  We study the vacuum geometry prescribed by the gauge invariant operators of
the MSSM via the Plethystic Programme. This is achieved by using several tricks
to perform the highly computationally challenging Molien-Weyl integral, from
which we extract the Hilbert series, encoding the invariants of the geometry at
all degrees. The fully refined Hilbert series is presented as the explicit sum
of 1422 rational functions. We found a good choice of weights to unrefine the
Hilbert series into a rational function of a single variable, from which we can
read off the dimension and the degree of the vacuum moduli space of the MSSM
gauge invariants. All data in Mathematica format are also presented.
