  The algebraic molecular model is used in $^{12}$C to construct densities and
transition densities connecting low-lying states of the rotovibrational
spectrum, first and foremost those belonging to the rotational bands based on
the ground and the Hoyle states. These densities are then used as basic
ingredients to calculate, besides electromagnetic transition probabilities,
nuclear potentials and formfactors to describe elastic and inelastic
$\alpha$+$^{12}$C scattering processes. The calculated densities and transition
densities are also compared with those obtained by directly solving the problem
of three interacting alpha's within a three-body approach where continuum
effects, relevant in particular for the Hoyle state, are properly taken into
account.
