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We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcalK}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ andits closure $\overline{{\mathcal S}}$ are polynomial images of ${\mathbb R}^3$.The former techniques cannot be extended in general to represent suchsemialgebraic sets ${\mathcal S}$ and $\overline{{\mathcal S}}$ as polynomialimages of ${\mathbb R}^n$ if $n\geq4$.

On the complements of 3-dimensional convex polyhedra as polynomial images of ${\mathbb R}^3$