A polyhedral friction cone is a set of reaction wrenches that an object can experience whilst in contact with its environment. This polyhedron is a powerful tool to control an object's motion and interaction with the environment. It can be derived analytically, upon knowledge of object and environment geometries, contact point locations and friction coefficients. We propose to estimate the polyhedral friction cone so that a priori knowledge of these quantities is no longer required. Additionally, we introduce a solution to transform the estimated friction cone to avoid re-estimation while the object moves. We present an analysis of the estimated polyhedral friction cone and demonstrate its application for manipulating an object in simulation and with a real robot.