Summary: In [Fundam. Math. 151, 47--52 (1996; Zbl 0860.54028)], \textit{M.~Levin} proved that the set of all Bing maps of a compact metric space to the unit interval is a dense \(G_\delta\)-subset of the space of all maps. In [Bull. Pol. Acad. Sci. Math. 44, 147--156 (1996; Zbl 0867.54020)], \textit{J.~Krasinkiewicz} independently proved that the set of all Bing maps of a compact metric space to an \(n\)-dimensional manifold (\(n \geq 1\)) is a dense \(G_\delta\)-subset of the space of maps. In [Fundam. Math. 163, 229--239 (2000; Zbl 0971.54013)], \textit{J.~Song} and \textit{E.~D.~Tymchatyn}, solving some problems of \textit{J.~Krasinkiewicz} [loc. cit.] proved that the set of all Bing maps of a compact metric space to a nondegenerate connected polyhedron is a dense \(G_\delta\)-subset of the space of maps. We investigate the existence of surjective Bing maps from continua to polyhedra.