Return to Free Library

Return to Science Menu

Previous Article                                                                         Next Article


In the last article we discussed what subatomic particle interactions are and the rules they are bound by.

In Part A of this article we will discuss the evolution of the search for the singular geometry that defines all the myriad subatomic particle interactions.

We will discover that this singular geometry is the amplitudehedron which is based upon the star tetrahedron, or two interlocking tetrahedra.  We will then examine the concept of the photon (in Article 124B : Part 4) and find it is tetrahedral in nature.  We will also examine how the photon is related to the amplitudehedron.



Previous Attempts to Unite Subatomic Particle Interactions into a Singular Geometry



Murray Gell-Mann & the Eightfold Way

American physicist Murray Gell-Mann (1929-present) made one of the first attempts to unify subatomic particle interactions into a singular geometry.

He received the 1969 Nobel Prize in physics for his work on the theory of elementary particles.

He came up with the “Eightfold Way” model of quarks that is tetrahedral.  Interestingly, he used the term “Eightfold Way” after the Buddhist concept of the Noble Eightfold Path which offers a guide to the end of suffering:

  1. Right understanding – free from superstition and delusion
  2. Right thought – elevated and worthy of intelligence
  3. Right speech – kindly, open and truthful
  4. Right action – peaceful, honest and pure
  5. Right livelihood – bringing hurt or danger to no living being
  6. Right effort – in self-training and in self-control
  7. Right mindfulness – the active watchful mind
  8. Right concentration – deeply meditating on the realities of life

The Perennial Philosophy teaches that science and spirituality are inextricably linked though it may take time for our societies to fully grasp this important truth.


Gell-Mann built a model of how quarks are unified into a singular pattern.  They are pieces that start out geometric and can only break off in certain ways.

He found them only in tetrahedral and cuboctahedral patterns.

The movement of subatomic particles is very precise.

Mesons fall into neat hexagonal patterns known as the meson octet. (Pictured below.)


Baryons fall into the same neat hexagonal pattern known as the baryon octet. (Pictured below.)


Baryons can also fall into a neat triangle shape composed of 9 smaller triangles known as the baryon decuplet. (Pictured below.)


Below is the baryon supermultiplet.  It falls neatly into a tetrahedral shape.



Richard Feynman & Feynman Diagrams

Richard Feynman (1918-1988) was an American theoretical physicist who won the Nobel Prize in physics in 1965.

He worked on the Manhattan Project and simplified physics to a great degree.

He replaced “Fock Space” with Feynman diagrams – pictorial representations of amplitudes or particle reactions describing the behavior of subatomic particles.

These Feynman diagrams are related to the space-time diagrams created from interactions seen in bubble chambers.

Wikipedia states, “A Feynman diagram is a representation of quantum field theory processes in terms of particle interactions. The particles are represented by the lines of the diagram, which can be squiggly or straight, with an arrow or without, depending on the type of particle. A point where lines connect to other lines is a vertex, and this is where the particles meet and interact: by emitting or absorbing new particles, deflecting one another, or changing type.

Feynman diagrams are often confused with space-time diagrams and bubble chamber images because they all describe particle scattering. Feynman diagrams are graphs that represent the interaction of particles rather than the physical position of the particle during a scattering process.”

Below is an example of a Feynman diagram:


Each diagram requires 90 pages or more of long hand calculations [partial example below] and there are a massive number of Feynman diagrams!

“The number of Feynman diagrams is so explosively large that even computations of really simple processes weren’t done until the age of computers”…A seemingly simple event, such as two subatomic particles called gluons colliding to produce four less energetic gluons (which happens billions of times a second during collisions at the Large Hadron Collider), involves 220 diagrams, which collectively contribute thousands of terms to the calculation of the scattering amplitude.”1

Feynman diagrams are one aspect that led to super string theory.


Note the Feynman diagrams below and how they are all hexagonal in nature.  There are many other Feynman diagrams than these, but they are all geometric and/or looping in structure.


More Feynman diagrams are pictured below.  Note the 6-point geometry.



Sir Roger Penrose & Twistor Theory

Sir Roger Penrose (1931-present) is an English mathematical physicist and the winner of numerous physics awards.

He re-interpreted general relativity and proved black holes can be created from dying stars.

He was also involved in the study of black holes with Stephen Hawking.

He did not agree with the Big Bang and had a falling out with Hawking.  Read The Nature of Space and Time by Roger Penrose and Stephen Hawking to hear their debate.

Penrose said space and time do not exist, but they come from an underlying energy that behaves like a fluid that vibrates in geometric patterns.

He believes all of space and time is an emanation of a single geometric form.  (The universe has a geometric intelligence.)

He also understood the importance of consciousness in relation to discovering how the universe works.  He said, “Consciousness is part of our universe, so any physical theory which makes no proper place for it falls fundamentally short of providing a genuine description of the world.”

Read The Emperor’s New Mind by Roger Penrose for more about consciousness.


Penrose also pioneered ‘twistor theory’ – getting rid of quantum mechanics.

“Twistor theory has been developed by Roger Penrose and his associates since the 1960s. He realized that using the space-time continuum picture to describe physical processes is inadequate not only at the Planck scale of 10-33 cm but also at the much larger scales of elementary particles, or perhaps atoms, where the quantum effects become important. He believes that space-time is created out of quantum processes themselves at the subatomic level.  [This aligns nicely with the concept of Aether units creating space, time and matter.]  The mathematical tool in field theories is not suitable for the new formulation since the field equations are based on well-behaved functions varying smoothly in space-time. Thus his mathematical tool is geometry instead of differential equations.

The initial attempt to formulate discrete space-time used spinor as the building block.  (Spinor or ‘twistor’ pictured below.)

The spinor is a mathematical object that is used in the quantum theory to describe the spin of the elementary particles. It is the simplest quantum object having only two possible states – spin up or spin down. It is argued that if the distinction between a spin up and a spin down is to have meaning within a quantum theory set in empty space, it seems to imply the spinors actually create their own spaces – a sort of quantum version of the more familiar space-time.”2


Note how this spinor (or twistor) resembles the toroidal flow talked about so much in Cosmic Core.

This spinor is a parallel concept of a toroidal Aether unit – the fundmental subquantum process that forms space and time.  Twistor theory, however, does not include an Aether.  It is an incomplete theory, yet interesting nonetheless.



The Amplitudehedron is the Geometric Singularity Structure of Particle Interactions

The Amplitudehedron (Positive Grassmanian) has been found to be the “singularity structure” of particle interactions.

It was discovered in 2013 by two physicists Nima Arkani-Hamed and Jaroslav Trnka.

In the article, A Jewel at the Heart of Quantum Physics, published September 17, 2013 it reads:

“The amplitudehedron is a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions.  Encoded in its volume are the most basic features of reality that can be calculated – the probabilities of outcomes of particle interactions.”3

“Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.

In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry.”4


The amplitudehedron was built off Penrose models of twistor diagrams.  Every part is a tetrahedron.  Look at the image below of the amplitudehedron.  It is clearly composed of four tetrahedra.


Twistor diagrams and Feynman diagrams are both ways of computing the volume of the amplitudehedron piece by piece, but the Feynman diagrams are much less efficient.

All the Feynman diagrams can be derived from the amplitudehedron!  Think about that!  Think about the incredible complexity involved in all Feynman diagrams and how they ALL can be condensed and understood by a fairly simple and straightforward geometric structure.

Geometry has the ability to accurately simplify that which takes thousands upon thousands of pages of complex Calculus equations.


Notice below how the shape of the amplitudehedron drawn by Arkani-Hamed & Trnka) appears identical to one corner of the star tetrahedron.

One corner of the star tetrahedron would consist of 2 of the 8 vertexes.  Also remember that the star tetrahedron is also called the stellated octahedron and Merkaba.

Credit: David Wilcock


The Amplitudehedron creates the universe in its image.  It is a shape that creates amplitudes that jiggle particle tracks in bubble chambers.  See the artistic rendering of the amplitudehedron below.  This image reminds us that the amplitudehedron (like the photon) is not a ‘thing’.  It is an energetic wave structure composed of wavelengths, frequencies and harmonics.  All wave structures are embedded with geometry.

It shows the universe is an emanation of a single geometric form and the fractal-holographic model of the universe is correct!


As physicist Nassim Haramein notes, “Geometry is the underlying organizing principle and key to unifying and understanding interactions between the macro and microcosmic.”


The seed of universe has been found to be the Amplitudehedron.  This is the single geometric form from which all space and time emanate from.

“In a sense,” Arkani-Hamed says, “we would see that change arises from the structure of the object…but it’s not from the object changing.  The object is basically timeless.”5


Remember: Subatomic particle interactions (amplitudes) are a flow of energy in which particles are created and dissolved but the energy can only flow through certain ‘channels’.

All of these channels of quantum interactions were traditionally calculated with Feynman diagrams.

All of the hundreds of Feynman diagrams can be derived with one single structure – the Amplitudehedron.

Hence, all of space and time is an emanation from this single geometric form.


As we move forward we will discuss how the Amplitudehedron is related to the original photon and hence, the structure of all photons!  Remember, quantum theory tells us every photon is identical.

According to the work of David Wilcock, everything in the universe emanates from the original photon fractalizing outwards and inwards to form the fractal-holographic structure of the universe; and photons are shaped as star tetrahedra.  This is discussed in Article 124B.

The photon itself is the singularity structure of particle interactions.  Encoded in its volume are the most basic features of reality that can be calculated – the probabilities of subatomic particle interactions.


Remember, Photons spin and loop to create subatomic particles.

Subatomic particles form atoms.

Atoms form matter.

This process will be described in detail in Articles 125-128.


“[Dewey] Larson says that ‘all is motion’ which we can take as vibration, and that vibration, which is pure vibration is not physical in any way or form or density; the first product of that vibration is what we call the photon, the particle of light.  This light then can condense into material as we know it in our density, into all of our chemical elements because of rotations of the vibration at quantized intervals or units of angular velocity.”6


American physician and author Edwin D. Babbit writes, “Light reveals the glories of the external world and yet is the most glorious of them all.  It gives beauty, reveals beauty and is itself most beautiful.  It is the analyzer, the truth-teller and the exposer of shams, for it shows things as they are.

We shall do well, then, to consider this potential and beautiful principle of light and its component colors, for the more deeply we penetrate into its inner laws, the more will it present itself as a marvelous storehouse of power to vitalize, heal, refine, and delight mankind.”

We will look at the geometry of the photon in Part 4 of this article series.




In this article we have examined the geometry of subatomic particle interactions and the evolution of the search for the singular geometry of subatomic particle interactions.

We have seen the undeniable proof that at the tiniest quantum levels, geometry prevails…and not just any geometry, but Platonic solid geometry.

Both subatomic particle interactions and the photon are tetrahedral based.

It is to be remembered that the tetrahedron is dual with itself, so whenever one tetrahedron shows up, there is always another, pointing in the opposite direction to maintain symmetry.

Also remember that inside the star tetrahedron is an octahedron pointing at a 45 degree angle.


These tetrahedra and octahedra take us back to our discussion of the geometric matrix of the Aether, both on a subquantum scale and on a macrocosmic scale.

Remember the Isotropic Vector Matrix is a matrix of octahedra and tetrahedra and is believed to be the ground state matrix of the Aether by Buckminster Fuller and Nassim Haramein.

Also recall the shape of the cosmic gravitational cells per the work of Conrad Ranzan.  They were also octahedra and tetrahedra that tessellated on galactic cluster scales.

We will continue to see these same Platonic solids show up again and again on every scale as we move through Cosmic Core.

In a fractal-holographic universe this is to be expected.  If all matter is made of light, and light is tetrahedral in nature, then we would expect to see this shape show up again and again.

However, also remember that when one Platonic solid is present, they are all present.  They are not still shapes, but flow processes, and they flow, flip, expand and contract as they change from shape to shape.



  1. Wolchover, Natalie, Scientists Discover a Jewel at the Heart of Quantum Physics, 12/11/13,
  2. Twistor Theory,
  3. Wolchover, Natalie, Scientists Discover a Jewel at the Heart of Quantum Physics, 12/11/13,
  4. ibid.
  5. ibid.
  6. Elkins, Don, The Law of One, Session 27.14,
  7. Edmondson, Amy, A Fuller Explanation
  9. Wilcock, David, Divine Cosmos, Chapter 4,
  10. ibid.
  11. ibid.
  12. ibid.
  13. O’Connell, Cathal, What shape are photons? Quantum holography sheds light, 20 July 2016, Cosmos Magazine,
  14. Elkins, Rueckert, McCarty, The Law of One, Session 15.22,
  15. Melchizadek, Drunvalo, The Ancient Secret of the Flower of Life, Volume 2, Light Technology Publishing, 2000
  16. ibid.
  17. Critchlow, Keith, The Hidden Geometry of Flowers: Living Rhythms, Form and Number, Floris Books, 2011

Return to Free Library

Return to Science Menu

Previous Article                                                                         Next Article