  We construct a special embedding of the translation quiver $\mathbb{Z}Q$ in
the three-dimensional affine space $\mathbb{R}^{3}$ where $Q$ is a finite
connected acyclic quiver and $\mathbb{Z}Q$ contains a local slice whose quiver
is isomorphic to the opposite quiver $Q^{op}$ of $Q.$ Via this embedding, we
show that there exists an involutive anti-automorphism of the translation
quiver $\mathbb{Z}Q.$ As an immediate consequence, we characterize explicitly
the group of cluster automorphisms of the cluster algebras of seed $(X,Q)$,
where $Q$ and $Q^{op}$ are mutation equivalent.
