The hydrolysis of Ln(ClO4)3 in the presence of acetate leads to the assembly of the three largest known lanthanide-exclusive cluster complexes, [Nd104(ClO4)6(CH3COO)60(μ3-OH)168(μ4-O)30(H2O)112]·(ClO4)18·(CH3CH2OH)8·xH2O (1, x ≈ 158) and [Ln104(ClO4)6(CH3COO)56(μ3-OH)168(μ4-O)30(H2O)112]·(ClO4)22·(CH3CH2OH)2·xH2O (2, Ln = Nd; 3, Ln = Gd; x ≈ 140). The structure of the common 104-lanthanide core, abbreviated as Ln8@Ln48@Ln24@Ln24, 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 ΔS(m) = 46.9 J kg(-1) K(-1) at 2 K for ΔH = 7 T in the case of the Gd104 cluster is the largest among previously known lanthanide-exclusive cluster compounds.