VECTOR EQUILIBRIUM

(CUBOCTAHEDRON)

480 (168 A+, 168 A-,72 B+ ,72 B-) mods

The VECTOR EQUILIBRIUM or cuboctahedron is the polyhedral equivalent of the close-packed sphere model (12 unit radius spheres tangentially closepacked around one unit radius nuclear sphere). When the sphere centers are interconnected the resultant polyhedral form is the Vector Equilibrium, so named by Fuller because all vectors (radial and circumferential) are equilinear and equiangular. It is the basis for the coordinate system (isotropic vector matrix) of Fullers' Synergetic Geometry. The VE is comprised of 8 tetrahedra and 6 half octahedra. Note that the square faces on the model above are B modules (octa) and the triangular faces are A modules (tetra). The VE is not an allspace filler but it will fill allspace in complementation with octahedra, just as tetrahedra and octahedra fill allspace in complementation with each other in a 2:1 ratio. The MITE is a synthesis of the allspace filling polyhedral attributes of tetra and octa.

In Scott Childs' abstract on Synergetic Crystallography, he notes that:"Atomic sized clusters (<400 atoms) prefer to self-assemble with polyhedral morphology that can be described by the Platonic Solids and combinations of these polyhedra. By continuing this polyhedral description as the clusters get larger (400 to ~4000 atoms), the relationship between the quantum states that describe the smaller clusters and the evolving solid state properties of these clusters of clusters will be apparent. In this size range the icosahedral point group is still the dominant geometry. The phase shift to a regular lattice will occur sometime after ~4000 atoms are in a cluster."


If we add one eigth octahedron to each of the triangular faces of the VE we have a 2 frequency cube (supercube):