Intensity anomalies in the mass spectra of clusters with composition C
60M(x) and C70M(x) (x = 0-500; M is-an-element-of {Ca,Sr,Ba}) seem to
be caused by the completion of metal layers around a central fullerene
molecule. The first layer is complete when one metal atom is situated
above each of the 32 or 37 rings of the fullerene cage. This property
appears to make it possible to ''count the rings'' of fullerenes. The
first and additional layers are described in terms of a periodically
reoccurring structure having icosahedral symmetry.