The term synergetics was coined by Buckminster Fuller as the study of synergy, the behavior of systems of components unpredicted by the behavior of a single component taken in isolation. Synergy is the complement of energy; energy radiates outwards and synergy coordinates inwards. Our society is unbalanced in that it tends to ignore synergy and is preoccupied with energy.
Buckminster Fuller (Bucky) was one of the pre-eminent thinkers of the last century. He argued, contrary to popular Malthusian ("not enough to go around") and Darwinian ("survival of the fittest") ideas, that humanity could and should embark on an endless path of discovery and utilization of natural principles that allow us to accomplish progressively more with progressively less resources, allowing everyone on Earth to live a successful life.
Icosahedral geometry in buildings received a start in the form of geodesic domes, patented by Buckminster Fuller in 1954. However, in a typical geodesic dome the triangular faces of the basic icosahedron are subdivided into smaller triangles, with new vertexes extended out to make the surface curved, resulting in an approximately spherical shape. Thus the basic icosahedron tends to be invisible, and many people are not aware of the role that icosahedral geometry plays to make a geodesic dome extremely light and strong.
In Image 2 (below) we show the basic icosahedron with one face subdivided and curved out. When all faces are similarly curved out, you get the geodesic dome on the right.
A geodesic dome is strong because any force applied to any vertex in the structure is instantly distributed to the other vertexes. In a sense, the entire structure works together to support the load. The key to this synergetic effect is its geometry. The basic icosahedron (see Image 2) provides pentagonal vertexes; i.e. vertexes that are surrounded by five triangles. Forces are conducted by the edges between triangular faces, which correspond to load-bearing struts. When a force comes in to a pentagonal vertex, it gets divided (distributed) into two out-going struts (see Image 3). Those divided forces get divided again when they reach another pentagonal vertex.
