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In this article we will continue our discussion taking up where we left off in Articles 130 and 131 with the geometry of the atomic realm.

We will begin a nineteen-part series about the geometry of science, starting here with the geometry of molecules, then moving to the geometry of DNA, water, ice, minerals and crystals, then to the geometry of plants, viruses, bacteria, phytoplankton, radiolaria, sea creatures, insects, animals and human life.

These articles are the meat of Cosmic Core, explaining how everything in reality is built of geometry – specifically Platonic solid geometry and the Golden Ratio.

In later articles we again pick up this discussion to delve into the geometry of the planet, solar system, galaxies and galactic clusters, to finish up our discussion of the geometry of the universe.

The geometry at all scales is based upon the Platonic solids.

Keep in mind we are discussing how geometry relates to a fractal-holographic cosmos with self-similarity on all scales.



Samuel Colman writes in Nature’s Harmonic Unity, “As Nature loves variety, so she produces unexpected results by combining various forces, and while seemingly she deviates continually from the letter of her harmonic laws, she never does from their spirit.  We must not look for an uninterrupted identity of mathematically derived rules with natural phenomena.  The forces at work are so varied in their application that no one of them is uninfluenced by others.  Botanically, torsions will be found occasionally to displace symmetry in a flower, seismic disturbances will interfere with geologic formations, or the solar influence may destroy the ellipse of an approaching comet, but in no case, actual or imaginary, does Nature show any tendency to anarchy.  She abides by her rules, though through the veil of composite effects they are sometimes hard to trace.”


We discovered in Article 131, from Dr. Robert Moon’s work of the Manhattan Project, that each element of the period table is a Platonic solid or a set of nested Platonic solids.  This includes the cube, octahedron, icosahedron and dodecahedron, but not the tetrahedron.  The tetrahedron is the shape of the photon.


The Five Platonic Solids:


Each proton and electron of an atom is actually a corner of Platonic solid geometry.


Oxygen (8) is a cube.  Fluorine (9) is a cube with 1 point of an octahedron in the second shell.

Silicon (14) is afull cube in the first shell and a full octahedron in the second shell.

Iron (26) is a full cube (1st shell), full octahedron (2nd shell), and a full icosahedron (3rdshell).  See image below of an Iron (Fe) nucleus:


Palladium is a cube (1st), octahedron (2nd), icosahedron (3rd) and dodecahedron (4th shell), and so on.  See the image below of a Palladium (Pd) nucleus:


The first 46 elements reflect these four nested Platonic solids.  There are 92 (46 x 2) naturally occurring elements.  The second set of 46 involves two nests of geometry connected side by side or back-to-back.  See, for instance, the nucleus of a Radon atom below:


There are no particles!  Protons and electrons are really vertices of standing wave (vibration, oscillation, frequency) geometry.


We will begin now with the geometry of molecules.  This gets scientific in its nature and some parts may be quite dry to readers, but the important point is to note how the structure, properties and function of all molecules are dependent upon geometry.  Furthermore these geometric molecules form larger geometric lattices.  This means that at the smallest scales we (and all in reality) are both physically and metaphysically composed of geometry.  The order inherent in geometry allows for efficient structure, function, communication, growth and evolution to occur.  Without this order matter would not be able to form and reform and life simply would not work in any way and on any scale.



The Geometry of Molecules



“A molecule is a discrete group of two or more atoms held together in a definite geometrical arrangement.”1

A Single Caffeine Molecule


The geometry of a molecule has a profound influence on its properties.


Remember from previous articles, All is Motion.

Molecules are permanently in motion.


There are three types of motion to molecules:

  1. Translational motion

Has no effect on molecular structure.

This is when a molecule moves along in a straight line (or spiral or arc) from point to point.  This occurs in liquids and gases.


  1. Vibration (Oscillation)

Each nucleus in a molecule is displaced from its equilibrium position in a periodic manner.

Molecules have typically 1012 to 1014 vibrations per second.  This is quite fast.

The amplitude of molecular vibrations at room temperature amounts to several percent of the

inter-nuclear distance.

Vibration of molecules occurs in solids, liquids and gases.


  1. Rotation

A slight centrifugal distortion (moves around a central axis or point) – usually of no importance in molecular structure.  This occurs in gases and liquids, not solids.




Molecular Motion

“Molecular motion is the permutation of atomic nuclei within a molecule.”2  Atoms do not remain still in a molecule.  They move through various permutations of structure depending on their type.

“The equatorial and axial positions rapidly exchange positions through an intermediate square pyramidal structure.

It will have the same orientation afterward, only rotated 90 degrees.

Continuation of this process rapidly exchanges the atoms through all the equatorial and axial positions.”3

A molecule may appear to have a different shape from its true equilibrium geometry.

Watch below how a tetrahedron expands into a cuboctahedron and then contracts into an octahedron.  These types of transitions occur with molecules as well.  You have to imagine molecules attracting to the lines of force (edges and corners).  As they rotate, expand and contract, different geometry forms to allow for changes in the molecule.

This information aligns with the idea that the shifting geometry of the Aether is a flow process that transforms from geometry to geometry as it vibrates and rotates.  At certain points there will be extreme stability.  At other points in time there will be instability which allows for changes to occur in the molecule.

Due to the fractal and nesting properties of Platonic solid geometry, these transitions can easily occur in many, many ways in atoms and molecules. Nature uses Platonic solid geometry for these very reasons.  No other structures have this ability – only Platonic solids and their associated Archimedean & Catalan solids as well as all Platonic solid compounds, truncations and stellations.


Chemical Bond – when two or more atoms are held together sufficiently strongly to form a molecule.

Nonpolar covalent bonds in methane (CH4). The Lewis structure shows electrons shared between C and H atoms.


Bond Length – the distance between atomic nuclei bonded together.  The stronger the force of attraction in between the bonding atoms, the smaller is the length of the bond. However, the bigger the atom size, the longer the bond length.  Examples are shown below:

Credit: Bond Parameters


Bond Angle – the angles between the bonds formed by each atom.

Credit: Bond Parameters


Torsional Angle (dihedral angle) – the angles between the bonds on adjacent atoms, or the angle between two planes.  It defines the conformations around rotatable bonds. The dihedral angle changes only with the distance between the first and fourth atoms; the other inter atomic distances are controlled by the chemical bond lengths and bond angles.

Angle between two planes (α, β) in a third plane (pink) which cuts the line of intersection at right angles


Angles are of extreme importance in molecular chemistry.  Angles are simply a function of geometry.  We will discuss this in more detail below.

Robert Lawlor states, “Form relates to archetypal activity through the function of leverage; the principle that energies are controlled, specified and modified through the effects of angulation.”



Electron Density Distribution

As was discussed in the articles on the Atomic realm, electron density distribution is the measure of the probability of an electron being present at a specific location.

It is the arrangement of the electrons due to their constant motion and the fact that their paths cannot be precisely defined.

It can be determined by quantum mechanical calculations used to find the energy and geometry of a molecule.

“In practice it is only possible to carry out these calculations to a reasonable accuracy for small molecules consisting of light atoms.”4

Here is an example with hydrogen:

Atomic orbitals of the electron in a hydrogen atom at different energy levels. The probability of finding the electron is given by the color, as shown in the key at upper right.


It can also be determined by x-ray diffraction studies on crystalline solids – though it is very difficult to detect the small changes in the electron density distribution that occur.

See Article 177 for more information on x-ray diffraction studies on crystals.

Following Bragg’s law, each dot (or reflection) in this diffraction pattern forms from the constructive interference of X-rays passing through a crystal. The data can be used to determine the crystal’s atomic structure.


Note that molecules have concentric orbital shells of quantized energy levels just as atoms do – although they are more complex than single atoms.

Molecular orbital plot of CO.



Electron Orbitals

Electrons are arranged in concentric geometric shells (orbitals).

Electron density is an experimentally accessible real physical property of a molecule.

It is more readily understood than orbitals – which are abstract mathematical functions.

The nucleus and inner shells usually remain unchanged in molecule formation.  The centers are more stable than the perimeters.


Valence shell – the outer shell of an electron.

The valence shell is the only shell usually modified in molecular formation.

Electron pairs in the valence shell keep as far apart as possible – they repel each other.

A Tin (Sn) atom with 4 electrons in its valence shell.  Valence shell electrons align themselves geometrically as far as possible from other valence shell electrons.



Remember, these atoms are three-dimensional spheroids.  They are not flat discs as the images (like the one above) commonly show.


Three electron pairs in a valence shell form a planar triangle.


Four pairs in a valence shell form a tetrahedron.


Five pairs form a trigonal dipyramid.  (Two tetrahedra back-to-back; or one atom at the center and 5 atoms at the corners.)


Six pairs form an octahedron.



Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of the atoms that constitute a molecule.

It is important to understand the relationship between the electron density distribution and the bonds imagined to hold atoms together in a molecule.

Molecular geometry describes molecular structures with polyhedrons and polygons.


Polyhedron (3D) – encloses a 3D space with four or more polygons.

Polygon (2D) – encloses a portion of a plane with three or more straight lines.


Regular polyhedrons include the: cube, octahedron, tetrahedron, icosahedron, dodecahedron (The Platonic Solids).


Regular polygons include the: triangle, square, pentagon, hexagon, heptagon, octagon, nonagon, decagon…etc.



Prisms – two identical and parallel faces that are joined by a set of parallelograms.

Antiprisms – two identical and parallel faces, joined by a set of triangles.

There are an infinite number of prisms and antiprisms.



Pyramids – the square pyramid is an important molecular shape.  For example, BrF5.

Bipyramids – the trigonal bipyramidis another important molecular shape.  For example, PCl5.

Square bipyramid (octahedron), hexagonal bipyramid and decagonal bipyramid



Lewis Structures

Gilbert N. Lewis (1875-1946) was “an American physical chemist who discovered covalent bonds and his concept of electron pairs.”5

Gilbert Lewis


Lewis Structures are named from his conception of them in 1916.  A Lewis structure consists of an elemental symbol (the core of an atom) surrounded by one dot for each of its valence electrons.

For example, the Lewis structures for carbon tetrachloride and phosgene (toxic)


Lewis structures led to the octet rule since noble gases all have 8 electrons in their valence shell.

In compound formation atoms achieve noble gas electron configurations (8 electrons in the valence shell) by electron loss or gain or by sharing of one or more electron pairs.


Lewis diagrams can be written for many molecules in which each of the atoms has an octet of electrons in its valence shell.

In a completed valence shell all electrons may be considered to be arranged in pairs:

  • bonding pairs
  • non-bonding pairs – lone pairs or unshared pairs


A single shared pair of electrons is called a single bond.  A dash (or line) is sometimes used to indicate a shared pair of electrons.

A double bond forms when two pairs of electrons are shared between a pair of atoms.  This is represented by double lines.

A triple bond forms when three electron pairs are shared by a pair of atoms.  This is represented by triple lines.



Types of Molecular Bonding

Covalent:  A chemical bond that involves the sharing of electron pairs between atoms. (shared electrons)


Ionic:  A chemical bond that involves the electrostatic attraction between oppositely charged ions.  This is the primary interaction occurring in ionic compounds. (unshared electrons)


Hydrogen:  The electrostatic attraction between two polar groups that occurs when a hydrogen atom is covalently bound to a highly electronegative atom such as nitrogen, oxygen or fluorine experiences the electrostatic field of another highly electronegative atom nearby.


Three-center two-electron:  An electron-deficient chemical bond where three atoms share two electrons.




Isomers are types of molecules that share a chemical formula but have different geometries, resulting in very different properties.


VSEPR Model – Valence Shell Electron Pair Repulsion

The VSEPR model “assumes each atom in a molecule will achieve a geometry that minimizes the repulsion between electrons in the valence shell of that atom.”6



Molecular Angles

Recall Robert Lawlor’s quote from above, “Form relates to archetypal activity through the function of leverage; the principle that energies are controlled, specified and modified through the effects of angulation.”7

An angle is a relationship of two numbers.  Angles were used in ancient symbolism to designate a group of fixed relationships controlling interacting complexes or patterns.


Geometric optics reveal to us that each substance refracts light at its own particular angle.  This angle gives us the most precise definition of the substance.

Angles in bonding patterns of molecules largely determine the qualities of the substance.  These qualities include freezing, melting and boiling points, electrical conductivity, radioactivity, corrosivity, compatibility with other molecules, solubility in water and organic solvents, as well as many other chemical and physical properties.



Ideal Bond Angles

Name Angles
Tetrahedral 60º or 109.5º
Linear 180º
Triangular 60º or 120º
Square 90º
Centered octahedral 90º
No center octahedral 60º and 90º
Centered trigonalbipyramidal 90º and 120º


Keep noticing how the Platonic solids show up again and again!



Types of Molecular Structure

Linear: (see chart above)

The atoms are connected in a straightline.

Bond Angles – 180º

Examples: H2 ;HCl ; CS


Trigonal Planar: (see chart above)

The atoms are arranged somewhat triangular and exist in one plane.

Bond Angles – 120º

Examples: Bcl3; BCl2Br ; BClBr2 ; SO3 ; SO2


Tetrahedral: (see chart above)

There are four bonds all on one central atom.

No extra unshared electron pairs.

Bond Angles – 109.47º (arccos(-1/3))

Examples: CH4 ; CH3F ; NH3 ; H2O


Octahedral: (see chart above)

These molecules have eight faces.

Bond Angle – 90º

Examples: SF6 Sulfur hexafluoride ; XeF4


Trigonal Pyramidal:

These have a pyramid-like shape with a triangular base.

There are three pairs of bonded electrons, leaving one unshared lone pair.

Example: ammonia NH3


Trigonal Bipyramidial: (see chart above)

Examples: PCl5 ; PCl4F ; PCl3F2 ; SF4 ; ClF3


Pentagonal Bipyramidal:

Example: IF7



Single Molecule Images: IBM Scientists Capture Closest Photographs Showing Chemical Bonds – Evidence of Microscale Sacred Geometry

A team of IBM scientists at the Centre National de la Recherche Scientifique (CNRS) inToulouse –known for capturing the first close-up image of a single molecule in 2009– revealed incredibly detailed microscopic images that show the individual chemical bonds between atoms in 2012.8

Below is the image they captured of a nanographene molecule exhibiting carbon-carbon bonds of different length and bond order.


Notice how this molecule resembles the Flower of Life (left below) and the expanded Flower of Life (right below).

Here is an image of an isotropic vector matrix overlaid upon a Flower of Life.

Interestingly, in 1912 Samuel Colman published the book Nature’s Harmonic Unity with the following image (page 13) of molecular structure:

The similarity of these two images, published exactly 100 years apart, is striking to say the least.


Samuel Colman writes that “a system of ‘octaves’ closely corresponding to the theory of music, is the basic element of all growth in Nature, guiding her forms to their ultimate use and beauty.  Molecular structure, for example, is made of repeating particles or octants, which would be round if it were not for atmospheric pressure, but under the influence of this principle molecules are packed in the only possible way without interstices or waste room.  If masses of these circles are drawn on a small scale and regarded with the eye partly closed they will appear to be actual hexagons…This primal arrangement is under the inviolable influence of ‘polar force’ causing atom to lay itself to atom in a definite way but liable of course to accident; the law is superior to accident, however, for as we shall see angular magnitude is a principle ultimately enforced.”9



Molecular Lattices

“Modern chemistry is discovering molecular, atomic, and subatomic structures strikingly similar to the geometric patterns of Islamic art and architecture.”10

Molecular lattice structures have been found to resemble Islamic art tiling patterns.


Keep in mind that when you see an individual molecule they consist of a ‘part or piece’ of geometry.  For instance, you will often see a piece of a hexagon or pentagon, or a single straight line at a particular angle.

Protein molecule


Contemplate the fact that molecules don’t exist singly in nature except as gasses or under strict laboratory procedures.

For instance there are approximately 1.67 sextillion water molecules in a single drop of water!  That is 167 with 21 zeros after it.

In solids or liquids molecules attract together completing the partial geometry of their molecular structure.  They do not cluster and combine randomly or chaotically like a crumpled piece of paper or chaotic mass of particles.  As so many come together they will form very intricate and geometrically structured patterns that do indeed resemble the intricate geometric patterns of Islamic art.  They fall in line along invisible Aetheric flow fields that are geometric in structure – just as we saw in Cyamtics!

If they did not do this they would not be able to communicate as a whole structure.  If they could not communicate they could not change, grow, heal or transform according to the needs of whatever matter the molecules are making up.  Chemistry as we know it could not occur without this high level of order and communication across the molecular lattice.


This is fascinating to think about.  The matter of our bodies (and all else in nature) is physically composed of beautiful and intricate geometric patterns!  Our bodies are true and literal works of art…as well as everything else surrounding us.

Little geometry forms larger geometry.  We live in a fractal-holographic universe!

“Molecules containing predominately ionic bonds are not common because normally when oppositely charged ions are attracted together, they form a crystalline solid that consists of a regular periodic arrangement of ions in which no discrete molecules can be recognized.”11

Eight of the allotropes (different molecular configurations) that pure carbon can take:  a) Diamond; b) Graphite; c) Lonsdaleite; d) C60 (Buckminsterfullerene); e) C540; f) C70; g) Amorphous carbon; h) single-walled carbon nanotube



Molecular Lattice

A lattice is a regular (i.e. geometric) arrangement of particles.

They are arranged to achieve minimum stored energy.

These two principles of ‘regularity’ and ‘minimum stored energy’ are the principles of how and why the Platonic solid geometry is used.  It is all about efficiency.


Ions are bonded with ionic bonding creating a giant ionic lattice.

Ionic lattice of NaCl (table salt)


Atoms are bonded with covalent bonding creating a giant molecular lattice.

A molecular lattice of protein.


These lattices are beautiful microscopic works of art!

Rhodium Trichloride; Cobalt (II) Choride; and Iron (II) Chloride.


We will now shift gears slightly to discuss microclusters, a unique form of a molecule.



It was found that atoms naturally gather together in Platonic solid geometric patterns when they are set loose one at a time, in a given area.

The atoms are shot down a nozzle one at a time – they are attracted to one another and cluster together, forming microclusters shaped like Platonic Solids.  They do not just group together in an unorganized mess.  They fit together as Platonic solids!  There is an invisible Aetheric flow field that is attracting them and holding them in place – again, just as we saw in Cymatics!


Text reads: A series of electron micrographs showing a series of changes of a gold microcluster consisting of about 460 atoms.  The structure is constantly changing, alternating between geometries based on a sequence Platonic Solids – a transitional state between solid & liquid states.  Microclusters are an intermediate state between matter & Aether.


This led to the discovery of a new state of matter called microclusters.  These are also called monatomic elements or ORMUS elements.


The standard conception of molecular size is:

Molecules: 1-10 atoms (conventional view)

Microclusters: 10-1000 atoms

Fine particles: 1000-100,000 atoms

Bulk Matter: 100,000+ atoms


In microclusters, the electrons appear to orbit the center of the cluster, rather than the center of each atom.

This suggests there are no electrons.  There is only geometrically arranged electron clouds.

According to mainstream science, you cannot build an atom that way with particles.  Particles should not be able to break away from the orbit of the atom (the strong force) to orbit the cluster, yet nevertheless, they do just that.  This means that each microcluster creates its own local gravity field. Again, this should not be able to happen according to mainstream physics.

If you don’t hear about microclusters it is because it shatters the old scientific paradigm.  A new scientific paradigm must be built.

Microclusters are very strong, and temperature resistant.  The do not conduct electricity through the center.  They are highly conductive around the outside.

The clusters are constantly moving around.  They do not hold one shape.  They transform their geometry.  They illustrate a part of a greater fluid-like geometry of the cosmos.

It is to be noted that only certain “magic numbers” of atoms will gather together to form microclusters.

“Clear-cut evidence has been obtained such that microclusters of alkali and noble metal elements in the form of a cluster beam have a nearly spherical shape at the size of the so-called magic numbers.”11


For example:

Magic numbers for neutral Na clusters – 8, 20, 40, 58, 93

Magic numbers for gold atoms:  459 atoms form a cuboctahedron; 561 form an icosahedron.

Satoru Sugano and Hiryasu Koizumi’s Microcluster Physics, Volume 21 in a series of texts in the field of materials science states, “Recently, it has been discussed that stable shapes of microclusters are given by Plato’s five polyhedra; the tetrahedron, cube, octahedron, pentagonal dodecahedron, icosahedron and Kepler’s two polyhedra of rhombic faces; rhombic dodecahedron and rhombic triacontahedron.”12


At a level far too tiny for the naked eye, atoms are grouping together into perfect Platonic Solid formations.

Microclusters are tiny “particles” that present clear and straightforward evidence that atoms are vortexes in the aether that naturally assemble into Platonic Solid formations by their vibration/pulsation.”13




We have briefly discussed molecular geometry in this article, pointing out the important concepts and structural aspects of single molecules, molecular lattices and microclusters.  The important thing to get out of all of this is that molecules automatically form geometrically, or rather, geometry of the Aether forms the molecular structure.

This geometry is Platonic solid in nature.  It is not only the five regular Platonic solids, but also the Archimedean solids, Kepler solids and all truncations, stellations and combinations of these solids.

We see this at every scale from the subquantum up to the galactic cluster.  This is no coincidence.  There is intelligence imbedded within all life and matter that allows for this ordered, efficient formation to take place.

In the next article we will look at many molecular compounds paying particular attention to the geometry involved.  Take particular note of the pentagon/hexagon arrangement of atoms.



  1. Gillespie, Ronald J and IstvanHargittai, The VSPER Model of Molecular Geometry, Dover Publications, 1972
  2. ibid.
  3. ibid.
  4. ibid.
  6. Gillespie, Ronald J and IstvanHargittai, The VSPER Model of Molecular Geometry, Dover Publications, 1972
  7. Lawlor, Robert, Sacred Geometry: Philosophy & Practice, Thames & Hudson, 1982
  8. org, In world’s first, atomic force microscope sees chemical bonds in individual molecules, 13 September 2012,
  9. Colman, Samuel, Nature’s Harmonic Unity: A Treatise on Its Relation to Proportional Form, Forgotten Books, 2017
  10. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, HarperPerennial, 1995
  11. Gillespie, Ronald J and IstvanHargittai, The VSPER Model of Molecular Geometry, Dover Publications, 1972
  12. Sugano, Satoru and Hiryasu Koizumi,Microcluster Physics, 1991
  13. ibid.
  14. Wilcock, David, The Source Field Investigations, Dutton, 2011

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