The paper examines the assembling of cylindrical products consisting of sector parts with dihedral angles. A crucial issue in the assembly of such parts is the accuracy of dihedral angles during processing. Based on methods of analytical geometry, we proved that in order to achieve gapless assembly of three sectors, the sum of all dihedral angles of the sectors should be less than or equal to 360°. Since it is impossible to ensure the exact equality of the sum of all dihedral angles of 360°, characteristic “flatness deviation” is always formed during assembly. In order t obtain a gapless connection, we propose a new method for the selective assembly of sectors and developed a scheme of the dihedral angle controller. This selective assembly method will allow sectors to be selected in such a way that their “twist” angle in the assembled conditions is minimal.