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Hecke Triangle Groups and Dessins d'Enfants
We study finite-index subgroups of the Hecke triangle group $H_q$ of signature $(2,q,\infty)$ through the finite-edge tessellation, special polygons, and the associated dessins. The quotient finite-edge graph is a connected bipartite ribbon graph in which even vertices have degree $1$ or $2$ and odd
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