Spontaneous Symmetry Breaking -Conceptual Question

[BWV]

what is the relationship between unstable equilibria and spontaneous symmetry breaking?

Would this qualify as an example of spontaneous symmetry breaking?
Take a (perfectly round and unlabeled) pencil standing upright on its eraser so there is a U(1) symmetry on its original position which is spontaneously broken when the system is disturbed and the pencil falls over to point at some angle on a circle around its original position?

 

[mfb]

That is an example of spontaneous symmetry breaking, right.

An unstable equilibrium could be somewhere without symmetry.

 

[BWV]

Ok, thanks.