In Greek mythology, sailors feared the perils of getting near the whirlpool said to be created by the sea monster Charybdis, who created turbulence by swallowing huge amounts of water. Today, researchers are creating whirlpools in materials at the nano- and microscale, not from water but from magnetic spins or electric dipoles. In return, they have observed exotic phenomena and physics. On page 1050 of this issue, Guo et al. (1) provide another example of how the exacting control of materials is producing effects one thought impossible to achieve. They created self-assembled topological and toroidal polarization textures—that is, a toroidal polarization arrangement in which the polar toroidal dipole configuration corresponds to the field of a solenoid bent into a torus (see the figure, bottom) in ferroelectric polymers. Because of the exotic structure, this material exhibits properties not observed in its native state.