  Point polarizable molecules at fixed spatial positions have solvable
electrostatic properties in classical approximation, the most familiar being
the Clausius-Mossotti (CM) formula. This paper generalizes the model and
imagines various applications to nanosystems. The behavior is worked out for a
sequence of octahedral fragments of simple cubic crystals, and the crossover to
the bulk CM law is found. Some relations to fixed moment systems are discussed
and exploited. The one-dimensional dipole stack is introduced as an important
model system. The energy of interaction of parallel stacks is worked out, and
clarifies the diverse behavior found in different crystal structures. It also
suggests patterns of self-organization which polar molecules in solution might
adopt. A sum rule on the stack interaction is found and tested. Stability of
polarized states under thermal fluctuations is discussed, using the
one-dimensional domain wall as an example. Possible structures for polar hard
ellipsoids are considered. An idea is formulated for enhancing polarity of
nanosystems by intentionally adding metallic coatings.
