  In this article we deduce necessary and sufficient conditions for the
presence of `Conti-type', highly symmetric, exactly-stress free constructions
in the geometrically non-linear, planar $n$-well problem, generalising results
of [CKZ17]. Passing to the limit $n\rightarrow \infty$, this allows us to treat
solid crystals and nematic elastomer differential inclusions simultaneously. In
particular, we recover and generalise (non-linear) planar tripole star type
deformations which were experimentally observed in [MA80,MA80a,KK91]. Further
we discuss the corresponding geometrically linearised problem.
