The hydrolysis of Ln(ClO4)(3) in the presence of acetate leads to the assembly of the three largest known lanthanide-exclusive cluster complexes, [Nd-104(ClO4)(6)(CH3COO)(60)(mu(3)-OH)(168)(mu(4)-O)(30)(H2O)(112)].(ClO4)(18).(CH3CH2OH)(8).xH(2)O (1, x approximate to 158) and [Ln(104)(ClO4)(6)(CH3COO)(56)(mu(3)-OH)(168)(mu(4)-O)(30)(H2O)(112)].(ClO4)(22).(CH3CH2OH)(2).xH(2)O (2, Ln = Nd; 3, Ln = Gd; x approximate to 140). The structure of the common 104-lanthanide core, abbreviated as Ln(8)@Ln(48)@Ln(24)@Ln(24), features a four-shell arrangement of the metal atoms contained in an innermost cube (a Platonic solid) and, moving outward, three Archimedean solids: a truncated cuboctahedron, a truncated octahedron, and a rhombicuboctahedron. The magnetic entropy change of Delta Sm = 46.9 J kg(-1) K-1 at 2 K for Delta H = 7 T in the case of the Gd-104 cluster is the largest among previously known lanthanide-exclusive cluster compounds.