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Herradon has recently provided an example of a regular dessin d’enfant whose field of moduli is the non-abelian extension Q ( 3 √2) answering in this way a question due to Conder, Jones, Streit and Wolfart. In this paper we observe that Herradon’s example belongs naturally to an infinite series of such kind of examples; for each prime integer p  ≥ 3 we construct a regular dessin d’enfant whose field of moduli is the non-abelian extension Q ( p √2) ; for p  = 3 it coincides with Herradon’s example.

Regular dessins d'enfants with field of moduli Q(p√2)