Higher multipoles of highly symmetric charge distributions over Platonic solids

Abstract

Abstract We analyze higher multipole moments (beyond dipole and quadrupole) in the expansion of the electrostatic potential produced by discrete as well as volume, surface, and linear continuous distributions of charges over five Platonic solids. In the case of tetrahedron, the lowest non-zero multipole moment is octupole. As the number of polyhedron vertices grows, the first non-zero elements arise at higher multipoles. Namely, for octahedron and cube, the lowest non-zero multipole moment is hexadecapole (24-pole). For icosahedron and dodecahedron, non-zero elements appear first in the 26-pole moment tensors.