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. According to the invention, the support elements (4) in this portion each form 4- or 6-sided polygons, and the support elements (4) each have a longitudinal axis (L) which extends in a straight line between in each case two node regions (3) and runs parallel to the imaginary intersection line of the surface element planes associated with said portion, wherein the cross section of the support elements (4) normal to their longitudinal axis in each case has a relative twist angle of 0° along the entire longitudinal axis of the support element (4).