The rhombohedral unit cells of -boron crystals and of hypothetical -boron quasicrystals were investigated by applying ab initio quantum-chemical methods. The atomic decorations of such unit cells are generally based on a suitable arrangement of eight boron icosahedra, and thus the mechanism of their cohesion was simulated by relaxing a B 96 supercluster composed of icosahedral boron clusters located at the vertices of the rhombohedral unit cells. Also, several alternative structures of B 96 clusters were proposed and compared to the rhombohedral phases. To this end, total energies of those structures were computed on the basis of all-electron calculations at the Har-tree+Fock self-consistent 5eld level of theory using the standard STO3G basis set. Due to the large number of degrees of freedom, the geometries of all isomers were optimized under reasonable symmetry constraints, but using analytical gradient methods. The resulting total energies show that segments of nanotubes and quasiplanar sheets turn out to be more stable than the unit cells of -boron (quasi) crystals, indicating new kinds of materials.