  Within Landau theory, magnetism and polarity are homotopic, displaying a
one-to-one correspondence between most physical characteristics. However,
despite widely reported noncollinear magnetism, spontaneous noncollinear
electric dipole order as ground state is rare. Here a dioxydihalides family is
predicted to display noncollinear ferrielectricity, induced by competing
ferroelectric and antiferroelectric soft modes. This intrinsic noncollinearity
of dipoles generates unique physical properties, such as
$\mathbb{Z}_2\times\mathbb{Z}_2$ topological domains, atomic-scale dipole
vortices, and negative piezoelectricity.
