The Roots of Collaborative Innovation
4. CICT Understanding of Buckminster Fuller Rationale
The first appearance of COH is in the book titled “Archimedean Solids”, where Pappus of Alexandria lists solids, which he attributes to Archimedes in his Book V of his Collections, though Archimedes makes no mention of these solids in any of his works (Pappus, 2016). Long after, it reappears in Luca Pacioli’s book De divina proportione written around 1497, where all figures are drawn by Leonardo da Vinci (Pacioli, 1982). Johannes Kepler (1571-1630) rediscovered the 13 Archimedean solids and gave the first surviving proof that there are only 13. In Japan, cuboctahedra have been widely used as decorations in furniture and buildings. Lamps in the shape of cuboctahedra were used in Japan already in the 1200s, and they are still used today in certain religious ceremonies in memory of the dead (Miyazaki, 1993).
COH is the ideal state of the IVM and the IVM is formed by filling all space with cuboctahedra recursively. Remembering Richard Buckminster Fuller: “Any polygon with more than three sides is unstable. Only the triangle is inherently stable. Any polyhedron bounded by polygonal faces with more than three sides is unstable. Only polyhedra bounded by triangular faces are inherently stable” (Fuller, 1975/1997). Furthermore: “There are only three possible cases of fundamental omnisymmetrical, omnitriangulated, least-effort structural systems in nature: the tetrahedron with three triangles at each vertex, the octahedron with four triangles at each vertex, and the icosahedron with five triangles at each vertex. If there are six equilateral triangles around a vertex we cannot define a three-dimensional structural system, only a plane” (Fuller, 1975/1997). Eventually: “Omnitriangulated geodesic spheres consisting exclusively of three-way interacting great circles are realizations of gravitational field patterns. The gravitational field will ultimately be disclosed as ultra high-frequency tensegrity geodesic spheres. Nothing else”, according to the “Three Way Grid” (OAC, 2019).