Surface area of hexagon = 613=6eh + 3e²√3. 3√3=5.196152 approx.

Therefore h=(613-3e²√3)/(6e).

There is no unique solution but since h is positive, e must be less than 10.86mm approx.

Here are some related values.

e (mm) | h (mm) |

0.5 | 203.90 |

1 | 101.30 |

1.5 | 66.81 |

2 | 49.35 |

2.5 | 38.70 |

3 | 31.46 |

3.5 | 26.16 |

4 | 22.08 |

4.5 | 18.81 |

5 | 16.10 |

5.5 | 13.81 |

6 | 11.83 |

6.5 | 10.09 |

7 | 8.53 |

7.5 | 7.13 |

8 | 5.84 |

8.5 | 4.66 |

9 | 3.56 |

9.5 | 2.53 |

10 | 1.56 |

10.5 | 0.64 |

When the height and edge are equal h=e=7.3994mm approx.

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