I am looking for software for computing/estimating volume of high-dimensional convex polyhedra. More specifically, I am interested in a program, which can handle bodies with $n$ vertices in $d$-dimensional space with parameters bounded roughly as follows: $d \le 50$ and $n \le 1000$. Note, that there is no guarantee on the number of faces.
Jeff Erickson's page has a link to a program Vinci-1.0.5, which has a hard limit of 255 faces. This is a limitation of the implementation, the algorithm itself can probably handle more faces in reasonable time.
I couldn't find any implementations of the Markov chains based method for estimation, although I guess they will be even less efficient.
Is there any software, that can handle the range of parameters described above or some moderate relaxation of it? I would be very grateful for any other references as well.