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We propose a novel procedure to calculate the scattering from faceted bodies based on the use of universal bases that are obtained by applying the SVD procedure to PO-derived basis function. These bases, which are constructed totally bypassing any MoM-type approach, can be used for all angles of incidence and their use leads to a matrix whose dimensions are relatively small. Moreover, it can be shown that the matrix dimensions are weakly dependent upon the size of the facets of the scatterer. The method enables us to solve scattering problems in a computationally efficient and numerically rigorous manner, and yields good results both for 2D and 3D problems.