%0 Journal Article
%T On the complements of 3-dimensional convex polyhedra as polynomial images of ${\mathbb R}^3$
%A Jos¨¦ F. Fernando
%A Carlos Ueno
%J Mathematics
%D 2012
%I arXiv
%X We prove that the complement ${\mathcal S}:={\mathbb R}^3\setminus{\mathcal K}$ of a 3-dimensional convex polyhedron ${\mathcal K}\subset{\mathbb R}^3$ and its closure $\overline{{\mathcal S}}$ are polynomial images of ${\mathbb R}^3$. The former techniques cannot be extended in general to represent such semialgebraic sets ${\mathcal S}$ and $\overline{{\mathcal S}}$ as polynomial images of ${\mathbb R}^n$ if $n\geq4$.
%U http://arxiv.org/abs/1212.1815v3