Beltrami vector fields with an icosahedral symmetry

Abstract

A vector field is called a Beltrami vector field, if B×(∇×B)=0. In this paper we construct two unique Beltrami vector fields I and Y, such that ∇×I=I, ∇×Y=Y, and such that both have an orientation-preserving icosahedral symmetry. Both of them have an additional symmetry with respect to a non-trivial automorphism of the number field Q(5).