Negami's Planar Cover Conjecture

Let $G$ be a connected finite simple graph. A finite planar cover of $G$ is a finite graph that covers $G$ in the graph-theoretic sense, with the covering graph planar. Negami's Planar Cover Conjecture. The graph $G$ has a finite planar cover if and only if it can be embedded on the projective plane. The sufficiency is clear, while the necessity remains open; the rotation-compatible version has already been proved.