Abstract

Herradon has recently provided an example of a regular dessin d'enfant whose field of moduli is the non-abelian extension Q(3 root 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 root 2); for p = 3 it coincides with Herradon's example.