  The nuclear magnetic octupole moment is revisited as a potentially useful
observable for nuclear structure studies. The magnetic octupole moment,
$\Omega$, is examined in terms of the nuclear collective model including weak
and strong coupling. Single-particle formulation is additionally considered in
the overall comparison of theoretical predictions with available experimental
data. Mirror nuclei symmetry is examined in terms of the magnetic octupole
moment isoscalar and isovector terms. A full list of predictions for $\Omega$
of odd-proton and odd-neutron nuclei in medium-heavy mass regimes of the
nuclear chart is produced aiming at providing starting values for future
experimental endeavors.
