Polarizabilities of platonic solids

This article presents results of a numerical effort to determine the dielectric polarizabilities of the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The polarizability is calculated by solving a surface integral equation, in which the unknown potential is exp...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2004-09, Vol.52 (9), p.2226-2233
Main Authors: Sihvola, A., Yla-Oijala, P., Jarvenpaa, S., Avelin, J.
Format: Article
Language:English
Subjects:
Anisotropic magnetoresistance
Antennas
Applied classical electromagnetism
Approximation
Dielectric constant
Dielectrics
Electromagnetic scattering
Electromagnetism
electron and ion optics
Electrostatic analysis
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Geometry
Integral equations
Mathematical analysis
Mathematical models
Permittivity
Physics
Polarization
Polyhedrons
Shape
Solids
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article presents results of a numerical effort to determine the dielectric polarizabilities of the five regular polyhedra: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The polarizability is calculated by solving a surface integral equation, in which the unknown potential is expanded using third-order basis functions. The resulting polarizabilities are accurate to the order of 10/sup -4/. Approximation formulas are given for the polarizabilities as functions of permittivity. Among other results, it is found that the polarizability of a regular polyhedron correlates more strongly with the number of edges than with the number of faces, vertices, or the solid angle seen from a vertex.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2004.834081