A vector field is called a Beltrami vector field, if $B\times(\nabla\times B)=0$. In this paper we construct two unique Beltrami vector fields $\mathfrak{I}$ and $\mathfrak{Y}$, such that $\nabla\times\mathfrak{I}=\mathfrak{I}$, $\nabla\times\mathfrak{Y}=\mathfrak{Y}$, 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 $\mathbb{Q}(\,\sqrt{5}\,)$.

中文翻译：

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具有二十面体对称性的贝尔特拉米矢量场

如果$B\times(\nabla\times B)=0$，则向量场称为Beltrami 向量场。在本文中，我们构造了两个唯一的贝尔特拉米向量场 $\mathfrak{I}$ 和 $\mathfrak{Y}$，使得 $\nabla\times\mathfrak{I}=\mathfrak{I}$, $\nabla\ times\mathfrak{Y}=\mathfrak{Y}$，并且两者都具有保持方向的二十面体对称性。对于数域 $\mathbb{Q}(\,\sqrt{5}\,)$ 的非平凡自同构，它们都具有额外的对称性。