Density functional theory is demonstrated to reproduce the 13C and 11B NMR chemical shifts of icosahedral boron carbides with sufficient accuracy to extract previously unresolved structural information from experimental NMR spectra. B4C can be viewed as an arrangement of 3-atom linear chains and 12-atom icosahedra. According to our results, all the chains have a CBC structure. Most of the icosahedra have a B11C structure with the C atom placed in a polar site, and a few percent have a B (12) structure or a B10C2 structure with the two C atoms placed in two antipodal polar sites.