  Denote Hrushovski's non-collapsed ab initio construction for an $n$-ary
relation by $\mathcal{M}_{\not\sim}$ and the analogous construction for a
symmetric $n$-ary relation by $\mathcal{M}_{\sim}$. We show that
$\mathcal{M}_{\not\sim}$ is isomorphic to a proper reduct of
$\mathcal{M}_{\sim}$ and vice versa, and that the combinatorial pregeometries
associated with both structures are isomorphic.
