  A topological RNA structure is derived from a diagram and its shape is
obtained by collapsing the stacks of the structure into single arcs and by
removing any arcs of length one. Shapes contain key topological, information
and for fixed topological genus there exist only finitely many such shapes. We
shall express topological RNA structures as unicellular maps, i.e. graphs
together with a cyclic ordering of their half-edges. In this paper we prove a
bijection of shapes of topological RNA structures. We furthermore derive a
linear time algorithm generating shapes of fixed topological genus. We derive
explicit expressions for the coefficients of the generating polynomial of these
shapes and the generating function of RNA structures of genus $g$. Furthermore
we outline how shapes can be used in order to extract essential information of
RNA structure databases.
