  The Kreweras complementation map is an anti-isomorphism on the lattice of
noncrossing partitions. We consider an analogous operation for plane trees
motivated by the molecular biology problem of RNA folding. In this context, we
explicitly count the orbits of Kreweras' map according to their length as the
number of appropriate symmetry classes of trees in the plane. These enumeration
results are consolidated into a single implicit formula under the cyclic
sieving phenomenon.
