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Amy C. Edmondson
A Fuller Explanation
Chapter 15, From Geodesics to Tensegrity: The Invisible Made Visible
pages 251 through 255

Tensegrity Polyhedra

Tensegrities can be derived from all polyhedra, whether regular, semiregular, high-frequency geodesic, or irregular, typically with one strut representing each edge of the polyhedron. Struts do not come in contact with each other, but instead are held in place by a network of tension elements, or strings—producing completely stable sculptural systems. The complexity of molecular interactions aside, the two types of components are characterized by axial-force states, thereby using materials most efficiently, because components can be far lighter than would be required to withstand bending. The technical sound of the words in no way prepares you for the exquisite appearance of these structures. Photograph 15-1 shows a tensegrity icosahedron and tetrahedron, while Photograph 15-2 displays a 3v tensegrity icosahedron, as representative tensegrity polyhedra. However, there's no substitute for actual models.

Tensegrity icosahedron and tensegrity tetrahedron. Photograph by Amy C. Edmondson
Photo. 15-1. Tensegrity icosahedron and tensegrity tetrahedron.
Photograph by Amy C. Edmondson.
Click on thumbnail for larger image.

3v tensegrity icosahedron with 90 struts
Photo. 15-2. 3v tensegrity icosahedron with 90 struts.
Photograph courtesy of Thomas T. K. Zung, Buckminster Fuller, Sadao and Zung Architects. Cleveland, Ohio.
Click on thumbnail for larger image.

      At last, says Bucky, we are able to experience at first hand the truth about structure: systems cohere through tensional continuity, and nothing in Universe touches anything else:

      ... Tensegrity structures satisfy our conceptual requirement that we may not have two events passing through the same point at the same time. Vectors [i.e., struts] converge in tensegrity, but they never actually get together; they only get into critical proximities and twist by each other. (716.11)

      A tensegrity icosahedron, therefore, is more honest than a tooth-pick-marshmallow structure which seems to have five edges touching at each vertex. In the tensegrity, edges all come within critical proximity of the location of a "vertex" and "twist by each other." Figure 15-11 illustrates the relationship between the tensegrtty icosahedron and its Platonic counterpart. Instead of a five-valent "point" with the illusion of continuity, each convergence is marked by a pentagon of string, thus illustrating the fact that individual energy events do not touch but instead hover in a state of dynamic equilibrium. Tensegrity structures provide a visible, tangible illustration of an invisible truth. Forces and their interactions are brought out in the open.

Relationship of tensegrity icosahedron to its Platonic (planar) counterpart
Fig. 15-11. Relationship of tensegrity icosahedron to its Platonic (planar) counterpart.
Click on thumbnail for larger image.

      Perhaps the most significant lesson from tensegrity structures lies in their unexpected strength. A tensegrity's apparent extreme fragility is completely deceptive. The uninformed observer will usually approach such a structure with great caution, touch it hesitantly and gently so as not to break the delicate model, and (if persistent) ultimately realize that a tensegrity can be thrown around the room without harm. The erroneous initial assumption is a result of a deeply ingrained bias in favor of compression as the reliable source of structure. We perceive string and cable as flimsy, but actually the magnitude of a force that can be carried by "delicate" tension materials can far exceed the corresponding capacity of compression elements. Humanity's perception is in need of retuning.

      The other aspect of a tensegrity's remarkable strength is the rapid omnidirectional distribution of applied forces. One of the advantages of a network of tension elements is efficient dispersal of loads around a structure, enabling the whole system to withstand forces far greater than could be predicted by engineering analysis of the separate components. Welcome back, synergy:

      This is not the behavior we are used to in any structures of previous experiences... Ordinary beams deflect locally... The tensegrity "beam" does not act independently but acts only in concert with "the whole building", which contracts only symmetrically when the beam is loaded... . The tensegrity system is synergetic. ...(724.33-4)

This "whole system" behavior can be detected by pushing or pulling on two opposite struts of certain tensegrities. The entire system will contract or expand symmetrically like a balloon, and also will spring back to its equilibrium configuration when the applied force is removed. (Photo 15-3 shows the simple six-strut tensegrity, which is arguably the most elegant illustration of this uniform contraction or expansion in response to a unidirectional force.) Similarly, this synergetic behavior insures a balanced distribution of stresses:

Six-strut 'expanded octahedron' tensegrity
Photo. 15-3. Six-strut "expanded octahedron" tensegrity.
Photograph courtesy of the Buckminster Fuller Institute, Los Angeles, Calif.
Click on thumbnail for larger image.

      If you... tauten one point in a tensegrity system, all the other parts of it tighten evenly. If you twang any tension member anywhere in the structure, it will give the same resonant note as the others. (720.10)

Fuller felt that this dispersal is not really understood by most engineers, and as a result, they have been unable to predict or analyze the extraordinary capabilities of tensegrities and geodesic domes. Note that discontinuous compression and continuous tension also characterize geodesic domes, but as these structures lack the visually legible quality of the geometric models, one cannot at a glance identify the operative forces:

      Structural analysis and engineering—design strategies... were predicated upon the stress analysis of individual beams, columns, and cantilevers as separate components... [and] could in no way predict, let alone rely upon, the synergetic behaviors of geodesics... . Engineering was, therefore, and as yet is, utterly unable to analyze effectively and correctly tensegrity geodesic structural spheres in which none of the compression members ever touch one another and only the tension is continuous. (640.02)

The ultimate result of this conceptualizing and model building is that the barrier to ever-larger clear-spanning enclosures has been removed. By understanding the crucial role of tension, we can learn to manipulate it in preferred ways. "We are able to reach unlimited spans because our only limitation is tension, where there is no inherent limit to cross-section due to length" (764.02). Cosmic zoning laws are repealed.

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