  We develop a general stability analysis for objective structures, which
constitute a far reaching generalization of crystal lattice systems. We show
that these particle systems, although in general neither periodic nor space
filling, allow for the identification of stability constants in terms of
representations of the underlying symmetry group and interaction potentials.
From our representation results a general computational algorithm to test
objective structures for their stability is derived. By way of example we show
that our method can be applied to verify the stability of carbon nanotubes with
chirality.
