Synergetics is a selfdiscipline pioneered by the late R. Buckminster Fuller, who needed a language rooted in first hand experience, trustworthy and comprehensive enough to sustain him through a career involving plenty of heavy duty service on behalf of omnihumanity. He was not the first to shoot for a comprehensivist's viewpoint, and Fuller hoped the results he obtained, with collaborators, including the two Synergetics volumes with E.J. Applewhite, would encourage many more "little me" individuals to likewise go for stellar careers as competent anticipatory design scientists  or whatever  this time with the advantage of synergetics to assist them. 
Readers of Synergetics may find it works best to approach it as a work in the humanities, as a philosophy, despite the engineering mathematics and geometry it contains. The language is frequently psychological and metaphoric, while many key terms come with an alien spin  a fact Fuller addresses in Remoteness of Synergetics Vocabulary. This is not a popularization of other people's thinking, but one individual's slant on the whole of Universe  perhaps inspiring others to likewise roll their own. "Dare to be naive" is the moral of this highly sophisticated piece of literature. 

Synergetics connects to the visual arts via Euler's Law (V+F=E+2). Euler discovered a relationship between the relative abundance of edges, faces and vertices. These socalled 'topological features' Fuller took as primitive aspects of our visual and tactile experience.  
Artists using raytracing software describe a scene in terms of its Eulerian topology, before applying various textures. The textures provide visual cues which the viewer interprets as 'solid,' 'liquid' or 'empty space.' When a scene moves from a simple wireframe to a true landscape, we might think of something abstract becoming 'energized' i.e. becoming reality. 
Solids, liquids and gases are characterized by different freedoms of relative motion among their constituent molecules: solids hold molecules in relatively fixed arrays, as in crystaline formations; liquids allow currents and flow patterns; gases are comprised of molecules free to move quasiindependently of oneanother. Fuller sought to abbreviate these phases using a topological shorthand: facebonded, edgebonded and vertexbonded tetrahedra for solids, liquids and gases respectively. His purpose was to signify an Eulerian aspect to the Phase Rule, thereby unifying Euler and Gibbs into a yet more general formulation of exceptionless principles.[2] 

Synergetics is a ' geometry of lumps' in which even points occupy volume, however infinitesimal. All objects in synergetic prefrequency topology have the same dimensional characteristics. Nor are 'perfect solids' ever defined. Every surface is permeable. Faces or planes are edgeframed windowopenings, not impermeable surfaces. These are differences at the level of definition, with synergetics having the advantage of more hindsight: since Euclid's day: science has shown solid matter to consist mostly of empty space. 
Whereas Euclidean space has no boundary, Fullerian conceptual space has a definite shape. The volume with the fewest Eulerian characteristics is the tetrahedron. Six edges meet at four vertices to define four windows. This wireframe separates an internal from an external region and so defines our concept of volume by giving it a definite shape. Fuller accordingly makes this shape his unit of volume, pointing out its more economical topology visavis the cube's eight vertices, twelve edges and six framed openings. Synergetics is therefore a nonEuclidean, non Cartesian approach to geometry. Its topological primitives are not defined according to the Euclidean template, and its unit of volume is not the cube, nor is its coordinate system xyz, nor is Fullerian space defined to contain infinite volume with no internal or external shape. 

Once the regular tetrahedron is posited as a primitive beginning, a more elaborate framework of geometric relationships is defined around it, in the form of a concentric hierarchy of additional polyhedra. The tetrahedron is its own dual, and two interpenetrating tetrahedra comprise the duotet cube, with a relative volume of three. 
The centerpoint of this cube defines six halfoctahedra (irregular) of volume 3/6 or 1/2. These are known as halfcouplers in synergetics. Halfcouplers facebonded to the six faces of the cube, mirroring the six internal halfcouplers, create a rhombic dodecahedron of volume six. The rhombic dodecahedron is a spacefilling shape. When packed together without intervening gaps, the arrangement is coincident with a spherepacking arrangement familiar to all supermarket grocery clerks and crystallographers. 

The rods running between the centers of adjacent spacefilling rhombic dodecahedra, equal in length to the edge of our original tetrahedron, describe a skeleton of spacefilling tetrahedra (volume 1) and octahedra (volume 4). Each center is connected by twelve rods to twelve adjacent centers. The surrounding centers form the vertices of a cuboctahedron of volume 20 relative to the initial tetrahedron.[3] 
And so we have a concentric hierarchy of rationally interelated polyhedra:

By striving for comprehensivity, synergetics gives its student a means to translate inputs and discoveries from many walks of life into an efficient storage and retrieval system. In this sense, it links up with the memory arts as passed down through the hermetic tradition, is a kind of computer programming language. 
Ray tracings by R. Hawkins
and K. Urner (dodeca mesh)  except the
fullerene
Synergetics on the Web
maintained by Kirby Urner