521+
Found by Bhavithran Ananthan
in July 2026. 		5.

s = 3.21972+
Found by Aristotle Papowitz
in July 2026. 		6.

s = 3.54952+
Found by Jonathan Viquerat
in May 2026.

7.

s = 3.79749+
Found by Jonathan Viquerat
in May 2026. 		8.

s = 4.14916+
Found by Bhavithran Ananthan
in July 2026. 		9.

s = 4.34314+
Found by Jonathan Viquerat
in May 2026.

10.

s = 4.55810+
Found by Jonathan Viquerat
in May 2026. 		11.

s = 4.71959+
Found by Bhavithran Ananthan
in July 2026. 		12.

s = 4.91850+
Found by Jonathan Viquerat
in May 2026.

13.

s = 5.10107+
Found by Bhavithran Ananthan
in July 2026. 		14.

s = 5.29198+
Found by Jake Loyd
in June 2026. 		15.

s = 5.41337+
Found by Jake Loyd
in June 2026.

16.

s = 5.61408+
Found by Aapo Lipponen
in October 2026. 		17.

s = 5.82103+
Found by Jake Loyd
in June 2026. 		18.

s = 5.94471+
Found by Jonathan Viquerat
in May 2026.

19.

s = 6.10976+
Found by Aapo Lipponen
in October 2026. 		20.

s = 6.24666+
Found by Aapo Lipponen
in October 2026. 		21.

s = 6.39213+
Found by Yanis Gomes
in October 2026.

22.

s = 6.53471+
Found by Aapo Lipponen
in October 2026. 		23.

s = 6.66271+
Found by Jake Loyd
in June 2026. 		24.

s = 6.77465+
Found by Aapo Lipponen
in October 2026.

25.

s = 6.89098+
Found by Bhavithran Ananthan
in July 2026. 		26.

s = 7.04732+
Found by Joshua Wolk
in September 2026. 		27.

s = 7.15176+
Found by Joshua Wolk
in September 2026.

28.

s = 7.24760+
Found by Yanis Gomes
in October 2026. 		29.

s = 7.37819+
Found by Joshua Wolk
in September 2026. 		30.

s = 7.45985+
Found by Aristotle Papowitz
in July 2026.

31.

s = 7.63254+
Found by Jonathan Viquerat
in August 2026. 		32.

s = 7.76407+
Found by Joshua Wolk
in September 2026. 		33.

s = 7.87345+
Found by Joshua Wolk
in September 2026.

34.

s = 7.97409+
Found by Yanis Gomes
in October 2026. 		35.

s = 8.09708+
Found by Joshua Wolk
in September 2026. 		36.

s = 8.21782+
Found by Beppe Björkland
in October 2026.

37.

s = 8.32409+
Found by Joshua Wolk
in September 2026. 		38.

s = 8.41316+
Found by Joshua Wolk
in September 2026. 		39.

s = 8.50595+
Found by Joshua Wolk
in September 2026.

40.

s = 8.61451+
Found by Joshua Wolk
in September 2026. 		41.

s = 8.70242+
Found by Joshua Wolk
in September 2026. 		42.

s = 8.80402+
Found by Joshua Wolk
in September 2026.

43.

s = 8.87601+
Found by Joshua Wolk
in September 2026. 		44.

s = 8.98351+
Found by Yanis Gomes
in October 2026. 		45.

s = 9.06731+
Found by Joshua Wolk
in September 2026.

46.

s = 9.17225+
Found by Yanis Gomes
in October 2026. 		47.

s = 9.26611+
Found by Joshua Wolk
in September 2026. 		48.

s = 9.32231+
Found by Beppe Björkland
in October 2026.

49.

s = 9.44600+
Found by Joshua Wolk
in September 2026. 		50.

s = 9.55416+
Found by Joshua Wolk
in September 2026.