These images represent the visualization of a general class of (N,S;P1,P2, . . . , PM) tensegrity structures consisting of N compression members (ie struts) and S tensile members (ie cables). The structure has M stages with PM struts per stage.
The word "tensegrity" is a contraction of the words ``tensional integrity", and has been loosely defined as a "structural relationship in which structural shape is guaranteed by the interaction between a continuous network of members in tension and a set of members in compression". Such structures are mechanically stable because of the way in which the structures balance and distribute the mechanical stress, and not principally as a result of the strength of the individual components. An example is the "Needle Tower" sculpture of Kenneth Snelson which appears in the Koeller Museum, The Netherlands.
If an (N,S;P1,P2, . . . , PM) tensegrity system has N struts, its external geometry is characterized by the 2N coordinates of the "nodes", or "ends", of the struts. The resulting "shape" of the tensegrity then depends on the properties of the constituent components (that is, on the lengths of the struts and the rest lengths of the cables), the internal geometry (or topology) of how the struts and cables are connected, and on the existence of self stress, or pretension, which is necessary in order to provide rigidity for the structure.
Each of the illustrated structures represents an equivalence class. The complete class is defined from the given representative by a continuous change in the lengths of the struts, and a continuous change in the rest lengths of the cables subject to the constraints that all cable tensions remain strictly positive, and no two struts come into contact with each other.
Further details may be found at Darrell Williamson's web site.