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

1. s = 1 Trivial. | 2. s = 2 Trivial. | 3. s = 2 Trivial. |

4. s = 7/3 = 2.333+ Trivial. | 5. s = 8/3 = 2.666+ Found by Erich Friedman in March 2015. | 6-7. s = 5/√3 = 2.886+ Found by Maurizio Morandi in April 2015. |

8. s = (51+5√3)/18 = 3.314+ Found by Maurizio Morandi in April 2015. | 9. s = (24+5√3)/9 = 3.628+ Found by Maurizio Morandi in April 2015. | 10. s = 2 + √3 = 3.732+ Found by Maurizio Morandi in April 2015. |

11. s = 5(3 + √3)/6 = 3.943+ Found by Maurizio Morandi in April 2015. | 12-13. s = 4 Trivial. | 14. s = 37√3/15 = 4.272+ Found by Maurizio Morandi in April 2015. |

15. s = (73+35√3)/30 = 4.454+ Found by Maurizio Morandi in April 2015. | 16. s = 55√3/21 = 4.536+ Found by Maurizio Morandi in April 2015. | 17-19. s = 8/√3 = 4.618+ Found by Maurizio Morandi in April 2015. |

20-21. s = 5 Trivial. | 22. s = (39+8√3)/10 = 5.285+ Found by Maurizio Morandi in April 2015. | 23. s = 38/7 = 5.428+ Found by Maurizio Morandi in April 2015. |

24. s = 19√3/6 = 5.484+ Found by Maurizio Morandi in April 2015. |