Abstract: A spherical structure is formed by assembling a plurality of elementary constructs each of which is composed of three first triangular elements, three second triangular elements, three third triangular elements, and three fourth triangular elements. These triangular basic elements are different-sized triangular frameworks covered by respectively corresponding panels. A self-supporting spherical radome or other spherical structures can be constructed from a random distribution of these four basic elements by repeatedly arranging the elementary constructs assembled by the basic elements. Only four different triangular basic elements are required for constructing and dovetailing the whole spherical structure.