  We give a complete combinatorial characterization of all possible
polarizations of powers of the graded maximal ideal $(x_1,x_2,\cdots,x_m)^n$ of
a polynomial ring in $m$ variables. We also give a combinatorial description of
the Alexander duals of such polarizations. In the three variable case $m=3$ and
also in the power two case $n=2$ the descriptions are easily visualized and we
show that every polarization defines a (shellable) simplicial ball. We give
conjectures relating to topological properties and to algebraic geometry, in
particular that any polarization of an Artinian monomial ideal defines a
simplicial ball.
