The Quest for a Bicubic Planar Dessin D'Enfants

Question

The basic building block in any cubic bipartite graph is the following:

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This fragment is taken from the french wiki page on Dessin D'Enfants (for a english translation go here), but, up to now, I've never seen a full-blown example of a bicubic graph, that qualifies as a dessin. By the latter, I mean, given such a graph, what is the corresponding $p(x)$?

Can anyone point towards a (simple) worked-out example?

UPDATE Looks like I found something

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Unfortunately the paper "Bipartite graph embeddings, Riemann surfaces and Galois groups" by Gareth A. Jones is not freely available...

Answer 1

Okay, I found something in

"The field of moduli and fields of definition of dessins d’enfants" by Moises Herradon Cueto

As an example, we can take the cube dessin on the sphere

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... This holomorphic map is given by the equation $$ f(z)=-\frac{1}{12\sqrt 3} \frac{(z^4-2\sqrt 3 z^2 -1)^3}{z^2(z^4+1)^2}$$