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bounding a polygon

I am looking for a function which takes two lists, one representing a polygon and 
one representing a rectangular region of space, which returns a new polygon that is 
the old polygon "cut" by the second region. To be clearer: Suppose I had a polygon 
called P. If I use Show[Graphics[Polygon[P]]] then I get the entire polygon. If I 
use Show[Graphics[Polygon[P]], PlotRange->SomeArea] I get a polygon that is P but 
cut off by SomeArea. Does anyone know a way to get just that area of P in the region 
SomeArea so that if I type Show[Graphics[Polygon[F[P]]]] I get the same thing?

Any help is appreciated. Thanks.

--Jonathan Lee

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