Polarizabilities of Platonic Solids

摘要

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 from a vertex.