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

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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Abstract

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 3.0).
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Onaka, S. Superspheres: Intermediate Shapes between Spheres and Polyhedra. Symmetry 2012, 4, 336-343.

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