  We have built a database of ab-initio total energies for elemental Boron in
over 60 hypothetical crystal structures of varying coordination $Z$, such that
every atom is equivalent. Fitting to each subset with a particular $Z$, we
extract a classical effective potential, written as a sum over coordination
shells and dominated by three-atom (bond angle dependent) terms. In the case
Z=6 (lowest in energy and most relevant), the classical potential has a typical
error of 0.1 eV/atom, and favours the ``inverted-umbrells'' environment seen in
real Boron.
