one of the methods of formation of geometric networks of arches of the same radius using regular spherical polyhedra is Investigated. The conditions of the task of placing the specified network on the sphere are set. The criterion for evaluating the effectiveness of solving the problem is the minimum number of standard sizes of segments of the dome arches, the possibility of using technologies of enlarging assembly. The solution of one variant of the problem of placing a geometric network on a spherical cube and, accordingly, on a sphere is given. Placement on the sphere of arches of one radius, different from placement in the form of meridians, has an effective solution in the form of a network with minimal dimensions of arch segments and nodes of paired arches formed on the basis of circles of identical radii formed on the basis of regular spherical polyhedra. The problem is solved by constructing an independent framework of arches of the same radius on the basis of paired circles of the same radius in the spherical cube system.