The 212 species of structural phase transitions which break macroscopic symmetry are analyzed with respect to the occurrence of time-reversal invariant vector and bidirector order parameters. The possibility of discerning the orientational domain states of the low-symmetry phase by these `vectorlike physical properties has been derived using a computer algorithm exploiting the concept of polar, axial, chiral and neutral dipoles. It is argued that for species 32 > 3, 422 > 4 and 622 > 6, Bogdanov-Yablonskii phenomenological theory for a ferromagnetic Bloch Skyrmions applies also to the ferroelectric Bloch Skyrmions. In these fully-ferroelectric and nonferroelastic species, the Ginzburg Landau functional allows a pseudo-Lifshitz invariant of chiral bidirector symmetry, analogous to the chiral Dzyaloshinskii-Moria term assumed in magnetic Bloch Skyrmion theory.
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