2. Leonardo da Vinci

Since the system is so simple, I could not imagine that it had not been invented before. The first names that came into my mind were Kenneth Snelson and Buckminster Fuller. In their work I found related drawings of patterns, however the constructions derived from them are all made from rods and wires (tensegrity). In the end I have found only one comparable source. On a page from one of the notebooks by Leonardo da Vinci, Codex Atlanticus f. 328 v-a, we find among others three patterns with exactly the properties of the bar grids defined above (see figures 7, 8, 9).

Figure 7: Pattern 1.
Figure 8: Pattern 2.
Figure 9: Pattern 3.
A reprint of this page can be found in Carlo Pedretti’s book Leonardo Architect. As a description of the contents of this page Carlo Pedretti gives: “Studies of wooden roofing made up of parts that fit together.” And in the text it is described as: “’Geodesic’ roofing for vast area of land, anticipating the daring constructions of Buckminster Fuller”. In view of the way in which the patterns are drawn, oblong forms that seem to lie on each other, the most direct interpretation is that here we have to do with stacking construction build from straight rods. On making a model this leads exactly to the domes that I found. So the conjecture seems justified that Leonardo da Vinci is the first inventor of these constructions, although we cannot be sure about this.

3. Spheres

In the domes it is gravity that keeps the loose rods together. It follows that continuing the construction as far as a complete sphere is not possible. Yet it turns out that using the above construction system objects can be formed where only the elements themselves, instead of gravity, keep the construction together. For example, we can assemble a sphere from a number of rods, or more generally elements, without using connecting materials like wire or glue. The number of connecting points per elements and the connecting rules do not change. It is only the form of the elements that changes. For a sphere we use curved rods instead of the straight rods for a dome.