Geometry of depolarizing channels

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.