We investigate the symmetry of the boron buckyball and a related boron nanotube. Using large-scale ab initio calculations up to second-order Moller-Plesset perturbation theory, we have determined unambiguously the equilibrium geometry/symmetry of two structurally related boron clusters: the B-80 fullerene and the finite-length (5 0) boron nanotube. The B-80 cluster was found to have the same symmetry, I-h, as the C-60 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 D-5d instead of C-5v 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. (C) 2010 Elsevier B.V. All rights reserved.