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How to use faces of a polytope as variables?

Hello, I am very new to using computer algebras system, and I can't figure out the following: I need to create a 3D polytope (in fact, an associahedron) and then do some computations in the algebra of rational functions in variables that correspond to faces of associahedron. How do I do that? I know writing something like Frac(ZZ['x,y,z']) creates the algebra that I need, but how do I make formal symbols x,y,z remember that they once were faces of a polytope (so that I could check if one was a subface of another, or something like that...)?