In 1985, L. D. James and G. A. Jones proved that the complete graph K-n defines a clean dessin d'enfant (the bipartite graph is given by taking as the black vertices the vertices of K-n and the white vertices as middle points of edges) if and only if n = p(e), where p is a prime. Later, in 2010, G. A. Jones, M. Streit and J. Wolfart computed the minimal field of definition of them. The minimal genus g > 1 of these types of clean dessins d'enfant is g = 7, obtained for p = 2 and e = 3. In that case, there are exactly two such clean dessins d'enfant (previously known as Edmonds maps), both of them defining the Fricke-Macbeath curve (the only Hurwitz curve of genus 7) and both forming a chiral pair. The uniqueness of the Fricke-Macbeath curve asserts that it is definable over Q, but both Edmonds maps cannot be defined over Qin fact they have as minimal field of definition the quadratic field Q (root-7). It seems that no explicit models for the Edmonds maps over Q (root-7) are written in the literature. In this paper we start with an explicit model X for the Fricke-Macbeath curve provided by Macbeath, which is defined over Q (e(2 pi i/7)), and we construct an explicit birational isomorphism L : X -> Z, where Z is defined over Q (root-7), so that both Edmonds maps are also defined over that field. Author Keywords:Riemann surfacealgebraic curvedessin d'enfantRegular 2015FONDECYTFONDECYT