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 Z2 × Z2 topological domains, atomic-scale dipole vortices, and negative piezoelectricity.The Landau theory of phase transitions provides an elegant common framework for both magnetic and polar systems. The one-to-one correspondence between physical characteristics, such as ordered phases -ferromagnetic (FM) vs ferroelectric (FE) states, antiferromagnetic (AFM) vs antiferroelectric (AFE) states [see Figs. 1(ab)]-, hysteresis loops, domains, and other properties is well recognized. However, ferrielectric (FiE) systems, with partially compensated collinear dipoles [Figs. 1(cd)], are rare (except in liquid crystals and in a few solids like hybrid improper ferroelectrics [1]) [2], while ferrimagnetic (FiM) materials are fairly common, e.g. Fe 3 O 4 .This incompleteness of dipole orders is even more dramatic with regards to noncollinearity. For magnets, spin noncollinearity has been widely studied [3,4], leading to exotic magnetism-driven polarization (P ) [5], skyrmions [6], and topological anomalous Hall effect [7]. There are several mechanisms to generate these crucial noncollinear spin orders. For example, in geometrically frustrated systems, such as two-dimensional (2D) triangular lattices, the AFM coupling between nearest-neighbor (NN) spins can generate the 120 • order [3]. For other lattices, the exchange frustration, typically involving competition between NN FM (J 1 ) and next-nearest-neighbor (NNN) AFM (J 2 ) couplings, can generate magnetic cycloid or helical arrangements [4].