I have got the following task here:
Prove, that you can't cover the "Plane" with convex polygons, which have more than $\,6\,$ vertices!
The answer is pretty obvious for $\,n=3\,$ vertices, because $ 6\cdot 60^\circ = 360^\circ$.
For $\,n=4\,$ it works too, because $4\cdot 90^\circ = 360^\circ$.
I think that $\,n=6\,$ is good too, but how do I prove, that other than that, it isn't possible to do that?