Abstract: We consider closed polyhedral manifolds which are non-negatively curved in the sense of Alexandrov. We show that there exists a smooth Ricci flow, starting from such a polyhedral manifold, which has positive curvature operator for positive times. Even more, for positive times the flow has positive co-sectional curvature, which confirms a conjecture of Petrunin. This is joint work with Man-Chun Lee and Felix Schulze.