  In an effort to understand the low temperature behavior of recently
synthesized molecular magnets we present numerical evidence for the existence
of a rotational band in systems of quantum spins interacting with
nearest-neighbor antiferromagnetic Heisenberg exchange. While this result has
previously been noted for ring arrays with an even number of spin sites, we
find that it also applies for rings with an odd number of sites as well as for
all of the polytope configurations we have investigated (tetrahedron, cube,
octahedron, icosahedron, triangular prism, and axially truncated icosahedron).
It is demonstrated how the rotational band levels can in many cases be
accurately predicted using the underlying sublattice structure of the spin
array. We illustrate how the characteristics of the rotational band can provide
valuable estimates for the low temperature magnetic susceptibility.
