Complex sentence: Every geometric polyhedron corresponds to an abstract polyhedron in this way, and has an abstract dual polyhedron, but for some types of non-convex geometric polyhedron, the dual polyhedron may not be realized geometrically.
Split into simpler sentences: Every geometric polyhedron corresponds to an abstract polyhedron in this way, and has an abstract dual polyhedron. However, for some types of non-convex geometric polyhedron, the dual polyhedron may not be realized geometrically.