%0 Journal Article
%T Superspheres: Intermediate Shapes between Spheres and Polyhedra
%A Susumu Onaka
%J Symmetry
%D 2012
%I MDPI AG
%R 10.3390/sym4030336
%X 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.
%K supersphere
%K particle
%K precipitate
%K materials science
%K crystallography
%U http://www.mdpi.com/2073-8994/4/3/336