Is this a fundamental domain of 2-torus under the action of Z2?

Question

Let $U$ be a vector with relatively prime integer coordinates in $\mathbb{R}^2$. And let $V$ be another vector that is orthogonal to $U$ and the rectangle spanned by $U$ and $V$ are $1$. Is this rectangle a fundamental domain for $2$-torus under the $Z^2$-action?

Thank you.