Let $G$ and $H$ be connected graphs with the same labelled edge set $E$. Suppose that, under the identity map on $E$, the cycles of $H$ are exactly the bonds of $G$, and the bonds of $H$ are exactly the cycles of $G$. Then $G$ has a cellular embedding in the sphere for which $H$ is a geometric dual graph. Conversely, every geometric dual pair of connected plane graphs has this cycle-bond correspondence.