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Symmetry 2012, 4(3), 336-343; doi:10.3390/sym4030336

Superspheres: Intermediate Shapes between Spheres and Polyhedra

Department of Materials Science and Engineering, Tokyo Institute of Technology, 4259-J2-63 Nagatsuta, Yokohama 226-8502, Japan
Received: 16 May 2012 / Revised: 20 June 2012 / Accepted: 25 June 2012 / Published: 3 July 2012
(This article belongs to the Special Issue Polyhedra)
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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.
Keywords: supersphere; particle; precipitate; materials science; crystallography supersphere; particle; precipitate; materials science; crystallography
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Onaka, S. Superspheres: Intermediate Shapes between Spheres and Polyhedra. Symmetry 2012, 4, 336-343.

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