  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 (NF) 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.

Soft Condensed Matter;Materials Science