Atomic Geometry

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Atomic Geometry
Summary

Atomic geometry is the world's first comprehensive geometric model of the atom, that visualises the electron cloud through three dimensional polyhedra. Whereas other models of the atom describe the atom from the perspective of energy, this model observes the geometric patterns of space generated by the 4 types of Orbital S, P, D and F. Drawing inspiration from Schrödinger's wave equations, we find the electrons fall into distinct geometric arrangements, which can be translated directly into Platonic and Archimedean Solids. These are perfectly nested inside of each other to produce a 3D representation of the stable elements on the Periodic table.

KEY POINTS

✔ Atomic geometry is the world 1st completely geometric model of the atom.
✔ S, P , D and F orbitals are 2D shapes found in the completion of the Seed of Life Mandala
✔ Orbitals combine to form geometries that can be represented as a nested set of Platonic and Archimedean Solids

Introduction

Image if you could hold a 3D model of an atom in your hands. Well, now you can! Atomic Geometry can be created using simple card, scissors, and glue, that form 3D polyhedra. When created with specific side lengths, these polyhedra can be nested inside one another in such a way as to reflect the geometry of the electron cloud.  This tactile exploration of the atom is a fantastic tool for younger children to comprehend the depths of atomic theory. We have found through running workshops in atomic geometry that children as young as seven years of age are able to cognise complex ideas such as, the electron configuration, orbital shells S,P D and F, the atomic nucleus, and electron pairing.

In2Infinity - Atomic Geometry - holding model in hand

History of Atomic geometry

Atomic Geometry offers a completely new perspective of the Atom, which was conceived in 2015, by Colin Power, co-founder of In2Infinity. The inspiration for this model came about through his exploration of compass construction. Throughout the history of humanity, this technique has revealed many scientific laws and discoveries. From the ancient world of Plato and Pythagoras, Euclid’s ‘The Elements’, to great thinkers such as Leonard Da Vinci, and Astronomers such as Johannes Kepler, all have employed the drawing compass in their exploration of the Universe.

Now, for the first time, these geometric techniques have been applied to the structure of the electron cloud. It is no surprise that it brings truly revolutionary perceptions of the Atom, that solves many mysteries of the quantum world.

It all began in 2013, when I built my first set of Platonic Solids and nested them inside of each other. Whilst doing this, I rearranged the metaphysical concept of the five elements, breaking traditional convention. This gave me a completely new perception of these forms and their relationship to each other.

Shortly afterwards, in February 2014, I began writing a book on geometric concepts, drawing inspiration from ‘God’s secret formula‘ by Peter Plichta.  This book exposed some interesting revelations about the Periodic table: there are only 81 stable elements with a strange anomaly: Element 43 and 61 were missing. Being intrigued about this mystery, I started to turn my attention to the Atomic Structure.

I remember the day when I first found out that P-electron orbitals resembled the configuration of an Octahedron, one of the five Platonic Solids. On examining the other types of orbital shell, it became exceptionally clear to me that the Atom was based on geometry. The fact that this geometric structure had not been recognised by mainstream science was quite astonishing to me. The orbitals clearly present simple forms: S look like a circle, P, a line, D, a square and F, a hexagon.

Amazingly, this pattern was exactly the same as a famous geometry that I had been drawing for years: the Seed of Life. In spiritual teachings, the Seed of Life is known as the ‘Blueprint of Creation’, in scientific terms, it maps the Atomic Structure. Once I discovered this connection, I delved deeply into quantum physics with more vigour than ever.

In spiritual teachings, the Seed of Life is known as the 'Blueprint of Creation', in scientific terms, it maps the Atomic Structure. Click To Tweet

It was in 2015 when founding In2Infinity, that I began to rewrite my first book. This included many new concepts around the geometry of the Atom. As I ploughed through various quantum physical concepts, I was surprised at how neatly they fit this new geometric model.

In May 2015, whilst preparing a course on Metatron’s Cube, I build the nested atomic set for the first time. This provided me with another great revelation: The Atomic Blueprint can be mapped in 2D using the Fruit of Life as a template. Each shell of the Atom appeared to me in perfect order. Over the course of two weeks I built the whole set of solids and nested them, to complete the world’s first geometric model of the Atom without the need of a computer. Instead, it can be build as a tangible object. As far as I am aware, this is the only model of the Atom that you can hold in your hand.

The Atomic Blueprint can be mapped in 2D using the Fruit of Life as a template. Click To Tweet

The further I examined this structure, the more I began to see a completely different perspective of reality. The Atom was no longer a nucleus, surrounded by an apparently chaotic and probabilistic electron cloud, instead, the cloud was highly structured. Through investigation, I began to see reasons for the quantisation of atomic shells, the stability of the atomic structure, and the mechanisms by which a wave can collapse into a particle.

Today, Atomic Geometry is still in its infancy. However, we believe we have finally gathered enough evidence to suggest that it is a viable theory for scientific investigation. We therefore encourage people to build the geometry and start educating themselves about the concepts of Atomic Geometry, which I believe will advance our understanding of the Atom and the universe at large.

Colin Power

The Atom

Almost everyone today is aware that reality is made up of Atoms. Each is formed of a nucleus made of protons and neutrons that accounts for over 99.99% of the atoms mass. this is surrounded by an electron cloud, which falls into distinct shells spaced at specific distances from the nucleus. This is often depicted as a dot surrounded by circular orbits of electrons, termed the Bohr Model. These shells are subdivided into electron orbitals, that determine where they can and cannot exist, i.e. they are quantised. For that reason, the term ‘Quantum Physics’ has been invented to define that particular realm of reality. 

In2Infinity - Atomic Geometry - the Atom Proton Neutron Electron and Bohr Model

The Electron Cloud

However, this model was disproven in the 1920’s when it was discovered that electrons exhibit wave-like characteristics. So why is it, that the Bohr Model is still taught in schools? The answer appears to be, it is conceptually simple to understand and easy for chemists to work with. However, the downside is, most people have an outdated and inaccurate picture of the Atom, and how it really works.

The wave-like qualities of the electron led the hypothesis that they exist as a wave of probability. This was supported by the fact that the exact location of the electron defied measurement. As both light and electrons seemed to exhibited wave-particle phenomena, it was concluded that the act of measurement (observation) itself collapses the wave into a single particle. This established the ‘electron cloud’ as a function of probability, which is the prevailing model of today, called the Copenhagen Interpretation. Extensions of this theory conclude that the electron has the possibility of appearing anywhere in the Universe. Yet, the exact mechanism that accounts for this still remains an unsolved mystery.

In2Infinity - Atomic Geometry - the Atom Probability Cloud

However, there is an important fact that most people, even those who have studied physics, seem to miss. The shells of the Atom contain ‘sub-orbital’ types. These have been given the arbitrary labels of S, P, D and F. It is important to note that these are the only four that have ever been observed to exist. Often, sub-orbital G is placed along side this set, but this is a purely imaginary concept based on the extension of Schrödinger’s wave equations. In reality, the Atomic Structure can expand up to element 83 before it becomes unstable (radioactive).

A Geometric Persective

Thus far, all models of the Atom have been created by gathering data through energetic means. By using Alpha, Beta and Gamma rays, scientists have acquired a vast amount of data to get an understanding of the Atomic components and structure. This has resulted in concept of sub-orbital shells with specific configurations. It is this spatial arrangement which creates the characteristics of compounds and molecules within the discipline of Molecular Geometry. But so far, the underlying principles have never been explored in any detail. Yet when we do, we find the results are quite surprising.

From the perspective of Atomic Geometry, we can represent the sub-orbitals using 2D and 3D geometry. By doing so, it reveals that the electron cloud is highly geometric. Additionally, we are able to determine dynamic pathways, whereby energy is quantised via certain geometric processes, which starts to bring answers to some of the unsolved problems Quantum Physics is still facing today.

Atomic Geometry Video

To gain a clearer overview of Atomic Geometry, its principles and explanations, we have created a short animation video that shows how these four different orbitals combine to form an interlocking structure, based on Platonic and Archimedean Solids.

Electron Orbitals

The S, P, D and F-Orbitals of the Electron cloud define precise spaces around the nucleus where electrons appear with the ‘highest probability’. Current theories of Quantum Wave Mechanics have noted the relationship of these orbital formations to Spherical Harmonics. So far, this phenomenon seems not clearly understood.

In2Infinity Atomic Geometry Electronorbitals

Square number code

When we study the Electron cloud, it reveals that sub-orbitals appear in a specific order and number. The first is the S-Orbital, which appears once in each shell. Subsequently, P-orbitals appear in sets of 3, D-orbitals in sets of 5, and F-orbitals in sets of 7. It is interesting to note that 7 also appears to be the limitation for the maximum number of shells up to Uranium (92), the last naturally radioactive element.

The expanding numerical pattern of the orbitals of 1, 3, 5 and 7 is an odd number series, which conveniently falls into a triangular formation – our first geometric insight into the atomic structure.  More geometry comes apparent when we detail the orbitals within each sub-shell. When adding up all orbital pairs per shell, it exposes a numerical pattern from 1, 4, 9 and 16. 16 is the maximum number of electron pairs that can be found in a single shell.

In2Infinity - Atomic Geometry - Squaring Pattern Orbital Shells

This construct of 1, 4, 9, and 16 can be created from a square number series, i.e. 1², 2², 3² and 4². Before we even examined the geometry of the orbital types themselves, it already becomes a clear that a numerical mechanism is at play that limits the nature of the electron cloud. The combination of odd numbers 1-7, are compounded with each new shell, to generate square numbers which limit the number of electrons.

In2Infinity - Atomic Geometry - Quantum Numbers Geometry
NOTE:  Each orbital consists of 2 electrons which makes an ‘Electron Pair’. In Quantum Theory, these differentiate from each other by their spin (up or down). Furthermore, the electron is qualified by 4 Quantum Numbers.
  1. N = 1, 2, 3, 4, 5, 6, 7 = Shell (Energy level)
  2. L = 0, 1, 2, 3 = Orbital Type (Sub-shell, 0 = S, 1 = P, 2 = D, 3 = F,)
  3. M (L) = – L…L  (Type of Orbital L, i.e. 1S, 3P, 5S, 7F / Electron pair)
  4. M (S) = +1/2 or -1/2 (Spin of Electron within Electron pair)

 

2D orbital geometry

Examining the shapes of each sub-orbital reveals even more startling geometry. S-Orbitals are the only type that are completely spherical. Dividing the Sphere into two equal lopes is often referred to as dumbbells, which is the shape of P-Orbitals. The pattern continues as the lobe divides again to form the cross-shaped D-Orbitals. This process appears to follow a simple pattern driven by a process of division. But when it comes to the F-orbitals they fall into a hexagonal arrangement.

In2Infinity - Atomic Geometry - SPDF Orbital Space

Orbitals and Dimensions

Whilst the reason for this seems to have been overlooked by current Atomic Theories, geometry offers a simple solution. We can map the configuration of different sub-orbitals in accordance with conventional geometric laws that govern the expansion of dimensional space:

  • The dot exhibits zero dimension (0D).
  • The line is one dimensional (1D).
  • The Triangle, Square, Hexagon and Circle are two dimensional (2D).

The first S-Orbital forms in the inner most shell defined as the noble gas, Helium. In geometric terms, the S-Orbital can be related to a dot (or circle), from which dimensional space begins to expand. As P-orbitals exhibit two distinct lobes, the dot has divided, to generate a line (1D). The dot divides again to create a cross shaped D-Orbital, we call this 0², a concept that is extensively outlined in our new theory Universal Math. While the square is the container of the cross, a single electron does only occupy a linear space. Subsequently, the F-orbitals break the pattern of division, forming a hexagon. Again, a single electron appears in the space of a triangle, the smallest regular 3D shape.

In2Infinity - Atomic Geometry - SPDF Orbitals defined in Geometry as cot, line, cross and hexagon

Orbital Structure and the Seed of Life

The dot, line, triangle and square are the most fundamental forms in geometry which appear to structure the electron cloud. But why do F-Orbitals appear after the cross-shaped D-Orbitals?

From the perspective of geometry, we can derive a logical answer from drawing compass construction. By setting a set specific distance for the circle ratio, we can easily create a set of 7 interlocking circles. This image is termed the Seed of Life, and is a prominent symbol found through all cultures and religions.

The process of drawing the Seed of Life reveals exactly how the sub-orbitals of the electron cloud are able to form. Click To Tweet

The process of drawing the Seed of Life reveals exactly how the sub-orbitals of the electron cloud are able to form. After the first circle, which represents the S-Orbital, a second is added to generate a form called the Vesica Piscis. This form defines two points to create a line, the shape of a P-Orbital. Four overlapping circles create the Trion Re, which divides space into 4 quadrants, a cross, matching the geometry of D-orbitals. Notice, at this point there is no outer square boundary. The triangle and hexagon come into existence from the creation of the Seed of Life Mandala, indicative of F-orbitals.

In2Infinity -Atomic Geometry - Seed of Life maps SPDF Orbitals

The Cross and the Square

In this way, space has expanded in a dualistic manner. When we consider just one of the electron pairs, we see that D-orbitals express an interesting dual nature.

Are these orbitals square-shaped? Or are they 2D lines that cross each other?

We identify the cross and the square as different geometric entities. This concept is fully explained in our geometric principle we call ‘Inverse Geometry’.

In our new geometric theory of ‘Inverse Geometry, the cross is the inverse of the square, while the triangle is the inverse of a hexagon.

In the F-orbitals two equally overlapping triangles can be formed from opposite lobes that generate a very familiar image called the Star of David. In addition to the Vesica Piscis, and Trion Re, both the Cross (e.g. Celtic) and the Star of David have been found throughout ancient cultures and modern day religion. Now, for the first time we can identify the same symbolism embedded into the very fabric of reality.

In2Infinity - Atomic Geometry -Symbolism - D orbitals depict Celtic Cross and F orbitals Star of David

Positive and Negative Space

These observations allow us to construct a slightly different view of the 2nd dimension. Whilst D-Orbitals occupy a 2D plane, they are constructed from a pair of one dimensional lines. When placed upon a square tapestry, the cross will divide each square into four. F-orbitals consist from triangles, which is 2D shape. This is the final boundary of the atomic structure. Why there are not more sub-orbital shapes can be easily explained by the rules of geometry.

The only two regular shapes that can tessellate a 2D plane with just 2 colours is the square and the triangle. Therefore, it seems reasonable to assume that electron pairs can only exist within a lattice that is isotropic in nature: a completely flat space that is uniform in all directions from a point of origin, divided into a positive (up) and negative (down) space. This law of uniformity is reflected in our observations of the Universe at large. When the nature of the vacuum is considered, it appears to exist with a relatively constant background energy. In this way, Atoms can appear in quantised states, contained by the isotopic nature of two types of regular 2D space, the triangle and square.

In2Infinity - ATomic Geometry - 2types of 2D square and triangle up and down electron spin

Such a realisation is a quantum shift in thinking, because it unifies the concept of 2D and the atomic fabric of space in a completely new way. Through precise geometric principles, we have established a deep connection between the rules of 2D space and the structure of our reality.

3D orbital geometry

Having unified the sub-orbital types with geometric laws of the 2nd dimension, it is not surprising that this extends into 3D. Each sub-orbital is comprised of a specific number to form a complete set. Once complete, the next shell of the atom begins to fill. In the next part, we will consider these formations from the perspective of 3D.

The 5 Platonic & 13 Archimedean Solids

At the foundations of 3D space are the five Platonic Solids. Similar to the 2 types of regular tessellations (the triangle and square), these have the characteristic of being formed from equal-sided shapes. The Tetrahedron, Octahedron, and Icosahedron have triangular faces, the Cube has square faces, and the Dodecahedron pentagonal.

In2Infinity - Theory - Atomic Geometry - 5 Platonic Solids 2D shapes

From 5 Platonic Solids another set of semi-regular polyhedra, called the 13 Archimedean Solids can be derived.

In2Infinity - Theory - Atomic Geometry - 5 Platonic Solids Archimedean Solids

Three Geometric Processes

the 13 Archimedean Solids are produced from the 5 Platonic Solids through three geometric processes: truncation, explosion and twisting.

Truncation: Each side is divided into two or three and chopped off.

In2Infinity - Theory - Atomic Geometry - Truncation of Octahedron and Cube into Archimedean Solids

Explosion: A solid expands in space.

In2Infinity - Theory - Atomic Geometry - Explosion Platonic Solids

Twisting: a square can transform into two triangular faces.

In2Infinity - Theory - Atomic Geometry - Twisting Platonic Solids

Not only have we discovered that the sub-orbitals occupy spaces that can be defined by these polyhedra, we also suggest that it is these three geometric principles that are at work, transferring the energy of the electron instantaneously between shells, creating the quantisation effects found at the atomic scale.

S-Orbitals

S-orbitals are the first to be formed in the atom, and are the only ones to form the geometry of a sphere. Each s-orbital comprises of  two electrons, the are orientated in opposite directions, up and down. The orbital types are important in the formation of simple atomic bonds, as they are the first to appear on the outermost shell as the elements progress in number through the periodic table.

In2Infinity Atomic Geometry S-Orbitals

S-Orbitals and the Torus

In Geometry everything arises out of the dot.  When a drawing compass is opened the dot divides, and now the point marks the centre, as the circumference is draw by the pencil. The image of a dot with a circle surrounding it its one of the must fundamental ideas, ingrained into the consciousness of humanity. Even today the symbol is commonly used to represent the Sun.

By placing a pencil upon the dot, we can use a ruler to divide the circle in half. This creates two nodes where the straight line intersects the circumference.  We can mark these as the two electrons in an up and down opposing orientation by turning the line into a vector, (arrow).

A vector is a quantity that changes over time. Therefore we can imagine that as the vector grow over time, the circle is also expanding. If we inverse the downward facing arrow then this point is moving closer to the centre. Therefore the circle is diminishing in size. This expansion of a dot into a circle and vice versa is explicitly defined in our concept of inverse geometry.

Let us consider the details of the process of construction. The circle divided into two requires the application of 3 types of geometric dimensions. The dot (0D) , the line (1D), and the circle, (2D). However, 3D space exhibits an extra degree of rotation. This allows us to rotate the line (axis) at 90º to the 2D circle. Now as the circle expands, it can do so in an up or down direction. This motion is indicative of a 4D torus. More information on this can be found in our theory of Universal Geometry.

We can observe torus fields around planets, solar systems, and we believe they exist around each galaxy. Therefore to suggest that an S-orbital shell take the same form is just a natural extension of logic to the smaller scales of reality.

In2Infinity Atomic Geometry S-Orbitals

The Vesica Piscis and the Bohr Radius

Amazingly, we can also find the relationship of the atomic radii for hydrogen (1) and helium (2), which comprise the totality of the first shell. The Bohr radius ((a0)) is a scientific constant, use to define the radius of a hydrogen atom. It is derived from mathematical calculation rather than actual measurement. However, as it is incredibly difficult to measure an atom, is dos offer a reliable guide for simple atoms. According to this standard, the radius of the hydrogen atom is 53pm. and helium a radius of 31pm. The helium atom contracts as it has two protons and two neutrons within its nucleus, compared to the hydrogen atom that has just a single proton. This difference in mass exerts a greater force of the electron pair, contracting the radius.

When we divide 53 by 31 the answer is a very close approximation of √3. This difference in radius is found encoded into the Seed of Life. A circle placed outside of the hexagon has a diameter of 1 that represents the shell of the helium atom. The hydrogen atom has a shell that is √3 time larger. this can be drawn by creating a circle where the outer nodes of six circles intersect. The Seed of Life expresses the difference in atomic radii of Hydrogen and Helium.

The Seed of Life expresses the difference in atomic radii of Hydrogen and Helium. Click To Tweet

This is the relationship express as a mathematical formula. You can find out more about how and why √3 should appear as a factor between these two elements in our new theory of Dimensionless Science.

 

13÷3153=0.987

In2Infinity Atomic Geometry S-Orbitals

P-Orbitals

After the first two S-orbitals from, the first set of P-orbitals begin to appear. Starting with boron (element 5) the first set includes the essential components for biological life, namely, carbon (6), Nitrogen (7) and Oxygen (8). It is important to note that all non reactive noble gases (with the exception of Helium (2) are found when a full set of 6 p-orbital electrons complete the shell.

P-Orbitals and the Octahedron

After the spherical S-orbital the P-Orbitals are next to appear. These always come in sets of three, orientated at 90° to each other. Collectively they form a three dimensional cross, spanning an x, y, and z aixis. By connecting the centres of each lobe, produces the corners  points of an  Octahedron.

In2Infinity Atomic Geometry P-Orbitals make an Octahedron

4th Dimensional P-Orbitals

Whilst P-orbitals are often describes as exhibiting two distinct lobes,  closer examination of quantum theory suggest this is not the case. This traditional view is from a 3D perspective. It has been widely adopted in more advanced disciplines of chemistry, as it allows for a simplistic understanding of how atoms form molecular bonds and compounds. However, when it comes to examining the nature of the electron cloud, this 3D model is insufficient. Instead we must adopt a 4D image of each orbital. Viewed like this, each lope become connected through a torus. Therefore, the correct expression for a set of p-orbitals is of three interlocking torus fields. These are still easily mapped onto an octahedral form. We have suggested that the S-orbitals are 4D in nature and that this is the reason that electrons fall into pairs due. This view is supported by the fact that P-orbital lopes are actually 4D torus fields. When considering a completed set,  we find each lope is constructed by the intersection of two torus fields positioned at 90°to each other.

In2Infinity Atomic Geometry P-Orbitals make an Octahedron

Unifying 2D and 3D

The Octahedron is one of the five Platonic Solids. It has the unique characteristic of combining both the square and triangle is a single form. As we have shown, the square and triangle are the only shapes to tessellate a 2D plain with just two colours. The Octahedron is produced from these two forms. In this way we can ascribe a clear link between the rules of the 2nd dimension of space, leading to the formation of 3D Octahedral Space. This notion of space emerging from the 2nd dimension into the 3rd is explained in greater detail in our theory of Universal geometry.

In2Infinity Atomic Geometry P-Orbitals make an Octahedron

Octahedral Space and Noble Gases

This realisation allows us to postulate the reasons as to why noble gases are completely non-reactive to other elements. With the exception of the first nobler gas (helium) that is formed from the first S-orbital, all other noble gasses occur as a set of p-orbitals complete. It is this non-reactive nature that forms the foundations for the bonds form by subsequent atoms. For example,, Neon (10) is the first noble gas formed form a p-orbital Configuration.  after this the next S-orbital shell begins to form. These ‘valence electrons’, can be used to form bonds with other atoms. However, this is not true of the electrons contained within the Octahedron. These are beyond the reach of other electrons and so are unable to for bonds. On the periodic table, the noble gasses are listed in the column at the far right of the table, after which a new row (shell) begins. Therefore we can say it is the Octahedral nature of the P-orbitals that defines each row on the periodic table.

It is the Octahedral nature of the P-orbitals that defines each row on the periodic table. Click To Tweet

Every atom in complied through the same structure, this means that every atomic nucleus is surrounded by a 4D Octahedral space. We propose that it it the nature of space to conform to an octahedral structure. We cal this particular aspect of space ‘Octahedral Space.’

In2Infinity Atomic Geometry P-Orbitals make an Octahedron

P-Orbitals and the Flower of Life

Thus far we have establish a link between 3D Octahedral space, and the square and triangular tessellations of 2D space. Additionally, Octahedral Space can be mapped through simple geometry. The flower of Life is a natural extension from the seed of Life. 19 circles unify to create an set of 7 whole circles. The outer perimeter is not three times the size of the inner circle. If we place the first 4 element within the central circle, then the six circles can be labelled with the first set of P-orbitals.  These numbers can be place in order around the circle to represent the correct order in which the electrons fill the p-orbital sub-shell, (see the Paull exclusion principle). Mapped in the way each P-orbital lope is separated from is opposite the the central circle (the first two S-orbitals). when viewed from the 4th dimension, the torus fields can be envisioned, with the hole at the centre deified by the central circle.

According to the Val Da Waal radius,  the first noble gas, neon,  has a diameter of around  308pm. When divided into 3 the result is just over 100. We ascribe this to the diameter of each whole circle found in the flower of Life. Thus we have defined the spacial dimensions of Neon Gas. As these measurements of atomic radius are only accurate to within 5pm, we can suggest that the Flower of Life maps the diameter of the first octahedral noble gas, Neon.

The Flower of Life maps the diameter of the first octahedral noble gas, Neon. Click To Tweet

Other examples of the ratios of other elements is described in more detail within our theory of ‘Harmonic Chemistry’

In2Infinity Atomic Geometry P-Orbitals make an Octahedron

D-Orbitals

After the first two P-orbitals form in the 2nd and 3rd shell of the atom, another pair of S-orbitals appear in the 4th shell. Subsequently a set of D-orbitals forms in the 3rd shell. D-orbitals appear like the division of a P-orbital to form 4 lobes that resemble the cross. If we divide a complete set of 3 P-orbitals, we find that 3 D-orbitals are arranged to fill a a cubic space. This produces the geometry of a set of 8 cubes complied together to form a larger cube, that is contained within an S-orbital sphere.

In2Infinity Atomic Geometry D-Orbitals make a Cube

D-Orbitals and the Cube

In quantum physics the D-orbital configuration is derived from the Schroedinger Equations, which are so complicated the exact solution is beyond even the most advanced computer. However from the perspective of geometry the solution becomes quite simple. The Cube is the dual of an Octahedron. This means the the 6 corners of the Octahedron define the centre of each face of the Cube and vice versa. Therefore an Octahedron will nest inside the cube perfectly.

Platonic duals are a well established geometric fact, so it surprising that no one has thought to apply the same logic to the P and D orbital sets. The simplicity of this solution provides concrete reasons as to why D-orbitals should appear in this specific manner. The P and D orbital configuration of the atom is exactly modelled by an octahedron nested inside a cube. It is simple geometric law.

The P and D orbital configuration of the atom is exactly modelled by an octahedron nested inside a cube. Click To Tweet
In2Infinity Atomic Geometry D-Orbitals make a Cube

D-Orbital Torus and the Rhombi-Cuboctahedron

However, this only accounts for 3 out of 5 of the D-orbital pairs. Another forms a torus, with a lope extruded in a north and south orientation.  Again more evidence that the electron cloud is a 4D entity. The last orbital resides on the flat plain formed by this torus. This orbital is rotated at 45° to the existing D-orbital that formed the cube. When these two are viewed together, it produces an octagon. In Atomic geometry, we ascribe this to the Rhombi-cuboctahedron, which is an Archimedean Solid. This solid can be deconstructed into 3 sections.  The midsection is formed of an octagonal prism that is able to rotate freely, whilst the two ‘caps’ are held in place. This is the only one out the whole set of 13 Archimedean Solid that exhibits this quality. Geometrically, this can be seen to emulate the rotation of an object around a central axis, just as the Earth spins on it axis within a generated electromagnetic field.

In2Infinity Atomic Geometry D-Orbitals make a Torus Rhombicuboctahedron

The Rhombi-Cuboctahedron is formed through the explosion of a Cube and Octahedron, the two polyhedra that form P- and D orbitals. Thus we are able to postulate that the reason for the appearance of the toroidal D-orbitals is due to the explosion of octahedral and cubic orbitals that proceed it, which form a Rhombic-Cuboctahedron.

The reason for the appearance of the toroidal D-orbitals is due to the explosion of octahedral and cubic orbitals that proceed it, which form a Rhombic-Cuboctahedron. Click To Tweet
In2Infinity Atomic Geometry D-Orbitals make a Torus Rhombicuboctahedron

Conventional knowledge of D-orbital configurations is still rather limited. Yet they are the elements used in magnets and electrical wire, as thy are the best at conducting these kinds of energies. We believe that Atomic Geometry offers new insights into how they function, that will begin to revolutionise our perception of electricity and magnetism, and the means by which these phenomena are produced and utilised.

F-Orbitals

The F-orbtial that appear in the 4th shell form some of the largest atoms on the periodic table, even larger than the last D-orbtial set that follows. After this the final set of P-orbitals fails to complete in the 5th shell, at the atom collapses, forming only radioactive elements beyond that point.

The final orbital type to appear in the structure of the electron cloud electron are the F-orbitals. It is important to note that our current scientific exploration of these orbitals is extremely limited.  Conformation of these orbitals is derived by energising a simple hydrogen atom. However, through geometric principles and logic we can begin to explain why the various orbitals should produce particular arrangements.

F-Orbitals and the Star-Tetrahedron

To begin we can follow the logic that produces the cubic D-orbital set from the division of each P-orbital set. The two D-orbtials that are orientated at 45° to each other divide to form two Cubic Orbitals. Notice the each electron pair now falls into a Tetrahedron. When the two combine it produces a form called the Star-tetrahedron. there are two of these orbitals types, off-set at 45° to each other, as they are derived from the D-orbitals that appear rotated to the same degree. Notice that this division is formed from through the atoms horizontal plain, which is the rotational plain of the torus field.

In2Infinity Atomic Geometry F-Orbitals make Star-Tetrahedron

F-Orbitals Torus and the Icosahedron

In the same way that the rotated D-orbitals are bound by a single torus, the F-orbital Star-tetrahedra are bound by a double torus. Just as the Rhombi-cubotahedron  is only one Archimedean Solid that exhibits a ‘rotational’ property, so we find the same within the set of 5 Platonic Solids. The Icosahedron can also be deconstructed into three sections. This time the mid-section prism is formed from a pentagon. Unlike the rhombi-cuboctahedron, whose prism is forms from square sides, the Icosahedron has a prism constructed from triangles. This means the top and the bottom pentagons are offset 180° to each other. We postulate that this is the reason for the formation of the double torus is formed. Just as the set of Star-tetrahedral F-orbitals expands from the horizontal plain, so  does the double torus. Again a division from the horizontal axis.

In2Infinity Atomic Geometry F-Orbitals make a double torus Icosahedron

F-Orbitals and the Cuboctahedron

With the double torus and Star-etrahedrial orbitals accounted for, this leave 4 more hexagonal F-orbitals that need to be accommodated.In order to gain a clearer understanding of how these orbital operate we must leave the limited discription provided by quantum physics, and instead turn our attention to their chemical compounds.

A compound is a physical material that is constructed from a single type of atom. compounds fall into various geometric point matrices. these fall into two main types, hexagonal and cubic. Cubic packing is based upon the nature of 8 spheres  places on the corner of each cube. A second variety sees the centre face of each cube filled by an extra atom, and can be geometrically considered as an Octahedron nested inside the cube.

In2Infinity Atomic Geometry F-Orbitals make a Cuboctahedron

The second type, ‘Hexagonal packing, is derived from the Cuboctahedron. this is an Archimedean Solid that is derived from the Truncation of a Cube or Octahedron’s side length into two. This polyhedra was coined by Buckminster fuller as the Vector Equilibrium, due to the fact that each corner is exactly the same distance from the centre as its side length. This means it is blueprint that provides the most efficient way to nest spheres in space. We can deconstruct the form into three distinct sections, just as we did with the Icosahedron and rhombicuboctahedron. The mid section comprises of a ring of six spheres with a seventh as its centre. The two ‘caps’ are each formed of three spheres orientated 180° to each other.

Hexagonal packing can also appear in an inverted form, with its caps each made of seven spheres, and the mid section  containing three spheres. another configuration also sees the midsection removed, to produce two hexagonal rings each made of seven spheres. With this understanding we are now able to examine the nature of the F-orbital elements and the point matricies fromed by each compound.

In2Infinity Atomic Geometry F-Orbitals make a Cuboctahedron

Within the stable elements there exists only one set of F-orbtials. These begin with element 57, Lanthanum, and continue sequentially up for element 70, Ytterbium.  The compounds of the first 5 elements conform to hexagonal close packing, that are formed of two hexagonal rings place on top of each other.  Cerium (58), the second element of the set, is unique as it can also conform to a body centred cubic formation. This can be explained as two F-orbitals can be either represented as a Star-tetrahedron, or two hexagonal orbitals.

The next important point to notice is the fifth element (61), Promethium, is actually not stable. This means it cannot be found in nature and has to be manufactured in a laboratory. this instability occurs at a point matrices begin to change shape from hexagonal to cubic. Samarium,  element 62, forms a compound the is cubic in nature. However, the cube is slanted, with uneven angles. this is termed ​rhombohedral. This is rectified when the 7th element of the set, Gadolinium (63), forms a regular cubic compound. Element 63 produces a cubic configuration at the exact halfway point. Subsiquent element produce compounds that fall into the hexagonal arrangement. However this time, the two hexagonal rings become separated with three each atoms appearing between the two. The inverted cuboctahedron. This pattern continue up until the last element, Ytterbium (70), that suddenly falls into a body centre cubic arrangement.The image below shows how the compounds of each element transform.

In2Infinity Atomic Geometry F-Orbitals make a Cuboctahedron

Similar Models

As a quick comparison between atomic models, we would like to present a table, which explains the various advantages and disadvantages of atomic geometry, compared to the Copenhagen interpretation, the Pilot Wave model and the MCAS model. The MCAS model is probably the least well known.

Therefore, as we can see, there are unique properties of Atomic Geometry. And the way it is being taught as a tactile experience becomes applicable for younger people to comprehend, and is completely in alignment with the logic of space and geometry.

Geometric Theory of the Universe

Atomic Geometry presents a complimentary model of the Atom that is compatible with existing models such as the Copenhagen interpretation and the De Broglie Pilot Wave Model. However, it also brings new concepts to the arena of quantum physics. 

From the perspective of Atomic Geometry, we suggest that the nucleus of every Atom is surrounded by a particular type of geometric space. This gives rise to the quantised energy states, a fundamental characteristic of all quantum investigation. Yet, as to how this may occur has never been fully explained.

We propose that this space is not just three dimensional. In fact, orbitals have been noticed to exist in the fourth dimension and we postulate possibly the fifth. By this, we do not mean abstract concepts of dimension based on string theory rather than 1D, 2D, 3D, 4D and 5D axioms based on Euclidean geometry, such as the Platonic and Archimedean Solids. 

In2Infinity - Atomic Geometry -. Euclidian Space 0D to 3D

Unsolved Phenomena

In today’s Atomic Models exist still many challenges unsolved such as:

  • Quantisation of electron shells
  • Why electrons do not collapse into the nucleus
  • Electron spins
  • Pauli exclusion principle

With our presentation of Atomic Geometry, we offer a novel solution to each problem, that is based on simple to understand geometric laws and principles.

Discovering the Quantisation of the Atom

The fact that reality is quantised is one of the greatest enigmas of quantum physics.

At the beginning of the 19th century, when classical mechanics failed to predict results of the blackbody experiment another solution was needed. It was Max Planck who first postulated that light waves themselves were quantised into discrete packets. With the discovery of h, the Planck constant, Einstein was able to derive the concept of a photon. This suggested that reality was quantised at a fundamental level.

Subsequently, in 1911/1913 Rutherford, and Bohr collectively discovered the structure of the atom and found that the shells were also quantised. This meant that the electron could only appear at specific orbital distances, away from the atomic nucleus. The reasons for this are rather ambiguous and no forthcoming explanation is readily available, even today. In fact, the reason why electrons do not fall into the nucleus is also not clearly understood.

What can be said is that electrons can jump into a higher shell instantaneously. This occurs when it receives an energy such as a photon that charges the atom. When the atom absorbs this energy, electrons become excited and move into a higher shell. This is only sustained for a momentary period before the electron collapses back into the lower shell to release the photon. In this way, electromagnetic waves are propagated between atoms. But so far, there has been no solid conclusion why these shells exist, or why they are so stable.

In2Infinity - Atomic Geometry - Electron jumps between shells by absorbing and emitting a photon

Solving Quantisation and Electron Stability

In2Infinity - Atomic Geometry - Projecting Flattening Space from 5D 4D and 3D to 2D

Atomic Geometry proposes a fourth-dimensional (4D) version of the atom. From this perspective, we are able to easily reconcile the quantisation effects of the electrons. To cognise this, let’s flatten a three-dimensional (3D) space into a two-dimensional (2D) surface, such as a circle. This is common practice to visualise 4D in a 3D space.

We can draw two concentric circles that represent the electron cloud of the first two shells of the atom. The electrons, in this case, will be centred upon the inner shell. When an energetic wave such as a photon strikes the atom, the energy is absorbed. This triggers a response in the electrons moving them out of 3D and into 4D. As the electrons circulate through this toroidal form, they emerge into the third dimension in a higher shell (excited state). Here, they will remain until passing through 3D into 4D again to cycle back into the inner shell (ground state).

In2Infinity - Atomic Geometry - Electron Quantisation 4D torus

This model of fourth dimensional space is based on the torus. If we examine the very first elements on the Periodic table, they consist of two S-orbitals, with the characteristic of a toroidal dynamic in 3D. The reason we are unable to detect the movement of the electrons from shell to shell is because they move through 4D space.

As this process occurs, the vibration of an atom becomes apparent. Vibration, therefore, is the transformation of an electron through 4D space, as it passes through 3D, and back again. This motion can be repeated indefinitely, and explains why electrons fail to fall into the nucleus. A torus as a 4D polyhedra, that can exist with a hole in it middle. It is this ‘inner space’ , that acts as a boundary to prevent the electrons from collapsing into the nucleus.

In2Infinity - Atomic Geometry - 5 dimensions of Space and Time

We cannot perceive the fourth dimension. We can only estimate its existence through logic, and understanding of the law of geometry. This law tells us that 4D incorporates the three dimensions of 3D space and the fourth dimension of time, which keeps the toroidal dynamic in motion. A fourth dimension of time can now be ascribed to Torus movement. It begins to paint a different picture of time that is placed within a geometric construct, which, in turn, can be ascribed a relativistic property that can account for time dilation.

As simple as it seams, this hypothesis answers one of the greatest problems facing modern physics. The quantisation of reality appears to be in direct contrast to the laws on Newtonian Physics that describe the everyday world. This, in turn, is a foundation stone in the resolution of quantum gravity, the holy grail of modern physics. 

Solving the Pauli Exclusion Principle

Atomic Geometry can also explain the nature of electron configurations, which follow the Pauli Exclusion Principle. Electrons are conventionally occupying an up or down spin. Notice, that these are the only two states they can exist in. Electrons increase in number around the nucleus, filling each shell in an ordered fashion. However, the ‘up spin’ electrons only fill one half of a shell before completing the opposite spin.

From the perspective of 4D, ‘up’ literally means to move out of the 3D plane and into 4D in an upwards direction. We postulate that this creates a negative ‘anti-electron’ that is currently termed the positron. In the case of a simple S-orbital, the positron can attract a second electron to complete the shell. Only when the S-orbital is filled other orbital types are next.

This insight solves many questions in quantum physics. We now know why electron will always form pairs, and why those pairs will be orientated in opposite directions. They can move up or down over the surface of the torus. In doing so they leave 3D space, and are able to magically appear in the shell above.

The benefit of this view is that is complies with the phenomena of magnetic attraction. Magnets produce a north and south pole. A magnetic field flows north, and wraps around the physical matter. i.e the metallic elements of the magnet. No energy is lost in the process, as the loop returns back into the south pole. The south pole develops an attractive force, that will draw the north of a second magnet towards it. When they touch the magnetic field is extended. The two magnets now operate as one.

In2Infinity - Atomic Geometry - Electronspins and Pauli Exclusion Principle

Why Electronpairs?

We suggest that this magnetic mechanism is the reason for electron pairing and is also the cause of all simple bonds. The only difference is that in 4D, a completed shell forms a balanced energy state, which become an impenetrable boundary. This occurs as the very first pair of electrons forms around the nucleus, to produce helium. This element is the first noble gas an is completely inert, i.e it does not want to form a bond with any other atom. Whilst the reason for this is a mystery viewed from traditional scientific theory, Atomic Geometry can easily explain why this should be so. Helium is non-reactive as the electron configuration complete a torus.

Atomic Geometry also provides for a clear reason why noble gases are so stable and non-reactive.

The first Noble Gas is Helium, the second element on the Periodic Table. Filling the S-Orbital with 2 Electrons completes the first shell of the atom. Its stability can be explained by the nature of the Torus field. It is a  completed entity, a stable structure that has no need to bond with other atoms. Subsequent to the formation of the Torus field, we find a second set S-orbital which fills up with element 4, Barium. However, this shell is not complete as sets of P-orbitals follow. Once the three P-orbitals are filled with a total of six electrons, it forms the next noble gas, Neon, element 10.

From this moment on, we find that all following noble gases exhibit the same octahedral structure, which we believe is a structure that exists in space as a fundamental blueprint.

In2Infinity - Atomic Geometry - Noble Gases Octahedral Structure

The nature of fourth dimensional space around the atom provides a clear reason for the existence of noble gases. The characteristic of noble gases is the fact that they are the last element of each shell, i.e. all orbitals of that shell are filled with electrons, which accounts for their stability, being non-reactive to any chemical processes.

When examining noble gases, we see that the first one, Helium (2), consists of a nucleus with two protons and two neutrons,  completing the 1st shell. This S-orbital, a Sphere, is surrounded by a Torus field which completes with the second S-Orbital in the 2nd shell. Here, electrons are not stationary, but we suggest they move between these two S-orbitals through the 4D Torus as described earlier, which accounts for the phenomenon of atomic vibration in 3D. Alongside the S-Orbital, we find the first set of P-Orbitals in the 2nd shell, which form an Octahedral Structure, characteristic of all other noble gases from this point on.

The Torus pushes the energy from beneath, filling like a balloon to expand the S-orbitals into the 3rd shell. This encapsulates the Octahedron within a Torus. In fact, P-orbitals are often described as dumbbell shaped with spherical definition. Yet, the more, we advance through geometry, we see that also P-orbitals are toroidal in nature. i.e. three Torus fields align themselves  in an octahedral formation.

The first noble gas in this is Neon (10), in the 2nd shell, followed by Argon (18) in the 3rd. In the 4th, additionally to S- and P-Orbitals, appears the first set of D-Orbitals. Filling all D-Orbitals with Electrons does not result in a Noble gas, instead, they form metallic bonds. The reason for their metallic properties are related to their cubic nature of D-Orbitals. The noble gas of this shell is Krypton (36) and is expressed as an Octahedron-Cube Compound. In the 5th shell is Xenon (54) and the final noble gas is Radon (86), which is in the radioactive section of the Periodic Table. Thus, it is not a stable element. And lastly, the Elements 81 to 83 form half a P-orbital shell.

We suggest that the Octahedral nature of Noble Gases is based on the nature of octahedral space, underlying the fabric of reality. The 5 P-orbitals are encased within 7 S-orbitals and 3 D-orbitals. In this way, we notice that 4th dimensional space builds through a chronological order that applies to simple geometric principles. The Octahedron being the Dual of the cube provides us a clear explanation as to how cubic space can come into existence.

Any electron falling inside of a noble gas becomes fixed, unable to be removed from the atom. Electrons of the outer shell that are not completing that shell are called valence electrons, which are able to take part in molecular bonding.

In classical quantum theory, electron were ascribed a negative charge, and protons a positive. When an atom absorbed a photon, the electrons would move into a higher shell.  This increase in energy intensifies the electromagnetic attraction between the electron and proton, pulling the electron into a lower shell. At this point the electron would emit its energy as a wave of light. This in turn would bring about an equilibrium of charge, and the process could be repeated. When electrons we found to exist as opposite pairs, a new concept was developed that would accommodate this phenomena. Electron spin.

. In geometric terms it can be described as a sphere, which holds one electron pair.

Reason for the Instability of Element 43

The 4D nature of D-orbitals suggests an explanation for the instability of Element 43, Technetium. The 7 shells of the Periodic Table are structured through a distinct pattern of increasing and decreasing orbitals types, peaking in the 4th shell with S, P, D and F.  Notice, within this structure, there are three shells that contain D-orbitals, which are cubic in nature and stand for metallic elements.

We call them the Copper, Silver and Gold Cubes.

In2Infinity Atomic Geometry Orbital Pattern shells

A Cube within a Cube forms the Hypercube or Tesseract, a 4D Cube, similar to the Torus, while three Cubes are 5th dimensional. Element 43, falls exactly in the middle of the central Cube (Silver). We suggest that this marks a break point where Silver swaps with the Copper Cube via 4D, and in 5D with the Gold Cube. The fifth dimensional perspective, shows us that the middle Cube is shared between the lower and upper Cube – some may refer to this as ‘Heaven and Earth’.

The 4D Cube exhibits a time function that extends to the fifth dimension. In this way, reality moments are rendered within the cubic space in which we live,  we identify this as the Copper cube. The Silver cube above, is the fourth dimensional counterpart to our current existence that we represent with the Truncated Cube. The Gold Cube runs from elements, 71, to 80 and contains gold. We consider this cube to be a dimension of a higher space, we are not aware of within this reality. This shares the second half of the Silver Cube, which operates in 4D. Therefore, we have an upper and a lower 4th dimension unified within the concept of the Silver cube, breaking at element 43, which is the reason why it is not stable.

More information on this idea can be found in a Heaven and Earth chapter.

Reason for the Instability of Element 61

The three D-Orbital shells being interpreted as 4D and 5D Cubes also start to explain the instability of element 61, Promethium, on the Periodic Table.

It is in the 4th shell, where both, Element 43 and 61 appear, the peak of the atomic structure. Whilst Element 43 is the midpoint of the D-Orbitals in this shell, Element 61, falls exactly into the midpoint of the F-Orbitals, which is expressed as a Cuboctahedron.

The Cuboctahedron has as a dual (opposite form), which is the Rhombic Dodecahedron. The Cube, Truncated Octahedron and Rhombic Dodecahedron are the ‘Space-Filling-Polyhera’, which means they can fill space completely by itself. This property is unique to these three forms in Atomic Geometry. While the Cube is a Platonic Solid, and the Truncated Octahedron, an Archimedean Solid, the Rhombic Dodecahedron is a Catalan Solid, which does not appear as part of the Atomic Structure, yet forms the blueprint of a 4D Cube, i.e. Hypercube or Tesseract. Just as the Metatronscube maps the 3D Platonic Solids on a 2D plane, the Rhombic Dodecahedron is the 3D template for the 4D Cube.

Inside of the Rhombic Dodecahedron we can nest a second Cuboctahedron with a side-length of one, which is not part of the F-Orbitals. This Cuboctahedron can fit perfectly inside of Argon, Element 18, in the 3rd shell, as the empty space made from Tetrahedra. Just as the Rhombic Dodechaerdon, this Cuboctahedron can be described to exist in an almost anti-matter fashion. In this way, the nature of 4D is unified in the tetrahedral space in the 3rd shell with the Rhombic Dodecahedron in the 4th.

Seeing how shapes can transform according to Buckminster Fuller, the Cuboctahedron (F-orbitals) can collapse into the Octahedron (P-Orbitals) through the Jitterbug transformation. This Octahedron will have a side-length of 2 and represents the noble gas Krypton (36). This gives the F-Orbitals the unique property to switch in scale between the first two Noble gases of the Octahedral Structure, Argon (18) and Krypton (36) via the Cuboctahedron.

In Atomic Geometry, we even postulate that this space exists even before the electrons are charged in order to fill the shell. Therefore, the mechanism of reality can be seen to operate through a spatial dynamic of 4D and 5D.

Why Element 83 is the last stable Element

Finally, let’s explain the reason why element 83, Bismuth, is the last stable element on the Periodic Table. Elements subsequent to 83 are naturally radioactive decaying from Uranium (90) and Thorium (92) which appear in nature. The reasons for this are not clear yet. According to Big Bang Theory, these elements should have decayed and moved out of the blueprint of creation.

It has been noticed that under closer investigation Bismuth is actually slightly radioactive. We postulate that this is due to the fact that it exists on the boundary of space. The outer S-orbital in the 7th shell can only hold a maximum of five electrons. This is similar to the break at 43 and 61, which also correlates between the number five in the D- and F-orbitals. These five electrons are the only ones that can fill the P-orbitals.

This indicates that the number five is key to the nature of 4D and 5D space. Within the Platonic Solids, only two solids are able to contain the five-pointed star configuration. In the case of the Icosahedron, it exhibits a central section as a pentagonal prism that can be rotated. From the perspective of Electron pairs the number five seems like an unstable configuration. However, when we view it from the Icosahedron, these five electrons fill a space within the toroidal field, which is beyond 3D.

The double Torus of the F-orbitals can also be classified as a 5D object. We utilise the Icosahedron in our model to represent this particular F-orbital. Therefore, the nature of five is defined by the Icosahedron as a particular number that signifies breaks within the atomic structure at 43, 61 and the last element, 83.


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In 2 Infinity - established in 2015 -