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From what I understand of your question, you could scale the polyhedron by the lcm of the denominators of the coordinates of the vertices. This will give you a polyhedron with integer vertices.

Nevertheless, in general, it is not true that every (combinatorial type of) polyhedron object has a 0/1 V-representation. So your example should have a special structure that allows this to be possible.

Unfortunately, we can not help further since we don't have an explicit example...