  The prism over a graph $G$ is the Cartesian product of $G$ with the complete
graph $K_2$. A graph $G$ is hamiltonian if there exists a spanning cycle in
$G$, and $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. In
[M.~Rosenfeld, D.~Barnette, Hamiltonian circuits in certain prisms, Discrete
Math. 5 (1973), 389--394] the authors conjectured that every 3-connected planar
graph is prism-hamiltonian. We construct a counterexample to the conjecture.
