As stated above, the geodesic dome is made of convex-concave elements that are assembled in an approximate fashion. By "approximate" is meant that the elements are assembled one next to the other according to some principle such as overlapping or tangentially touching adjacent elements, yet randomly in the sense that particular exemplars of the elements do not necessarily have to be placed or fastened along predetermined great circle gridlines, nor do they have to be placed in a particular sequence or at a particular location. In an initial embodiment of the structure , identical, shallow, cone-shaped elements, also referred to as "hub elements," are used as the convex-concave elements and are assembled in an overlapping configuration, typically from the top of the structure downward, although a structure could just as well be assembled from the bottom up.

The structure is self-adjusting because the hub elements are not necessarily precisely spaced from each other, but are, rather, assembled in an approximate arranged according to some general principle with virtual struts automatically forming along the single-axis curvature that extends from vertex to vertex. The geodesic dome thus constructed will have an overall shape with a curvature that corresponds to an average curvature of all the hub elements, as will be discussed below. Furthermore, the geodesic dome is self-triangulated. If lines are drawn from each vertex to adjacent vertexes, one can see that the entire structure is divided into triangles, albeit triangles of varying dimensions, including scalene triangles in which each leg of the triangle is a different length.

Cones were used as the hub elements in a Preferred Embodiment of the geodesic dome because cones are easier to work with and less costly than continuously curved elements. Cones can be easily fabricated from a flat circular sheet of construction material by eliminating a section of material from the center to the outer edge of the hub, thereby forming what is hereinafter referred to as an angular deficit in the sheet. This angular deficit determines the curvature of the hub element, discussed in greater detail below, and is easily formed either by folding that section of the material from the vertex to the outer edge or by cutting the section from the element, and reattaching the cut edges to form the cone. Thus, no machining or shaping of curved elements is required. The cone shape also imparts improved strength and rigidity to the material. Thus, materials that are relatively thin and/or inexpensive can be used to create large spacious enclosures. The elements can be made of a variety of stiffly flexible materials, including but not limited to such materials as paperboard, plywood, oriented-strandboard, cardboard, sheet metal, and sheet plastic or fiberglass material. It is possible, however, to use several different sizes or shapes of hub elements and arrange them in an evenly alternating pattern to form the structure. For example, hub elements of two shapes, i.e., having the same diameter at the outer perimeter, but having different angular deficits, can be assembled in an alternating pattern for an aesthetic effect.