Anyone know of software (preferably in Mathematica) that computes the intersection of polytopes, or at least polygons? I'd like to explore some more random-nonempty-intersection problems, and it'd be very helpful to be able to do numerical experiments in a flexible setting. For instance, how many sides on average does the intersection of P, Q+v, and R+w have, conditioned on the event that the intersection is nonempty, where P, Q, and R are fixed parallelograms, and v and w are random translation vectors? (The usual caveats and clarifications about "random translation vectors" apply.) The answer might be that it depends on P, Q, and R, or it might be 4 (no matter what), or it might be some other number; maybe one of you can see a non-experimental approach, but I don't, so doing experiments is the next step for me. But I don't trust myself to write correct infrastructural code for handling polygons. Jim Propp PS: I'm still mulling over Veit's two puzzles about averages. I'm guessing that a key tool for solving his first puzzle is "V-E+F=2", or rather "V-E+F is negligible when V, E, and F are large", but I don't see what the answer is.