  We investigate the state space of bipartite qutrits. For states which are
locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for
bipartite qubits--a magic simplex W. This is obtained via the Weyl group which
is a kind of ``quantization'' of classical phase space. We analyze how this
simplex W is embedded in the whole state space of two qutrits and discuss
symmetries and equivalences inside the simplex W. Because we are explicitly
able to construct optimal entanglement witnesses we obtain the border between
separable and entangled states. With our method we find also the total area of
bound entangled states of the parameter subspace under intervestigation. Our
considerations can also be applied to higher dimensions.
