Clusters often grow by adding concentric layers of atoms in such a way
that the overall symmetry of the cluster is left unchanged. Icosahedr
al shell structure was first envisioned by Mackay(1) while working on
the difficult geometric problem of sphere packing. Shells with icosahe
dral symmetry have since been identified in clusters composed of inert
-gas atoms,(2-4) metal atoms,(5,6) and even complex molecules. In this
report experimental evidence will be presented for shell structures b
ased on geometries other than the Mackay icosahedra. The results which
will be discussed include: (a) octahedral shells in Al and In cluster
s, (b) non-Mackay-like icosahedral shells of metal deposited expitaxia
lly on a C-60 molecule and (c) new data on very large cubic shells of
alkali halides. In all these cases, the evidence for shells consists o
f mass spectrometric anomalies that appear periodically when plotted o
n a (mass)(1/3) scale. Each geometry is associated with a unique perio
dicity.