Geodesic
Generic Dirichlet polygons and the modular group
Glasgow mathematical journal, Tome 26 (1985), pp. 129-141

Voir la notice de l'article provenant de la source Cambridge University Press

The concept of “marked polygon”, made explicit in this paper, is implicit in all studies of the relationships between the edges and vertices of a fundamental polygon for Fuchsian group, as well as in the topology of surfaces. Once the matching of the edges under the action of the group is known, one can deduce purely combinatorially the distribution of the vertices into equivalence classes, or cycles. Knowing a little more, the order of the rotation group fixing a vertex in each cycle, we can write down a presentation for the group. 
Macbeath, A. M. Generic Dirichlet polygons and the modular group. Glasgow mathematical journal, Tome 26 (1985), pp. 129-141. doi: 10.1017/S0017089500006133
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