The Raman and infrared spectra of α-rhombohedral boron B12 and of B4C boron carbide have been determined by accurate first-principles calculations based on density-functional perturbation theory. Our results account for all the features observed experimentally, including the characteristic Raman-active mode around 530 cm−1, which is attributed to the libration of the icosahedra. A comparison of the calculated vibrational spectra with experimental data allows the first unambiguous determination of the atomic structure of B4C. Analysis of our data shows that the high bulk moduli of α-rhombohedral boron and of B4C boron carbide – 220 and 240 GPa, respectively – are mainly determined by the stiff intramolecular bonding within each icosahedron. This finding is at variance with the current interpretation of recent neutron diffraction data on B4C in terms of a postulated larger stiffness of the intermolecular bonds in icosahedral solids (inverted molecular compressibility). Our results show that icosahedral boron-rich solids should be considered as members of a new class of covalently bonded materials.