Abstract: Supporting structure (8) for curved envelope geometries in buildings consisting of support elements (4) which are each combined to form N-sided polygons (N=3,4, . . . ) which span the envelope geometry and which each enclose a planar surface element (5), and the support elements (4) of adjacent N-sided polygons each form a common node region (3) in which the support elements (4) abut, and the plane of a surface element (5) and the respective planes of the surface elements (5) of two N-sided polygons which adjoin in non-parallel spatial directions lie in different planes in at least one portion of the envelope geometry.