Polarizabilities of platonic solids

Author

Sihvola, Ari ; Ylä-Oijala, Pasi ; Järvenpää, Seppo ; Avelin, Juha

Author_Institution

Electromagn. Lab., Helsinki Univ. of Technol., Espoo, Finland

Volume

52

Issue

9

fYear

2004

Firstpage

2226

Lastpage

2233

Abstract

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^-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.

Keywords

dielectric bodies; dielectric polarisation; integral equations; permittivity; cube polarisation; dielectric polarizability; dodecahedron polarisation; higher-order basis function; icosa-hedron polarisation; octahedron polarisation; permittivity; platonic solid; polyhedron correlation; polyhedron polarisation; solid angle; surface integral equation; tetrahedron polarisation; Anisotropic magnetoresistance; Dielectrics; Electromagnetic scattering; Electrostatic analysis; Geometry; Integral equations; Permittivity; Polarization; Shape; Solids; High-order basis functions; polarizability; polyhedra; surface integral equation;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2004.834081

Filename

1331608