  We use the symmetry-extended Maxwell rule established by Fowler and Guest to
detect states of self-stress in symmetric planar frameworks. The dimension of
the space of self-stresses that are detectable in this way may be expressed in
terms of the number of joints and bars that are unshifted by various symmetry
operations of the framework. Therefore, this method provides an efficient tool
to construct symmetric frameworks with many `fully-symmetric' states of
self-stress, or with `anti-symmetric' states of self-stress. Maximizing the
number of independent self-stresses of a planar framework, as well as
understanding their symmetry properties, has important practical applications,
for example in the design and construction of gridshells. We show the
usefulness of our method by applying it to some practical examples.
