Hi, the algorithm you are using is to enumerate all the intersections of the constraints, then filter out all the impossible ones, does this algorithm runs robust? even with some redundant constraints?
how about other algorithms? did you try? recently I am working on the same problem, and I just found the question following, then I implement the first "dual polytope" basic algorithm, but it failed about some cases? do you ever try this?
could you please explain why you select the intersection method to construct polytope finally??
the link following contains two answers, could you please show me your opinions?
https://stackoverflow.com/questions/26809630/how-to-convert-the-half-spaces-that-constitute-a-convex-hull-to-a-set-of-extreme

Best