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Using an x-y-z coordinate system, the equations of the superspheres have been extended to describe intermediate shapes between a sphere and various convex polyhedra. Near-polyhedral shapes composed of {100}, {111} and {110} surfaces with round edges are treated in the present study, where {100}, {111} and {110} are the Miller indices of crystals with cubic structures. The three parameters p, a and b are included to describe the {100}- {111}-{110} near-polyhedral shapes, where p describes the degree to which the shape is a polyhedron and a and b determine the ratios of the {100}, {111} and {110} surfaces. [ABSTRACT FROM AUTHOR]