Seven Touching Cylinders

Theorem
It is possible to arrange $7$ identical cylinders so that each one touches each of the others.

The cylinders must be such that their heights must be at least $\dfrac {7 \sqrt 3} 2$ of the diameters of their bases.

Proof

 * Seven-Touching-Cylinders.png

It remains to be proved that the heights of the cylinders must be at least $\dfrac {7 \sqrt 3} 2$ of the diameters of their bases.