Do there exist geometric figures with multiple centers of symmetry? 
Do there exist geometric figures with multiple centers of symmetry? Under what conditions does the center symmetry lie inside a geometric figure?

Recall the definition of a center of symmetry: A center of symmetry $O$ of a closed figure $\mathcal{F}$ is a point such that for any $X,Y$ on $\mathcal{F}$ with $X,O,Y$ collinear, $OX = OY$.
It would make sense that there are figures with multiple centers of symmetry, but I didn't think of any. Also, I conjecture that the center of symmetry always lies inside a convex geometric figure unless that figure is a point. This is obviously not true for nonconvex.

A figure consisting of two (sufficiently close) parallel segments has infinitely many centers of symmetry. Or consider two parallel plates. If the figure has to be connected, then connect a pair of corresponding ends to make a rectangular 'C' shape (you might need to adjust dimensions).
