There is a close similarity between the cubic α-phase in AlMnSi and the icosahedral phase i-AlMnSi or AlMn. A transmission electron microscopy (T.E.M.) study of a melt-spun ribbon where the two phases coexist, establishes clearly their relationships. It is shown that both structures can be described with common basic unit -a double Al-Mn icosahedra- connected in paralle1 orientation along their 3-fold axes by octahedral Mn bonds. A deterministic connection of the icosahedra in the i-phase appears to be consistent with a 3 dim-Penrose tiling. A large size i-skeleton is then computer generated, where the decoration by icosahedra of the tiling , prescribed by steric constraints, is solved by a graph theory algorithm. Projections of the model on planes perpendicular to symmetry axes and calculated diffraction patterns, once compared high resolution T.E.M. and diffraction data, indicate that it contains the main point of the i-phase structure in these alloys