1006.30 Vector Equilibrium Involvement Domain

1006.31 The unfrequenced vector equilibrium has 12 external vertexes and one internal vertex of the nuclear sphere embraced by the 12 uniradius closest-packed spheres around it; the omniinterconnecting vectors between the 12-around-one spheric centers define the vector equilibrium involvement domain.

1006.312 We learn from the complex jitterbugging of the VE and octahedra that as each sphere of closest-packed spheres becomes a space and each space becomes a sphere, each intertransformative component requires a tetravolume-12 “cubical” space, while both require 24 tetravolumes. The total internal-external closest-packed-spheres-and-their-interstitial-spaces involvement domains of the unffequenced 20-tetravolume VE is tetravolume-24. This equals either eight of the nuclear cube’s (unstable) tetravolume-3 or two of the rhombic dodecahedron’s (stable) tetravolume-6. The two tetravolume- 12 cubes or four tetravolume-6 dodecahedra are intertransformable aspects of the nuclear VE’s local-involvement domain. (See Fig. 1006.32.)

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Fig. 1006.32 Duo-Tet Star Polyhedron Defines Vector Equilibrium Involvement Domain: The Duo-Tet star polyhedron that first appears in Fig. 987.242A is shown here within a vector equilibrium net. The complex also illustrates the eight Eighth-Octa that must be added to the eight triangular faces of the vector equilibrium to form th nucleated cubethe total complex of which functions as the vector equilibrium nuclear involvement domain. A closest-sphere-packing evolution of this same transformation (adding eight Eighth-Octa to the VE’s six triangular faces) appears at Fig. 415.17.

1006.33 The vector equilibrium at initial frequency, which is frequency², manifests the fifth-powering of nature’s energy behaviors. Frequency begins at two. The vector equilibrium of frequency² has a preffequency inherent tetravolume of 160 (5x2⁵= 160) and a quanta-module volume of 120 x24=lx3x5x2⁸ nuclear-centered system as the integrated product of the first four prime numbers: 1, 2, 3, 5. Whereas a cube at the same frequency accommodates only eight cubes around a nonnucleated center. (Compare Sec. 1033.632.)

1006.34 For the first moment in history synergetics is providing operational comprehensibility of the fourth-and-fifth-dimensional-coordinated, most economical behaviors of physical Universe as well as of their intellectual, metaphysical conceptuality. We have arrived at a new phase of comprehension in discovering that all of the physical cases experimentally demonstrable are only special cases of the generalized principles of the subfrequency, subtime, and subsize patterning integrity of the nucleus-containing, closest-packed isotropic vector matrix system.

1006.35 With reference to our operational definition of a sphere (Sec. 224.07), we find that in an aggregation of closest-packed uniradius spheres:

Tetravolume 1 = minimum F Ftetrasphere

Tetravolume 5 = maximum F^h F¹ sphere

(h = high frequency geodesic icosasphere, Sec. 985.01)

Tetravolume 6 = maximum F^h F^ft sphere (high-frequency icosa plus the intersphere volumetric involvement domain of each closest-packed uniradius sphere = rhombic dodecahedron)

1006.36 In respect to each uniradius, omni-closest-packed spherical domain of 6:

Maximum = 5 plus tetra quanta inside icosa sphere F^h 1 minus tetra quantum outside

-integrating as +4

Tetra = 1 plus tetra quantum inside i .

_c , __n r • j b integrating as -4

Sphere 5 minus tetra quanta outside Change: fix eqn

1006.37 For other manifestations of the vector equilibrium involvement domain, review Sections 415.17 (Nucleated Cube) and 1033 (Intertransformability Models and Limits), passim.