Consider a hypergraph (of rank 3) $H = (V, E)$ (where the rank of $H$ is the maximum cardinality of a hyperedge). $H$ is said to be planar if we can construct a planar graph $G = (V, A)$, and a mapping $f$ from $E$ to the faces of $G$ such that $v \in E$ iff $v$ is adjacent to $f(E)$ in the drawing.

Further, a hypergraph is said to be 2-colorable if there is an assignment of the colors R, B to the vertices so that no edge is monochromatic.

It is known that $2$-coloring a hypergraph of rank 3 is NP-complete.

Is there anything known about the complexity of 2-coloring a *planar* hypergraph of rank 3 ?