  We study cluster tilting modules in mesh algebras of Dynkin type, providing a
new proof for their existence. In all but one case, we show that these are
precisely the maximal rigid modules, and that they are equivariant for a
certain automorphism. We further study their mutation, providing an example of
mutation in an abelian category which is not stably 2-Calabi-Yau, and
explicitly describe the combinatorics.
