  In this paper we complete the results of Sullivant and Sturmfels proving that
many of the algebraic group-based models for Markov processes on trees are
pseudo-toric. We also show in which cases these varieties are normal. This is
done by the generalization of the discrete Fourier transform approach. In the
next step, following Sullivant and Sturmfels, we describe a fast algorithm
finding a polytope associated to these algebraic models. However in our case we
apply the notions of sockets and networks extending the work of Buczynska and
Wisniewski who introduced it for the binary case.
