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Vector Equilibrium & Isotropic Vector Matrix

Vector Equilibrium (VE) is the most primary geometric energy array in the cosmos. According to Bucky Fuller, the VE is more appropriately referred to as a “system” than as a structure, due to it having square faces that are inherently unstable and therefore non-structural. Given its primary role in the vector-based forms of the cosmos, though, we include it in this section.

The Vector Equilibrium, as its name describes, is the only geometric form wherein all of the vectors are of equal length. This includes both from its center point out to its circumferential vertices, and the edges (vectors) connecting all of those vertices. Having the same form as a cuboctahedron, it was Buckminster Fuller who discovered the significance of the full vector symmetry in 1917 and called it the Vector Equilibrium in 1940. With all vectors being exactly the same length and angular relationship, from an energetic perspective, the VE represents the ultimate and perfect condition wherein the movement of energy comes to a state of absolute equilibrium.

 

Structure of the Unified Field - The VE and Isotropic Vector Matrix

The most fundamental aspect of the VE to understand is that, being a geometry of absolute equilibrium wherein all fluctuation (and therefore differential) ceases, it is conceptually the geometry of what we call the zero-point or Unified Field — also called the "vacuum" of space. In order for anything to become manifest in the universe, both physically (energy) and metaphysically (consciousness), it requires a fluctuation in the Unified Field, the result of which fluctuation and differential manifests as the Quantum and Spacetime fields that are observable and measurable. Prior to this fluctuation, though, the Unified Field exists as pure potential, and according to contemporary theory in physics it contains an infinite amount of energy (and in cosmometry, as well as spiritual philosophies, an infinite creative potential of consciousness).

Being a geometry of equal vectors and equal 60° angles, it is possible to extend this equilibrium array infinitely outward from the center point of the VE, producing what is called the Isotropic Vector Matrix (IVM). Isotropic means “all the same”, Vector means “line of energy”, and Matrix means “a pattern of lines of energy”. It is this full isotropic vector matrix that can be seen as the infinitely-present-at-all-scales-and-in-perfect-equilibrium geometry of the zero-point Unified Field. Every point in this matrix is a potential center point of a VE around which a condition of dynamic fluctuation may arise to manifest. And as has been stated and is seen in this image, this VE geometry is inherent in this matrix (the green lines comprise the VE):

The IVM also consists of a simple arrangement of alternating tetrahedron and octahedron geometries, as seen in this illustration:

In fact, the VE itself can be seen to consist of a symmetrical array of eight tetrahedons with their bases representing the triangular faces of the VE, and all pointing towards the VE’s center point. (The square faces are the bases of half-octahedron, like the form of the pyramids in Eqypt.)

Given this primary presence of tetrahedons in the VE and IVM, researcher Nassim Haramein sought to determine the most balanced symmetry of them that takes into account the positive and negative polarity of the IVM structure (i.e. “upward” and “downward” pointing tetrahedrons). He identified an arrangement of tetrahedrons in the IVM that, at a scale of complexity one level greater than the primary VE geometry, defines the most balanced array of energy structures (tetrahedons) wherein the positive and negative polarities are equal and without “gaps” in the symmetry. This arrangement consists of 32 positive and 32 negative tetrahedrons for a total 64, and looks like this (notice the underlying VE symmetry as well):

Beyond the VE’s primary zero-phase symmetry, the 64 Tetrahedron Grid, as it is known, represents the first conceptual fractal of structural wholeness in balanced integrity. It is noteworthy that the quantity of 64 is found in numerous systems in the cosmos, including the 64 codons in our DNA, the 64 hexagrams of the I Ching (Chinese Book of Changes), the 64 tantric arts of the Kama Sutra, as well as in the Mayan Calendar’s underlying structure. It appears that the 64-based quantitative value is of primary importance in the fundamental structure of the Unified Field and how that field manifests from its implicate (pre-manifest) order to its explicate (manifest) order, both physically and metaphysically. (See also the relationship between the Analog and Digital realms describing numerically how both the binary 64-based system and the Phi-based Fibonacci system are in intimate coordination.)

 

12 Spheres Around 1

Another way of deriving the geometry of the VE is by using 13 spheres of the same diameter. Using one sphere as the center point, we can then pack twelve spheres around this “nucleus” sphere, as seen in the illustration below. Given that the diameter is the same for all of the spheres, the centers of each sphere will be equidistant from all of their adjacent neighbors, including the center one. The lines connecting their centers are the vectors of the VE. Because it’s an array of 12 spheres around one central sphere, we can refer to the VE’s geometry as a 12-around-1 system. We can then consider this system when we examine the cosmometric relationships of 12-based systems such as the 12-tone music scale, the astrological zodiac, and the Sectors of Human Concern. (See also this figure from Fuller's Synergetics)

 

4 Hexagonal Planes

The VE also has the attribute of consisting of four hexagons symmetrically arrayed in four planes. As can be seen in the illustration below, there is one at the equator or horizon plane (red), one encircling the whole VE as if being viewed from directly above (blue), and two at left and right-tilting angles (green and purple). They are all 60°s from each other, and the angles they define are exactly the same as those of the faces of a tetrahedron. According to Fuller, this is the zero-tetrahedron, wherein the tetrahedron’s faces have all converged simultaneously on its center point. (It is also significant to note that the 8 triangular faces of the VE symmetrically match the 8 triangular faces of a star tetrahedron as well, this being a polar-balanced geometry of the tetrahedron’s most basic structural form; see the Tetrahedron page for more on this).

It is because the VE has these four hexagonal planes defining its spatial coordinates (and therefore, too, the IVM) that Fuller says that the foundation of the cosmic geometry is actually 4-dimensional, as opposed to the conventional 3-dimensional 90° X,Y,Z coordinate system historically assumed to be fundamental.

 

The Spherical VE or Genesa Crystal

It is to the symmetrical arrangement of these four hexagonal planes that we align the four phi double spiral field patterns in the basic model of cosmometry. In essence, the points of these hexagons all touch the surface of a sphere, and the phi double spiral boundaries define in the simplest manner the great-circle vectors of a spherical VE. This form, pictured below, is also known as the Genesa Crystal, and is purported to possess the property of balancing and cleansing the energy of the environment surrounding it for a distance of 2 miles when using a 16” diameter model. (See this link for more information on the Genesa Crystal, and this video of one inhabiting the center of the garden at the Perelandra Center for Nature Research in Virginia, USA). In essence, this simple form, even when built solely of copper or brass strips or tubing, sets up a resonance with the underlying structure of the Unified Field, thus creating an island of coherence is a sea of naturally occurring “chaos,” amplifying the equilibrium state throughout its surrounding local field.


4 Phi Double Spirals (red, blue, green, purple), VE and Torus

 

The VE’s Relationship to the Cube and Octahedron

In the terminology of basic geometry, the form that the VE defines as a solid is called a cuboctahedron (pronounced “cube-octahedron”). As is evident from its name, this form has a symmetrical relationship to both the cube and the octahedron, wherein the six square faces of the VE are symmetrical to the faces of a cube, and the eight triangular faces of the VE are symmetrical to the faces of an octahedron. Another way of seeing this is that the structures of both a cube and an octahedron can be “wrapped” around a VE:

This will be significant when we explore in the next section the dynamic nature of the VE’s ability to contract and expand and transfer energy and information seamlessly throughout the entire Unified Field across all scales instantaneously.

 

The Jitterbug

So far we have looked at the VE in its static state (or more correctly, its ultimate dynamic equilibrium zero state). In other words, we’ve looked at the form in its state of perfect symmetry. What is also quite remarkable about the VE is that, given it has six square faces and that squares are inherently non-structural (only triangles are structurally stable), the VE has the ability to “collapse” inward, drawing the twelve outer points symmetrically towards its center point. As it does so it goes from its state of perfect equilibrium (the zero-phase) into a dynamic “spin” that can contract in both clockwise and counterclockwise directions. When contracted and expanded alternating in both directions, it exhibits a dynamic “pumping” action that Fuller called the Jitterbug (after the dance of the 1930’s that was popular at the time he was exploring this phenomenon).

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