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https://en.wikipedia.org/wiki/Dessin_d%27enfant
Dessin d'enfant
Contents
1 History
1.1 19th century
1.2 20th century
2 Riemann surfaces and Belyi pairs
3 Maps and hypermaps
4 Regular maps and triangle groups
5 Trees and Shabat polynomials
6 The absolute Galois group and its invariants

Riemann surfaces and Belyi pairs
Each triangle in the triangulation has three vertices labeled 0 (for the black points), 1 (for the white points), or ∞. For each triangle, substitute a half-plane, either the upper half-plane for a triangle that has 0, 1, and ∞ in counterclockwise order or the lower half-plane for a triangle that has them in clockwise order, and for every adjacent pair of triangles glue the corresponding half-planes together along the portion of their boundaries indicated by the vertex labels. The resulting Riemann surface can be mapped to the Riemann sphere by using the identity map within each half-plane. Thus, the dessin d'enfant formed from f is sufficient to describe f itself up to biholomorphism. However, this construction identifies the Riemann surface only as a manifold with complex structure; it does not construct an embedding of this manifold as an algebraic curve in the complex projective plane, although such an embedding always exists.

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