{{DISPLAYTITLE:P2-irreducible manifold}} In mathematics, a P2-irreducible manifold is a 3-manifold that is irreducible and contains no 2-sided (real projective plane). An orientable manifold is P2-irreducible if and only if it is irreducible. Every non-orientable P2-irreducible manifold is a Haken manifold. References 3-manifolds