The Icosahedral Symmetry Antiferromagnetic Heisenberg Model
  The antiferromagnetic Heisenberg model on icosahedral symmetry $I_{h}$ fullerene clusters exhibits unconventional magnetic properties, despite the lack of anisotropic interactions. At the classical level, and for number of sites $n \leq 720$, the magnetization has two discontinuities in an external magnetic field, except from the dodecahedron where it has three, emphasizing the role of frustration introduced by the pentagons in the unusual magnetic properties. For spin magnitudes $s_{i}={1/2}$ there is a discontinuity of quantum character close to saturation for $n \leq 80$. This common magnetic behavior indicates that it is a generic feature of $I_{h}$ fullerene clusters, irrespectively of $n$. 
N.P. Konstantinidis