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In this paper, we remind previous results about the tilings $\{p,q\}$ of thehyperbolic plane. We introduce two new ways to split the hyperbolic plane inorder to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.

About a new splitting for the algorithmic study of the tilings $\{p,q\}$ of the hyperbolic plane when $q$ is odd