  There are continuum many clones on a three-element set even if they are
considered up to \emph{homomorphic equivalence}. The clones we use to prove
this fact are clones consisting of \emph{self-dual operations}, i.e.,
operations that preserve the relation $\{(0,1),(1,2),(2,0)\}$. However, there
are only countably many such clones when considered up to equivalence with
respect to \emph{minor-preserving maps} instead of clone homomorphisms. We give
a full description of the set of clones of self-dual operations, ordered by the
existence of minor-preserving maps. Our result can also be phrased as a
statement about structures on a three-element set, ordered by primitive
positive constructability, because there is a minor-preserving map from the
polymorphism clone of a finite structure $\mathfrak A$ to the polymorphism
clone of a finite structure $\mathfrak B$ if and only if there is a primitive
positive construction of $\mathfrak B$ in $\mathfrak A$.
