Superspheres: Intermediate shapes between spheres and polyhedra
type: Item
instance of: scholarly article
title: Superspheres: Intermediate shapes between spheres and polyhedra
zbMATH Open document ID: 1351.51022
author: Susumu Onaka
published in: Symmetry
publication date: 2016-12-09T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 74E15
zbMATH DE Number: 6662256
zbMATH Keywords: supersphere
zbMATH Keywords: particle
zbMATH Keywords: precipitate
zbMATH Keywords: materials science
zbMATH Keywords: crystallography
MaRDI profile type: Publication
full work available at URL: sym4030336
OpenAlex ID: W2050140992
cites work: Superspherical-shape approximation to describe the morphology of small crystalline particles having near-polyhedral shapes with round edges
DOI: 10.3390/SYM4030336
description: scientific article; zbMATH DE number 6662256