Computing volume of high-dimensional convex polyhedra

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.

• Well. IT is known that a polytope with $n$ vertices in $d$ dimensions has in the worst case $n^{\floor{d/2}}$ facets. Putting $n$ points on the moment curve in $d$ dimensions provide you with such a polytope. It seems to me unlikely that volume computation can be done faster than the nubmer of facets. So you really have to implement the random walk papers if you want better results.... – Sariel Har-Peled Jan 6 '12 at 2:22