  We have built an ab-initio LDA energy database with over 60 hypothetical
extended structures of pure Boron, in each of which the coordination
environment of each atom is equivalent. Focusing on eleven 6-coordinated
structures, which are most relevant to the observed Boron phases, we deduce a
nearest-neighbor-only 2-body interaction, refined by potentials that depend on
angles and asymmetry within the local atomic environment. The resulting
effective potentials describe the 6-coordinated structures with an average
error of 0.1 eV/atom, and favor the environment most often seen in real Boron.
