  A generalized depolarizing channel acts on an N-dimensional quantum system to
compress the ``Bloch ball'' in N^2-1 directions; it has a corresponding
compression vector. We investigate the geometry of these compression vectors
and prove a conjecture of Dixit and Sudarshan [1], namely that when N=2^d (i.e.
the system consists of d qubits) and we work in the Pauli basis then the set of
all compression vectors forms a simplex. We extend this result by investigating
the geometry in other bases; in particular we find precisely when the set of
all compression vectors forms a simplex.
