The Greeks were fascinated with regular forms whose faces were all the same, such as the cube. However, they failed to understand the delicate balancing act the cuboctahedron symbolizes. The Greeks never really comprehended the energetic properties of Vector Equilibrium, i.e. dynamic stability. They had a static, non-relativistic view of natural philosophy. Plato, Archimedes, and the Pythagoreans based much of their philosophical speculation around the nature of geometrical forms suggesting that mathematics and structural forms had substantial validity.
Throughout the centuries, various geometrical forms have been revered as expressions or metaphors of higher spiritual truths. These sacred forms and symbols are a natural part of the collective consciousness which emerges in every generation. We project them outwardly from within our psyche because they are so fundamental to our existence. This geometry lies within us all, it is part of the surrealistic quantum realm. The void state, or primal matrix, is "cosmic zero," and proportionately our most fundamental reality.
The notion of the eternal nature of sacred geometry is echoed in modern quantum theory. The central concept in Quantum Field Theory is that of the matrix:
All matter is not separate from its surrounding space. The matrix can take the form of quanta or particles. This quantum field is our fundamental physical entity and reality.
In R. Buckminster Fuller's geometrical tour de force, SYNERGETICS I & II. he demonstrates, that the whole is greater than the sum of its parts, because of the relativity of forces. The so-called "cosmic zero" was modeled by geometer/philosopher Fuller in the figure he called Vector Equilibrium. It might actually claim to be the first "Buckyball," the one Fuller himself described. Fuller asserted that, "zero pulsation in the Vector Equilibrium is the nearest approach we will ever know to eternity and god."
The Vector Equilibrium center is primal "emptiness." It is a mathematical anomaly where the normal laws of the space/time continuum break down. It is not a symbol of ultimate order. It looks like a very rational, orderly system, but it is ultimately irrational. It defies logic. Vector Equilibrium is the breeder of wave-particle duality and has the uncertainty principle, of non-locality at the quantum level. According to Fuller, it is a zone of neutral resonance where waves can pass through waves without interference. Yet, it never physically exists as a structure because nature abhors a vacuum.
Vector Equilibrium emanates/condenses from a center in twelve fundamental directions. This emergent energy moves outward through space/time in the form of a cuboctahedron, alternating with its mathematical reciprocal, an octahedron-within-a-cube. It is a truncated cube with 50 symmetrically positioned topological features. Vector Equilibrium has the same surface area as a sphere, yet contains no volume, i.e. it contains "nothing."
The Vector Equilibrium system has 12 vertices, 8 triangular faces, 24 edges, and 32 planes. It is an omnidirectional equilibrium symbolically and physically speaking. Thus, it is a perfect symbol for "holding the tension of the opposites," or "uniting the opposites." Yet, it is more than a metaphor. It is an archetypal image which connects the matrix with the universe or the universe with the matrix.
In the Vector Equilibrium figure, equilibrium between positive and negative is zero. It is the equalization of the forces of push/pull, radiation/gravitation, or tension/compression. Fuller stated it "represents the limits of the mind's ability to conceptualize 'in'." For Fuller, all of space/time is intertwined with a pre-geometric matrix, which is the infinite field of vector equilibria. An entire universe can be seeded from one Vector Equilibrium, self-generating to fill all space/time.
According to Fuller, there may be no ultimate physical building-block of matter, but there is one single entity that intertwines and composes everything in the universe, Vector Equilibrium.
