Discrete symmetries are spatially ubiquitous but are often hidden in internal states of systems where they can have especially profound consequences. In this work we create and verify exotic magnetic phases of atomic spinor Bose–Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete polytope symmetries in their topological defects. Using carefully tailored spinor rotations and microwave transitions, we engineer singular line defects whose quantization conditions, exchange statistics, and dynamics are fundamentally determined by these underlying symmetries. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries. Such defects, with their non-commutative properties, could provide unconventional realizations of quantum information and interferometry.

离散对称性在空间上无处不在，但通常隐藏在系统的内部状态中，它们可能会产生特别深远的影响。在这项工作中，我们创建并验证了原子旋量 Bose-Einstein 凝聚体的奇异磁相，尽管它们具有连续特征和固有的空间各向同性，但在其拓扑缺陷中表现出复杂的离散多面体对称性。使用精心定制的旋量旋转和微波跃迁，我们设计了奇异线缺陷，其量化条件、交换统计和动力学从根本上由这些潜在的对称性决定。我们展示了如何用各种不同相中的原子填充涡线奇点导致核心结构具有磁性界面，并具有丰富的离散和连续对称性组合。这样的缺陷，