The phonon dispersion relations and IR spectrum of a C-20-based solid recently identified experimentally [Iqbal et al. , Eur. Phys. J. B 31, 509 (2003)] have been computed by density functional perturbation theory. Other competitive structures made by assembling C-20 clusters have been considered as well. In particular, we have computed the structure and the Raman spectra of two-dimensional polymeric phases of hydrogenated C-20 clusters which might be formed under different synthesis conditions. Fingerprints of the different phases have been identified in the vibrational spectra which could be used in the experimental search of C-20-based solids.