  A novel method is presented which employs advanced numerical techniques used
in the engineering sciences to find and study the properties of nontrivial
vacua of gauged extended supergravity models. While this method only produces
approximate numerical data rather than analytic results, it overcomes the
previous limitation of only being able to find vacua with large residual
unbroken gauge symmetry groups. The effectiveness of this method is
demonstrated by applying it to the technically most challenging D>=3 scalar
potential -- that of SO(8) X SO(8) gauged N=16 Chern-Simons Supergravity in
D=3. Extensive data on the properties of 99 different vacua (92 of them new) of
this model are given. Furthermore, techniques are briefly discussed which
should allow using this numerical information as an input to the construction
of semi-automatic stringent analytic proofs on the locations and properties of
vacua. It hence is argued that these combined techniques presumably are
powerful enough to systematically map all the nontrivial vacua of every
supergravity model.
