We extend the notion of Rauzy induction interval exchange transformations to case toral $\mathbb{Z}^2$-rotation, i.e., $\mathbb{Z}^2$-action defined by rotations on a 2-torus. If $\mathcal{X}_{\mathcal{P},R}$ denotes symbolic dynamical system corresponding partition $\mathcal{P}$ and $R$ such that is Cartesian sub-domain $W$, we express 2-dimensional configurations in as image under $2$-dimensi...