Thanks very much for your advices!

Now I realize that it's really unpredictable for such large dimension. I'm thinking about using approximation for my problem.

I'm working on a Facet enumeration problem in around 20 dimension, and the number of input vertexes is around 2^20, could Polymake solve such a high dimensional problem?

I tried to solve it with Polymake, but there's just no any output when I typed in my code. It seems that it was calculating, but ...