How can I show that if a figure in $\mathbb R^n$ or has $2$ centers of symmetry, it has infinity in a mathematical way?
this is the defintion of center of simmetry in $\mathbb R^2$ = A point, within an object or figure, through which any straight line also passes through two points on the edge of the figure at the same distance from the centre but on opposite sides.
my consideration about this problem was to use the fact that it this figure has 2 centers of simmetry then it is similar to a line in $\mathbb R^2$ and the line has infinity centers . but how can i prove in a more solid way?