The established structure of α-rhombohedral boron, based on one B(12) icosahedron per unit cell only, is put in question. A careful evaluation of the IR-active phonons in comparison with B(6)O, B(4.3)C and β-rhombohedral boron makes it evident that-aside from the B(12) icosahedra-the α-rhombohedral boron structure also contains single boron atoms. We assume these single atoms replace the currently assumed inter-icosahedral three-centre-bonds by covalently saturating the outward directing bonds of the equatorial atoms of the three adjacent icosahedra. Indeed, the implied structure formula B(12)B(2) is not supported by previous density measurements. The IR-phonon spectra of the related structures are correlated and merely shifted relative to one another; significant features depend quantitatively on the actual structure, but they can be easily allocated.