So this is from Ratcliffe's text on hyperbolic manifolds. In it there is a part of a proof where he just states that for a polyhedron in $E^n$ with infinitely many sides it must contain a side that is a polyhedral wedge. I don't understand why this is true.
DEFINITION: The definition of a polyhedral wedge is a polyhedron such that the intersection of all its sides is nonempty(i.e. think of a triangular wedge in $E^3$ with two planes meeting at a line).
EDIT: I've included a copy of the proof in question.
EDIT: Sorry guys. I totally forgot to read all the assumptions in the lemma.
You don't seem to have understood the structure of the argument, which is by contradiction. Suppose $P$ is an infinite sided polyhedron so that all but finitely many sides of $P$ are wedges. That hypothesis already implies that there is at least ONE side which is a polyhedral wedge.