There are various methods for approximating a surface of revolution by origami. Among them, the rotational origami method using curved folds has been made progress by Palmer, Lang, Mitani, and others. The resulting origami model consists of approximating cylindrical surface segments (called gores) circumscribing the surface of revolution, each of which involves a flange outside. From the viewpoint of approximation, we want the area of the flanges as small as possible. In this paper, we apply the rotational method to not a flat or cylindrical but polyhedral piece of paper, to reduce the area of the flanges.