  Symmetry classification of the magnetic vortices and skyrmions has been
suggested. Relation between symmetry based predictions and direct calculation
has been shown. It was shown, that electric dipole moment of the vortex is
located inside the small vortex core. The antivortices and antiskyrmions do not
carry the total core electric dipole induced by the flexomagnetoelectric
interaction in the hexoctahedral cubic crystal. The volumetric bound electric
charge is distributed around the core. Switching of the core electric dipole
direction produces the switching of the core magnetization or vortex chirality
and vice versa. The vortices and skyrmions with time-invariant enantiomorphism
have two degenerative states: clockwise and counterclockwise state.
