Rhombic dodecahedra close pack to fill all space in exactly the same way that unit-radius spheres close pack around a central nucleus, as vector equilibria (VEs) of increasing frequency. That is, the polyhedral domain of each sphere in a close-packed nuclear array is in the shape of rhombic dodecahedron whose in-sphere radius is the radius… Read more

The quanta module construction of the isotropic vector matrix discloses two rhombic dodecahedra, one occupying the positions of the spheres, and the other the space between the spheres. The two constructions can be shown to exchange places during the jitterbug transformation.… Continue reading → Read more

Jitterbugging into and out of its ground state, the isotropic vector matrix seems to reach maximum disequilibrium (i.e. maximum expansion) when the contracting vector equilibria (VEs) and expanding octahedra both describe regular icosahedra. It can be shown, however, that the contracting VEs and expanding octahedra cannot pass through their icosahedral phases simultaneously. While one has… Read more

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… Read more

In radial close-packing, every sphere is surrounded by twelve others. Whether or not a given sphere is a nucleus is an arbitrary choice. But the selection of one determines the the regular distribution of all the others. Connecting the centers of unique nuclei forms a grid of rhombic dodecahedra, fourteen around one, not twelve, as… Read more

Regular icosahedra will not close pack to fill all space. They can, however, be edge-bonded to form icosahedral shells and lattices. The study of icosahedron shells may have implications for and resonance with the behavior of cell membranes and other semi-permeable barriers between systems.… Continue reading → Read more