  Discovery of topological polarization textures has put ferroelectrics at the
frontier of topological matter science. High-symmetry ferroelectric oxide
materials allowing for freedom of the polarization vector rotation offer a
fertile ground for emergent topological polar formations, like vortices,
skyrmions, merons, and Hopfions. It has been commonly accepted that uniaxial
ferroelectrics do not belong in the topological universe because strong
anisotropy imposes insurmountable energy barriers for topological excitations.
Here we show that uniaxial ferroelectrics provide unique opportunity for the
formation of topological polarization networks comprising branching intertwined
domains with opposite counterflowing polarization. We report that they host the
topological state of matter: a crisscrossing structure of topologically
protected colliding head-to-head and tail-to-tail polarization domains, which
for decades has been considered impossible from the electrostatic viewpoint.
The domain wall interfacing the counterflowing domains is a multiconnected
surface, propagating through the whole volume of the ferroelectric.
