The creation of a perfect hollow nanoscopic sphere of metal centers is clearly an unrealizable synthetic challenge. It is, however, an inspirational challenge from the viewpoint of chemical architecture and also as finite molecular species may provide unique microscopic insight into the origin and onset of phenomena such as topological spin-frustration effects found in infinite 2D and 3D systems. Herein, we report a series of high-symmetry gadolinium(III) (S = 7/2) polyhedra, Gd20, Gd32, Gd50, and Gd60, to test an approach based on assembling polymetallic fragments that contain different polygons. Structural analysis reveals that the Gd20 cage resembles a dodecahedron; the vertices of the Gd32 polyhedron exactly reveal symmetry Oh; Gd50 displays an unprecedented polyhedron in which an icosidodecahedron Gd30 core is encapsulated by an outer Gd20 dodecahedral shell with approximate Ih symmetry; and the Gd60 shows a truncated octahedron geometry. Experimental and theoretical magnetic studies show that this series produces the expected antiferromagnetic interaction that can be modeled based on classical spins at the Gd sites. From the magnetization analyses, we can roughly correlate the derivative bands to the Gd-O-Gd angles. Such a magneto-structural correlation may be used as "fingerprints" to identify these cages.