Another way to visualize the difference between the two equilibrium phases of the jitterbug—tensegrity equilibrium (see Jessen Orthogonal Icosahedron and Tensor Equilibrium, and Tensegrity) and vector equilibrium (see Vector Equilibrium and the “VE”)—is to observe the path followed by the triangles’ vertices. In the case of the tensegrity model of the isotropic vector matrix, and if the tendons are assumed be elastic and the struts to be non-compressible, the path follows the edges of the cube in the which the triangle rotates. In the vector model, the triangle’s vertices follow an arc coincident with the cube’s orthogonal planes and are identical with cube’s vertices at the VE and octahedron phases.
In the model below, tensegrity equilibrium is represented by an elastic cord stretched between three rings attached to the cube’s edges. Given negligible friction between the rings and the edges, the cord will find its natural equilibrium in the position shown, coinciding the the Jessen Orthogonal Icosahedron, i.e., the shape of the unstressed 6-strut tensegrity sphere.
Equilibrium in the vector model is represented in the illustration below by the pink spheres nestled in the valleys of the arcs followed by the vertices of the triangles’ triangles rotation in the jitterbug transformation—which coincides with the octahedron phase of the jitterbug. The instability of the de-nucleated VE (the removal its nucleus, or radial vectors, is what precipitates the jitterbug) is represented by the blue spheres when they are precariously perched at the peaks of the arcs.
The Geometry of Thinking 