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.