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

1. | 2. | 3. | ||

s = 1/√3 = .577+ Trivial. | s = √3/2 = .866+ Trivial. | s = √((6+√33)/12) = .989+ Found by Erich Friedman in April 2005. |

4. | 5. | 6. | ||

s = 1 Trivial. | s = 1 Trivial. | s = 1 Trivial. |

7. | 8. | 9. | ||

s = 1.277+ Found by David W. Cantrell in May 2005. | s = 1.356+ Found by David W. Cantrell in July 2012. | s = 1.434+ Found by Erich Friedman in April 2005. |

10. | 11. | 12. | ||

s = 3/2 = 1.500 Found by Erich Friedman in April 2005. | s = 3/2 = 1.500 Found by Erich Friedman in April 2005. | s = 1.627+ Found by Maurizio Morandi in May 2008. |

13. | 14. | 15. | ||

s = 5/3 = 1.666+ Found by Erich Friedman in April 2005. | s = 1.725+ Found by DWC after MM in August 2012. | s = 7/4 = 1.750 Found by Erich Friedman in April 2005. |

16. | 17. | 18. | ||

s = 9/5 = 1.800 Found by Maurizio Morandi in April 2008. | s = 11/6 = 1.833+ Found by Maurizio Morandi in April 2008. | s = 17/9 = 1.888+ Found by Maurizio Morandi in April 2008. |