Abstract: There is described a prefabricated structure for erecting a building, that comprises bays hinged together which can take a position with a reduced volume and a position of extension, in which each bay comprises in the structure erecting condition and from the geometrical point-of-view, two pairs of dihedrons facing one another by pairs and comprising respectively the roof, the underflooring and the frontages of the bay, each dihedron comprising two sides hinged together along the dihedron intersection line and the junction areas between the dihedrons are each comprised of a truncated polyhedron comprising four side surfaces hinged together along their converging edges, said edges converging towards an apex located outside the imaginary right angle between the intersection lines of two dihedrons, two of those edges opposite the converging edges of the polyhedron being hingedly joined to one of the dihedrons, the structure further comprising means for stabilizing the dihedron angles in the bay extension conditi