  Based on a numerical ab initio study, we discuss a structure model for a
broad boron sheet, which is the analog of a single graphite sheet, and the
precursor of boron nanotubes. The sheet has linear chains of sp hybridized
sigma bonds lying only along its armchair direction, a high stiffness, and
anisotropic bonds properties. The puckering of the sheet is explained as a
mechanism to stabilize the sp sigma bonds. The anisotropic bond properties of
the boron sheet lead to a two-dimensional reference lattice structure, which is
rectangular rather than triangular. As a consequence the chiral angles of
related boron nanotubes range from 0 to 90 degrees. Given the electronic
properties of the boron sheets, we demonstrate that all of the related boron
nanotubes are metallic, irrespective of their radius and chiral angle, and we
also postulate the existence of helical currents in ideal chiral nanotubes.
Furthermore, we show that the strain energy of boron nanotubes will depend on
their radii, as well as on their chiral angles. This is a rather unique
property among nanotubular systems, and it could be the basis of a different
type of structure control within nanotechnology.
