Multipolar physics and their hidden orders have been widely discussed in the context of heavy fermions and frustrated magnets. However, despite extensive research, there are few examples of purely multipolar systems in the absence of magnetic dipoles. Here, we show the magnetic behavior of an icosahedral quasicrystal is generally described by multipoles, and in a specific case by pure magnetic octupoles, resulting from the interplay of spin-orbit coupling and crystal field splitting. Importantly, we emphasize that non-crystallographic symmetries of quasicrystals result in multipolar degrees of freedom, in contrast to the conventional crystals. We first classify the characteristics of multipoles and derive the effective spin Hamiltonian. We then explore how frustration and quantum fluctuations induce entangled quantum phases. Our study presents the magnetic icosahedral quasicrystal as a platform for investigating the exotic multipolar physics.

多极物理及其隐藏秩序已在重费米子和受挫磁体的背景下得到广泛讨论。然而，尽管进行了广泛的研究，但在没有磁偶极子的情况下纯多极系统的例子却很少。在这里，我们展示了二十面体准晶体的磁性行为通常由多极子描述，在特定情况下由纯磁性八极子描述，这是由自旋轨道耦合和晶体场分裂的相互作用产生的。重要的是，我们强调，与传统晶体相比，准晶体的非晶体对称性导致多极自由度。我们首先对多极子的特征进行分类并推导有效自旋哈密顿量。然后我们探讨挫败和量子涨落如何引起纠缠的量子相。我们的研究将磁性二十面体准晶体作为研究奇异多极物理的平台。