An approach of the structural modelling of the decagonal phase and of the trigonal phase in Al80Mn20 is given, in terms of the icosahedral units existing in the icosahedral phase and the cubic α phase (AlMnSi). Structures of rings are proposed. Measurements of the density of the icosahedral and T phases suggest furthermore the existence of triacontahedra concentric to the icosahedra in both phases