  After recapitulating the procedure to find the bands and the states occurring
in the $\mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters
are placed at the vertexes of an equilateral triangle, we obtain the selection
rules for electromagnetic transitions. While the alpha cluster structure leads
to the cancellation of E1 transitions, the approximations carried out in
deriving the roto-vibrational hamiltonian lead to the disappearance of M1
transitions. Furthermore, although in general the lowest active modes are E2,
E3, $\cdots$ and M2, M3, $\cdots$, the cancellation of M2, M3 and M5
transitions between certain bands also occurs, as a result of the application
of group theoretical techniques drawn from molecular physics. These
implications can be very relevant for the spectroscopic analysis of
$\gamma$-ray spectra of $^{12}$C.
