  The antiferromagnetic Heisenberg model on the dodecahedron possesses a number
of ground state magnetization discontinuities in a field at the classical and
quantum level, even though it lacks magnetic anisotropy. Here the model is
considered for two dodecahedra coupled antiferromagnetically along one of their
faces, as a first step to determine the magnetic response of collections of
fullerene molecules. The magnetic response is determined from the competition
among the intra-, interdodecahedra exchange and magnetic field energies. At the
classical level the discontinuities of the isolated dodecahedron are
renormalized by the interdodecahedral coupling, while new ones show up, with
the maximum number of ground state discontinuities being six for a specific
range of the coupling. In the full quantum limit where the individual spin
magnitude s=1/2, there are two ground state discontinuities originating in the
single discontinuity of the isolated dodecahedron, and another one due to the
intermolecular coupling, generating a total of three discontinuities which come
one right after the other. These results show that the magnetic response of
more than one dodecahedra interacting together is quite richer than the one of
a single dodecahedron.
