The object of research is spatial structural coatings of buildings and methods of their formation. Areas of use of structural structures are premises of hall buildings and warehouses. Method. A method for solving problems of geometric and structural-technological formation of structures using graphic computer means and analytical methods using a mathematical model is known. Analytical methods of structural and technological formation of structures in the form of polygonal networks on the sphere, which were called "Antants," have been developed. The algorithm of the analytical solution of the problem of placing a triangular network on a sphere with the formation of quadrangular flat panels in the belts of the structure for building coverings is presented. Results. Results of formation of double-belt shells on the basis of spherical surfaces are presented, and version of structure on the basis of transfer surface is shown. Optimality and efficiency criteria for options are the minimum number of standard sizes of structural parts and the minimum number of mounting structural elements, the possibility of increased assembly of panels and volume blocks, the use of prestressing. The developed methods of forming the geometry of prefabricated spatial blocks of building structures "Antants" were used to cover buildings for various purposes.