Suppose $\mathcal{A}, \mathcal{B}\subset\mathbb{R}^2$ are polytopes. Suppose also that I know that there exists a polytope $\mathcal{X}$ such that $\mathcal{A}+\mathcal{X}=\mathcal{B}$.
Is $\mathcal{X}$ defined uniquely? (How about uniquely "up to translation"?)
This means that the idea of "subtraction", as the opposite of addition, makes sense. (I know that there is a subtraction defined for polytopes, but I am having some trouble connecting it to the above.)
The solution to my question follows from the "duplication" link as if $\mathcal{A}+\mathcal{X}=\mathcal{B}$ and $\mathcal{A}+\mathcal{Y}=\mathcal{B}$ then $\mathcal{A}+\mathcal{X}=\mathcal{A}+\mathcal{Y}$, and hence $\mathcal{X}=\mathcal{Y}$ as required.