Small isolated clusters of alkali halides and analogous divalent speci
es composed of closed-shell atomic ions are known to prefer densely pa
cked structures similar but not identical to the repent units found in
the solid state. Beyond the simple cube structure that occurs, for ex
ample, in alkali halide tetramers, no other ionic polyhedral structure
s containing only atomic ions are known. In this article, we explore t
he possibility of other three-dimensional structures, and we show comp
utationally that two molecules, Mg2Al4O8 and Na4Mg4O6, have very stabl
e distorted rhombic dodecahedron structures. We therefore suggest that
a wide variety of stable polyhedral structures could be constructed f
rom ions, and we offer a simple electrostatic model for predicting whi
ch polyhedral ionic structures should be stable and which should not.
We Feint out that several recently observed inorganic solid state mate
rials contain core structures that fit our predictions.