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In this work we prove constructively that the complementof a convex polyhedronand the complementof its interior are regular images of. If K is moreover bounded, we can assure thatandare also polynomial images of. The construction of such regular and polynomial maps is done by double induction on the number of facets (faces of maximal dimension) and the dimension of K; the careful placing (first and second trimming positions) 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.

On Complements of Convex Polyhedra as Polynomial and Regular Images of ℝ n