You are assuming that the faces don't intersect, and that the faces have edges that don't intersect. The easiest example of a polyhedron with self-intersecting behavior to wrap your head around is IMO the small stellated dodecahedron, made from twelve pentagrams.

If you want to dive in a bit into strange polyhedra, I can really recommend this YouTube video: https://www.youtube.com/watch?v=_hjRvZYkAgA