  Three mutually perpendicular symmetry axes of the second order, inversion,
and time reversal can be used to construct a double point group denoted by
D2h(TD). Properties of this group are analyzed in relation to the symmetry and
symmetry-breaking effects within the mean-field (Hartree-Fock) theories, both
in even and odd fermion systems. We enumerate space symmetries of local
one-body densities, and symmetries of electromagnetic moments, that appear when
some or all of the D2h(TD) elements represent self-consistent mean-field
symmetries.
