The relationships disclosed in Closest Packing Of Spheres are part of the geometrical model of energy configurations in Synergetics.
Each sphere is a model of a field of energy in which all forces are in equilibrium and whose vectors, consequently, are identical in length. When 12 spheres are packed closely around a central sphere, the resulting structure constitues a polyhedron with 14 faces, namely 6 squares and 8 triangles. The centres of the surrounding spheres are the 12 vertices of what Fuller called the vector equilibrium.
Vectors connecting the centres of contiguous spheres line up in 60 degree angular relationships. He suggests that there are peripheral "barrel-hooping" vectors which we can see as tending to hold the structure together against the expansive potential of the vectors radiating from its centre. Conversely, if the radial direction is reversed, the contraction of the structure is opposed by the circumferential archwork's resistance to its own compression.
By generalizing these ideas, synergetics purports to enable the conceptual modelling of patterns and processes which are normally represented only in an abstract, mathematical form, as in nuclear physics, for example.
THE FULLER MAP
© Paul Taylor 2001