  The physical properties of crystals are governed by their symmetry according
to Neumann's principle. However, we present a case that contradicts this
principle wherein the polarization is not invariant under its symmetry. We term
this phenomenon as unconventional ferroelectricity in violation of Neumann's
principle (UFVNP). Our group theory analysis reveals that 33 symmorphic space
groups have the potential for UFVNP, with 26 of these symmorphic space groups
belonging to non-polar groups. Notably, the polarization component in UFVNP
materials is quantized. Our theory can explain the experimentally proven
in-plane polarization of the monolayer {\alpha}-In2Se3, which has C3v symmetry.
Additionally, we employ first-principles calculations to demonstrate the
existence of UFVNP in Td phase AgBr, which was not initially anticipated to
exhibit polarization. Thus, UFVNP plays an integral role in characterizing and
exploring the possible applications of ferroelectrics, significantly expanding
the range of available materials for study.
