The controled growth of large single grain of quasicrystalline phase in metallic alloys is a difficult task that requires a detailled knowledge of the corresponding phase diagram. We discuss the metallurgical specificities of the ternary systems AlCuFe and AlPdMn with respect to single icosahedral grain elaboration. We show that adding a few percents of Silicon in the AlCuFe system leads to stabilize two low order cubic approximants one, α, based on Bergman clusters with a parent F-type icosahedral phase and the other, α', based on Mackay clusters with a parent P-type icosahedral phase. A section of this quaternary phase diagram at constant Si content shows that these cubic phases have no common stability region but are located on opposite sides of an orthorhombic phase that is expected to be a complex synthetic structure mixing both Mackay and Bergman type atomic clusters.