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We present the definition and computational algorithms for a new class of surfaces which are dual to the isosurface produced by the widely used marching cubes (MC) algorithm. These new isosurfaces have the same separating properties as the MC surfaces but they are comprised of quad patches that tend to eliminate the common negative aspect of poorly shaped triangles of the MC isosurfaces. Based upon the concept of this new dual operator, we describe a simple, but rather effective iterative scheme for producing smooth separating surfaces for binary, enumerated volumes which are often produced by segmentation algorithms. Both the dual surface algorithm and the iterative smoothing scheme are easily implemented.