Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (N_F) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

固体铁电体的自发电极化遵循晶轴的排列方向。不同取向的极化域由畴壁 (DW) 分隔，畴壁主要是平坦的，并沿着由整体平移顺序和样品表面决定的方向延伸。在这里，我们探索铁电向列 ( _NF) 液晶，它是一种具有极性长程取向有序但没有晶轴或晶面的流体。我们证明，在没有体积和表面对齐轴的情况下，DW 的形状为圆锥截面。二次曲线平分两个相邻极化场之间的角度以避免电荷。几千年来已知的圆锥截面的显着平分特性作为液体铁电体的固有特征起着核心作用。这些发现可能有助于设计电极化和空间电荷的模式。