The Symmetry of the Boron Buckyball and a Related Boron Nanotube

We investigate the symmetry of the boron buckyball and a related boron nanotube. Using large-scale ab-initio calculations up to second-order M{\o}ller Plesset perturbation theory, we have determined unambiguously the equilibrium geometry/symmetry of two structurally related boron clusters: the B80 fullerene and the finite-length (5,0) boron nanotube. The B80 cluster was found to have the same symmetry, Ih, as the C60 molecule since its 20 additional boron atoms are located exactly at the centers of the 20 hexagons. Additionally, we also show that the (5,0) boron nanotube does not suffer from atomic buckling and its symmetry is D5d instead of C5v as has been described by previous calculations. Therefore, we predict that all the boron nanotubes rolled from the \alpha -sheet will be free from structural distortions, which has a significant impact on their electronic properties.