Hexagons in Pentagons

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 = 5.61409+
Found by Jake Loyd
in June 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 = 6.10977+
Found by Jonathan Viquerat
in May 2026.

20.

s = 6.24667+
Found by Jake Loyd
in June 2026.

21.

s = 6.39214+
Found by Joshua Wolk
in September 2026.

22.

s = 6.53472+
Found by Bhavithran Ananthan
in July 2026.

23.

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

24.

s = 6.77466+
Found by Jake Loyd
in June 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 = 7.24761+
Found by Joshua Wolk
in September 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 = 7.97413+
Found by Joshua Wolk in September 2026.

35.

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

36.

s = 8.21783+
Found by Joshua Wolk in September 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 = 8.98357+
Found by Joshua Wolk in September 2026.

45.

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

46.

s = 9.17226+
Found by Joshua Wolk in September 2026.

47.

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

48.

s = 9.32263+
Found by Joshua Wolk in September 2026.

49.

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

50.

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