Summary: A polychromatic \(k\)-coloring of a map \(G\) on a surface is a \(k\)-coloring \(c: V(G)\to\{1,\dots, k\}\) such that each face of \(G\) has \(k\) distinct colors on its boundary vertices.
In this paper, we give a sufficient condition for quadrangulations on any surface to have a polychromatic proper 3-coloring. Moreover, the condition is necessary for quadrangulations on the projective plane.