  Depolarizing maps acting on an N dimensional system are completely positive
maps resulting into compression of the Bloch ball along the different
polarization directions. In the qubit case these maps are a convex sum of four
extremal maps and form a simplex in the space of compression coefficients along
the three polarization directions. We calculate the compression domain for
three and four level systems. For a three level system the region has curved
surfaces, but it is a simplex for a four level system. We conjecture that it is
a simplex in the case of 2^n level systems.
