Polyhedral cages (p-cages) describe the geometry of some families of artificial protein cages. We identify the p-cages made out of families of equivalent polygonal faces such that the faces of 1 family has 5 neighbours and P_1 edges, while those of the other family have 6 neighbours and P_2 edges. We restrict ourselves to polyhedral cages where the holes are adjacent to at most 4 faces. We characterise all the p-cages with a deformation of the faces, compared to regular polygons, not exceeding 10%.