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

Abstract

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

arXiv comment20 pages, 19 figures This version significantly improves version 1 of the paper, by answering questions remained open in the previous version and by bringing in a new solution to a case raised by the new study

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