  Maxwell's rule from 1864 gives a necessary condition for a framework to be
isostatic in 2D or in 3D. Given a framework with point group symmetry, group
representation theory is exploited to provide further necessary conditions.
This paper shows how, for an isostatic framework, these conditions imply very
simply stated restrictions on the numbers of those structural components that
are unshifted by the symmetry operations of the framework. In particular, it
turns out that an isostatic framework in 2D can belong to one of only six point
groups. Some conjectures and initial results are presented that would give
sufficient conditions (in both 2D and 3D) for a framework that is realized
generically for a given symmetry group to be an isostatic framework.
