A relation between the shape of Eden clusters and the number of perimeter sites per unit area of the surface is derived which is analogous to the Wulff construction of equilibrium shapes in thermodynamic systems. New data are presented for the surface width and the surface skewness of Eden clusters grown on a square lattice. The width depends on the average orientation of the surface with respect to the underlying lattice. Its corrections to scaling are discussed. The skewness has unexpected changes of sign.