  We present a new class of boron sheets, composed of triangular and hexagonal
motifs, that are more stable than structures considered to date and thus are
likely to be the precursors of boron nanotubes. We describe a simple and clear
picture of electronic bonding in boron sheets and highlight the importance of
three-center bonding and its competition with two-center bonding, which can
also explain the stability of recently discovered boron fullerenes. Our
findings call for reconsideration of the literature on boron sheets, nanotubes,
and clusters.
