A quasi-platonic action of the group G on the Riemann surface S is a conformal action of G on S such that S/G is a sphere and the projection S -> S/G is branched over {0,1,infinity}/. The action is induced by a triple of (a, b, c) in G^3, generating G, with abc = 1: The quasi-platonic action induces a regular dessin d'enfant on S, and S is defined over a number field. The absolute Galois group Gal(Q/Q) acts on dessins, hence quasi-platonic actions, by acting on the coefficients of a defining equation of S. The action of f in Gal(Q/Q) on triples is (a,b,c)-> (ua^tu^(-1), vb^tv^(-1),wa^tw^(-1)), for some (u,v,w) in G^3, according to the branch cycle argument. The integer t is characterized by the action of f on cyclotomic subfields of Q, and (u,v,w) is determined by the action of  f  away from cyclotomic subfieelds. In this talk we discuss the action of the absolute Galois group on quasi-platonic actions on some simple groups. In particular, we show that the Galois action on quasi-platonic actions of PSL2(q) depends only the action on cyclotomic subfields.