  In 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.
