Fernando Galván, José FranciscoUeno, Carlos2023-06-192023-06-1920141073-792810.1093/imrn/rnt112https://hdl.handle.net/20.500.14352/33886In this work we prove constructively that the complement $\R^n\setminus\pol$ of a convex polyhedron $\pol\subset\R^n$ and the complement $\R^n\setminus\Int(\pol)$ of its interior are regular images of $\R^n$. If $\pol$ is moreover bounded, we can assure that $\R^n\setminus\pol$ and $\R^n\setminus\Int(\pol)$ are also polynomial images of $\R^n$. The construction of such regular and polynomial maps is done by double induction on the number of \em facets \em (faces of maximal dimension) and the dimension of $\pol$; the careful placing (\em first \em and \em second trimming positions\em) of the involved convex polyhedra which appear in each inductive step has interest by its own and it is the crucial part of our technique.engjournal articlehttp://imrn.oxfordjournals.org/content/2014/18/5084http://arxiv.org/abs/1212.1813open access512Polynomial and regular maps and imagesconvex polyhedrafirst and second trimming positionstrimming mapsoptimizationPositivstellens¨atzeGeometria algebraica1201.01 Geometría Algebraica