Tensegrity or tensional integrity is a property of structures with an integrity based on a balance between tension and compression components. The idea has been applied to a broad range of phenomena from philosophy to cellular mechanics. As this entire website is dedicated to explaining tensegrity, this page mostly consists of links to other pages with more details.
The term 'Tensegrity' was coined by Fuller, though the definition of the word and the set of concepts to which it refers is subject to some passionate debate. For a good list of definitions, see the "definitions of tensegrity" page.
Tensegrity In Languages Other Than English
See Portal to Languages.
The Concept of Structural Tensegrity
Tensegrity structures are structures based on the combination of a few simple but subtle and deep design patterns:
- loading members only in pure compression or pure tension, which effectively means that the structure could fail if any cable yields or any rod buckles (unless redundancy is built-in).
- preload, which allows cables to be rigid in tension
- mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases
Because of these patterns, no structural member experiences a bending moment. This produces exceptionally rigid structures for their mass and for the cross section of the components.
Sadao offers a definition in the broad spirit of Fuller's usage. "To Fuller, tensegrity is nature's grand structural strategy. At the cosmic level, he saw that the spherical astro-islands of compression of the solar system are continuously controlled in their progressive repositioning in respect to one another by comprehensive tension of the system which Newton called 'gravity'. At the atomic level, man's probing within the atom disclosed the same bind of dicontinuous compression, continuous tension apparently governing the atom's structure.' 
Classification and typing of tensegrity constructions
There is no one widely accepted method of classifying tensegrities.
By Similarity to Polyhedra
A tensegrity that is composed of struts and filaments of fixed length will outline the shape of a well known polyhedron. The similarity of a given tensegrity to a given polyhedron is not a simple issue, as sometimes the faces are implied or asymmetrical.
Anthony Pugh (1976) attempted a comprehensive typology in the 1970's. His typology is polyhedra-centered. "First, he described the simplest figures superficially (both 2D and 3D), depending on the relative position of their tendons (passing through their centres or not), on the complexity of the compressed components (single elements or groups of struts), on the number of layers or stages, etc. Then, he described the three basic patterns that can be used to configure spherical or cylindrical tensegrity structure: Diamond pattern, Circuit pattern and Zigzag pattern. This classification was based on the relative position of the struts of the figures, as is explained in fig. 5.1. Finally, he related the way of joining systems together and the construction of larger figures. In that section some grids, masts and domes were described, but not in an in-depth manner."
Motro's refinement of Pugh
Motro refined Pugh's classification in his book, “Tensegrity, Structural Systems for the Future” (2003). His category highlights are
- Spherical systems: systems homeomorphic to a sphere, e.g. all cables can be mapped on a sphere without intersections between them and all the struts are inside the sphere
- T-prism and Rhombic configuration, corresponds to the Diamond Pattern established by Pugh. Tensegrity prisms (T-Prisms) are included in this section. Also includes the “simplex” and the “expanded octahedron” (also so-called “icosahedric tensegrity”).
- “Circuit” configuration, where compressed components are conformed by circuits of struts, closing the rhombus generated by the struts and cables of the diamond pattern tensegrities. Many regular and semiregular polyhedra can be built in this class, such as cuboctahedron, icosidodecahedron, snub cube, snub icosahedron, etc. Pugh notes that a circuit system is more rigid than a rhombic one with the same number of struts. This is understandable since the former evolves from the latter, but it becomes more compact and there is contact between its compressed elements.
- “Zigzag” configuration or “Type Z”. To build the zig-zag, take a rhombic system as a basisand change cables in such a way as to form a ‘Z’ of three non aligned tendons. Note that substitution of the cables must be done in such a way so as to preserve the stability of the system. Example: the “expanded octahedron” when rearranged into zig-zag pattern, becomes the “truncated tetrahedron”.
- Star systems. Though also spherical, stars are considered a derivation of zigzag. For example, taking as a basis one of the rhombic system, if a vertical strut is inserted in the centre following the main axis of symmetry and linked to the rest of the cables by means of tendons, a star system is created. Another possibility could be proposed by inserting a small spherical node instead of the central strut.
- Cylindrical systems: also a variation of the rhombic configuration, obtained by adding other layers of struts to the initial layer. For example, adding a second line to a four-strut rhombic cell that subsequently closes all around itself again, creates a cylindrical mast.
- Irregular systems. A catch-all class for everything that does not fit the above. It is here that Motro classifies most of Snelson’s sculptures
- Assemblies: Combinations of the above. They include Vertical Masts (or horizontal beams) that feature assembly along a single axis, or Grids, extension in two directions that describe a surface.
Tensegrity as a valid architectural principle
Fuller promoted tensegrity as a highly efficient architectural principle. He argued that buildings built with more efficient methods would use less material and therefore house more people in greater comfort. His arguments are compelling in both the rapid shelter deployment movement, that attempts to raise shelter quickly in disaster areas, and environmental movements, that seek to lower the impact of humanity upon the Earth's limited resources.
Snelson was openly skeptical of tensegrity's applicability to practical shelter. He wrote, "Over the past fifty years, if a clever architect, a real estate agent or a greedy entrepreneur had figured out a way to make tensegrity into a reasonable building system, or even an unreasonable one, the country would be dotted with novelty shopping centers or MacDonalds supported by tensegrity golden arches since, beyond all other attractions, novelty is great for commerce."  "Yes, Bucky Fuller exploited his puffed up tensegrity claims shamelessly even though he knew better."
Some bibliographies that may be useful: Bibliography written by Valentín Gómez Jáuregui
Links and References
 Letter from Kenneth Snelson to Maria Gough June 17, 2003, retrieved 18 Feb. 2010 from Burkhardt's website, http://www.trip.net/~bobwb/ts/synergetics/photos/snelson_gough.html