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 describe the atom from the perspective of energy, this one 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 nested perfectly inside each other to produce a 3D representation of all the stable elements on the Periodic table.
Overview
Image you could hold a 3D model of an atom in your hands. Well, now you can! We are presenting a 3D geometric model of the atom that you can create just with a drawing compass, ruler, card, scissors, and glue. It is based on 3D polyhedra of specific sidelengths, that can nest inside each other, just like Russian dolls, to accurately reflect the spatial arrangement of the electron cloud. This tactile exploration of the atom is a fantastic educational tool for students to comprehend the depths of atomic theory. With a lot of experience running workshops in Atomic Geometry children as young as seven years of age are able to recognise complex ideas such as the electron configuration, orbital shells S, P, D and F, the atomic nucleus, and electron pairing.
In the first part, we lay out the basic structure of the atom and its relationship to simple squares and triangles. Subsequently, we explore the four types of orbital S, P, D, and F from the perspective of 2D and then 3D. We will show how the electron configuration of the atom falls into a cube of empty space to form the atomic blueprint. Finally, we will provide a brief introduction into the field of Geoquantum Mechanics, and explain how we are able to predict the atomic radii so accurately.
Watch the Video
To gain a clearer overview of Atomic Geometry, its principles and explanations, we have created a short animation video that shows how the four different orbital types combine to form an interlocking structure, based on Platonic and Archimedean Solids.
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
THE
Concept
A Geometric perspective of the Atom
With Atomic Geometry we offer a completely new perspective of the atom, which was developed in 2015 by Colin Power, cofounder of In2Infinity. The inspiration for this model came from his indepth exploration of compass construction. Indeed, throughout the history of humanity, this drawing 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.
For the first time, we have applied these geometric techniques to the structure of the electron cloud. This journey of has brought many surprises that have revolutionised our perception of the atom, and new answers to the mysteries of the quantum world. And now, we would like to share them with you!
The Atom
The Electron Cloud
The Bohr Model was disproven in the 1920’s when Louis de Broglie discovered that electrons exhibit wavelike characteristics. So why is it, that the Bohr Model is still taught in schools?
The answer is, it is conceptually simple to understand and easy for chemists to work with. The downside is, most people have an outdated and inaccurate picture of the atom, and how it really works.
The wavelike qualities of the electron led Werner Heisenberg to 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 waveparticle 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.
While the attention is often on the strange behaviour of electrons, we want to highlight their spatial limitation. While most learn about the atomic shells in school, we can dive into more detail and highlight the sub shells, called ‘suborbitals‘. 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, suborbital G is placed along side this set, but this is a purely theoretical concept based on the extension of the aufbau principle. In reality, the atomic structure can expand up to element 83 before it becomes unstable (radioactive).
A geometric perspective
Thus far, all models of the atom have been created by gathering data through energetic means using alpha, beta and gamma rays. This has resulted in the discovery of suborbital shells with specific configurations. It is this spatial arrangement which creates the characteristics of compounds and molecules within the discipline of molecular geometry. However, so far, the underlying principles have never been explored from the perspective of geometry in any detail. Yet when we do, we find the results are quite surprising.
Atomic Geometry represents the suborbitals using simple 2D and 3D geometry. By doing so, it reveals that the electron cloud is highly geometric. Additionally, extending into the field of Geoquantum Mechanics we were able to model dynamic pathways, whereby energy can be quantised via certain geometric processes. From this geometric perspective we can explain why electron are quantised to specific energy levels, and why the atomic structure is completely stable. So far, these questions are still unsolved by traditional quantum theory.
Electron Orbitals
The S, P, D and Forbitals of the electron cloud define precise spaces around the nucleus where electrons can appear with the ‘highest probability’. Current theories of Quantum Wave Mechanics have noted the relationship of these orbital formations to spherical harmonics. Despite consistent experimental evidence, this phenomenon lacks so far a clear conclusion.
Square number code
When we study the electron cloud, it reveals that suborbitals appear in a specific order and number. This is termed the ‘Electron Configuration‘.
The first is the Sorbital, which appears once in each shell. Subsequently, Porbitals appear in sets of 3, Dorbitals in sets of 5, and Forbitals in sets of 7. It is interesting to note that the number 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 becomes apparent when we detail the orbitals within each subshell. When adding up all orbital pairs per shell, it exposes a numerical pattern from 1, 4, 9 and finally 16. 16 is the maximum number of electron pairs that can be found in a single shell.
This construct of 1, 4, 9, and 16 can be created from a square number series, i.e. 1², 2², 3² and 4². Before examining the geometry of the orbital types themselves, it already becomes clear that there is a numerical mechanism at play which limits the nature of the electron cloud. The combination of odd numbers 17, are compounded with each new shell, to generate square numbers which relate to the number of electrons.
Key point
The electron cloud is structured through a combination of odd numbers 17, that are compounded with each new shell, to generate square numbers series.
 N = 1, 2, 3, 4, 5, 6, 7 = shell (energy level)
 L = 0, 1, 2, 3 = orbital type (subshell, 0 = S, 1 = P, 2 = D, 3 = F,)
 M (L) = – L…L (type of orbital L, i.e. 1S, 3P, 5S, 7F / electron pair)
 M (S) = +1/2 or 1/2 (spin of electron within electron pair)
2D orbital geometry
Orbitals and Dimensions
Whilst the reason for this geometric pattern can be extrapolated from complicated Schrödinger equations, geometry does offers a far simpler solution. We can map the configuration of different suborbitals in accordance with conventional geometric laws that govern the expansion of dimensional space, from zero to 2D:
 The dot exhibits zero dimension (0D).
 The line is one dimensional (1D).
 The triangle, square, hexagon and circle are two dimensional (2D).
In geometric terms, the Sorbital can be related to a dot (or circle), from which dimensional space begins to expand. As Porbitals exhibit two distinct lobes, the dot has divided, to generate a line (1D). The dot divides again to create the square, or more accurately, the cross shaped Dorbital. A single electron from this pair now occupies two lobes, or a line, that cross the second electron at 90°. Finally, the Forbitals break the pattern of division, forming a hexagon. In this final stage a single electron occupies three lobes, to form a triangle, the smallest regular 2D shape.
Positive and Negative Space
These observations also allow us to see the second dimension in a new light. Dorbitals occupy a 2D plane, but are constructed from a pair of onedimensional lines. On a square tessellation, the cross will divide each square into four. Forbitals consist of three onedimensional lines arranged in a hexagon, which divide a hexagonal tessellation into triangles, the final boundary of the atomic structure. So, why are there not more suborbital shapes?
Again, we can find answers to this in the rules of geometry. The only two regular shapes that can tessellate a 2D plane with just two colours is the square and the triangle.
An electron can only fall into one of the two states, up or down. In order to differentiate these states requires a space that can be uniformly divided into just two ‘colours’. None of the surrounding space can exhibit the same state (colour), in the same way. This is similar to the mechanism of a computer where each byte is stored in an on/off state.
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). This enables electrons to appear in quantised states, restrained by the two types of regular 2D space, the triangle and square.
Based on this we suggest that the electron cloud is dividing the space around the nucleus in accordance with the laws of 2D geometry, and it is this that accounts for the two opposing quantum states of the electron, up and down, and the geometric orientation of S, P, D, and Forbitals.
Key point
The electron cloud is dividing the space around the nucleus in accordance with the laws of 2D geometry, and it is this that accounts for the two opposing quantum states of the electron, up and down.
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 suborbital types with geometric laws of the second dimension, it is not surprising that this extends into 3D. Each suborbital is comprised of a specific number to form a complete threedimensional set. Once the shape is filled, electrons will jump to the next shell of the atom. In the next part, we will consider these formations from the perspective of 3D.
The 5 Platonic and 13 Archimedean Solids
Before we proceed with a 3D geometric explanation of the electron cloud, we need to be clear about the limitations of 3D space. Just as 2D space is limited to only two regular polygons, 3D space is limited to only five regular polyhedra, called ‘Platonic Solids’. They are very unique as they all are made from the same regular polygons, all edges have the same length and all corners have the same distance to the center.
Three of these, the Tetrahedron, Octahedron, and Icosahedron have triangular faces, whilst the Cube has square faces, and the Dodecahedron is pentagonal.
The five Platonic Solids we transform into a set of 13 semiregular polyhedra, called the Archimedean Solids through the process of truncation, explosion and twisting. Aside from the Truncated Tetrahedron, 12 fall into two distinct categories. One is based on the Octahedron and Cube with octahedral symmetry, and another six are derived from the Dodecahedron and Icosahedron with icosahedral symmetry.
If you are not familiar with these forms, you can explore them in great detail in our Guide to Sacred Geometry.
SOrbitals
SOrbitals and the Torus
We can perceive Sorbitals from the perspective of a circle (2D), sphere (3D), or torus (4D). The circle is a shadow projection of a 3D sphere onto a 2D space, the sphere a 3D representation of a 4D torus. Let’s go through each dimension and how it relates to the electron pair.
In 2D, the two electrons appear opposite each other on the endpoints of the circle’s diameter, which refers to the up and down configuration. On a 3D sphere, these electrons will be exactly opposite on its surface, which represents the traditional view of particle physics. In a 4D torus, the electrons are still opposite but follow the flow of the field, explaining the up and down orientation.
The 4D torus is a dynamic field, which is in continuous motion and typically represents electromagnetic fields, who exhibit a north and south pole. Within these torus fields there is a unidirectional flow of energy, going up and down. We can represent this by simply drawing an arrow that stretches from the ‘down’ orientated electron, to pass through the centre (nucleus) and reach the ‘up’ orientated electron. The arrow represents the flow of energy through the centre of a toroidal structure.
In light of these different dimensions, we propose that the electron spin and the existence of electron pairs are a consequence of a 4D toroidal dynamic. As our perception of reality is limited to 3D, 4D phenomena do not appear to us as physical objects, but rather as electromagnetic fields found around planets, and solar systems. We also suggest that they exist around each galaxy. In fact, they seem to exist on every scale, a realisation far deeper than it may first appear.
The holy grail of quantum physics is to unify quantum gravity, the quantised phenomena of the micro scale, with the theory of general relativity, the smooth curvature of timespace at the macro scale. Could 4D geometry help us resolve this conundrum? We believe that the answers lies within geometry, which we have started to outline in Atomic Geometry and will reveal in more detail in our other ideas and theories.
POrbitals
POrbitals and the Octahedron
Key point
The set of porbitals is 3 interlocking torus fields, mapped onto an Octahedron.
4th Dimensional POrbitals
To conclude, we have suggested that Sorbitals are 4D in nature, which explains why electrons fall into pairs. Extending this to the Porbitals, we find that each lobe is constructed by the intersection of two torus fields positioned at 90°to each other.
DOrbitals
The first Dorbitals appear in the 3rd shell of the atom, between the S and Porbitals. This is not obvious when we look at the traditional periodic table, where the Dblock begins in the 4th row (shell). This is because the elements are laid out in terms of their increase in energy levels.
If we analyse it in terms of space, the arrangement would look quite different. After the noble gas argon (18), the next two electrons produce an Sorbital in the 4th shell. Subsequently, the first set of Dorbitals appear in the 3rd shell. Therefore, all Dorbital elements have two Sorbital electrons that can form bonds independently (exceptions to this are the elements that defines the Aufbau Principle).
This is why Dorbital element can create such a wide variety of metal alloys. They can form molecular configurations independently of their Sorbitals that appear in the shell above. Most of these metals can be oxidised, when a free oxygen atom forms a bond with the outer Sorbitals, producing the phenomena we call rust.
Another important fact is that there are only three sets of Dorbitals that are comprised of stable atoms. The fourth set (elements 103112) are highly radioactive, and do not appear in nature. They can only be manufactured within the lab, and tend to exist for just a fraction of a second. No element beyond 100 has ever be synthesised in any kind of macroscopic quantity observable by the human eye.
Therefore, only 3 sets of Dorbital electrons form stable atoms, which appear in the 3rd, 4th, and 5th shell. This suggests that the atom does not expand uniformly, rather, with each successive shell, the next type of orbital appears. This pattern continues up until the Forbitals in the forth shell. After this, successive shells have one less stable orbital type.
DOrbitals and the Cube
Out of the five Dorbitals, three fall upon the same x, y, z axis as the previous set of POrbitals. Each lobe of these ‘cross’ shaped orbitals are located above and below the existing Porbital. Viewed like this, the Dorbitals are derived from the division of a Porbital (line) into a cross (two intersecting lines). A simple process of division.
When these Dorbitals are combined they divide a Cube of empty space into eight parts. We can model this geometrically as set of eight small Cubes, complied to form a larger Cube.
Atomic Duals
We came up with the term ‘cubic space’ , which has distinctly different qualities to ‘octahedral space’. The Cube is unique amongst the set of the Platonic Solids, as it is the only form that can fill space uniformly by itself. This spacefilling property is descriptive of the space that we experience in daily life.
Objects are orientated in space, and can move through space without changing shape or dimension. Cubic space, as a uniform structure, is the only regular solid that can fulfil this function. Through such a uniform matrix, relative distances in space can be metered and measured.
Based on the foundations of the octahedron, which embodies both triangle and square planes, its platonic dual, the cube can form. The geometric pattern of the ‘matrix of space’ is perfectly described through the order and appearance of the electron orbital types.
Dorbitals and the Cuboctahedron
Let us next consider the spacial arrangement of a combined set of P and Dorbitals. To help us we can imagine a Cube of empty space. An Octahedron can be placed inside of a Cube in such a way that its 6 corners touch the centre of each face of the Cube. This is because the Cube and Octahedron are ‘Platonic Duals’. The Cube has 6 faces and the 8 corners, the Octahedron has 6 corners and 8 faces.
If we consider the position of the three Dorbitals, we find that they fall on the centre of each square. By connecting the set a new form appears, the Cuboctahedron. This Archimedean Solid is comprised of the faces from both the Cube and Octahedron. We will discuss this form in more detail in the section on FOrbitals.
By considering these orbitals as a collective occupying a cube of space, we can relate it to the geometric forms that underpin their appearance. The P and Dorbital configuration of the atom is exactly modelled by an Octahedron and Cuboctahedron nested inside a Cube of space.
Key point
The P and Dorbital configuration of the atom is exactly modelled by The Corners of an Octahedron Nested in a Cuboctahedron.
DOrbital Torus and the RhombiCuboctahedron
With three of the cross shaped Dorbitals dealt with, let us look at the orientation of the 4th. This orbital is rotated at 45° to the existing Dorbital along the x, and y axis. When the two are viewed together, it produces an Octagon.
The final orbital is of a completely different nature to the rest, as we suggest it expresses the nature of a torus field, with a lope extruded in a north and south orientation. The 45° octagonal Dorbital appears on the same plane as the torus ring. In consideration of theses geometric qualities, we postulate that it is the RhombicCuboctahedron, which serves as a container. The midsection is an octagonal prism that can rotate freely, whilst the two ‘caps’ are held in place. Out the whole set of 13 Archimedean Solids, the RhombicCuboctahedron is the only one that exhibits this quality. On top of that, it is the perfect form to map the final two Dorbital electron pairs.
FOrbitals
The final orbital type are Forbitals. These appear extrapolated from the order of elements in rows at the bottom of the periodic table. Just as with the Dorbitals, the periodic table suggests that the FOrbital appear in the 5th and 6th shell of the atom. However, there is only one stable set of Forbitals, which appears spatially in the 4th shell. The second set (elements 89103) are radioactive.
NOTE: It is quite strange that within this radioactive block, two elements, Thorium (90) and Uranium (92) still exist on planet earth. Technically, these element should have decayed into nonexistence, if they were created at the point of the Big Bang, just like all the other radioactive elements of this group. By accelerating the decay of (or depleting) Uranium or Thorium all other ‘naturally’ occurring radioactive elements (91 and 8984) are generated. The heat that is being emitted in this reaction is commonly used in the generation energy in nuclear power plants. Any elements above 92 include Plutonium (93), however, this is only found as a trace element embedded in Uranium ores. Beyond this, we have all ‘artificial’ elements up to 100 that have only been synthesised in the lab and never in macroscopic quantities. Atoms beyond that point exists for only fractions of a second, collapsing within the blink of an eye.
FOrbitals and the Cuboctahedron
Whereas Dorbitals from a ‘cross’, the most common orbital configuration found in the Forbitals are hexagonal. There are four sets in total that have been defined to fall along an x, y and z axis. At this juncture, our Atomic Geometry model takes a different view of these orientations. These four hexagonal rings are the perfect fit for a Cuboctahedron. We have shown that an Octahedron combines triangular faces with a the internal geometry of three squares. The Cuboctahedron has both, square and triangle faces, with an internal geometry made of four hexagons.
Viewed like this, the complete set of orbitals follow a simple expansion, from the triangle and square, to fulfil the blueprint with the hexagon. In 3D, this transformation follows the sequence of an Octahedron, transforming through the Cube into a Cuboctahedron.
FOrbitals and the RhombicCuboctahedron
FOrbitals and the StarTetrahedron
Amidst the Forbitals we find a rather unique looking cubic shaped pair. These are the only orbital types to exhibit a three dimension space. Closer examination reveals that each electron is contained with a tetrahedron. When the two interlock at 180° opposition, they define the corners of a Cube.
In geometry, this shape is called the Startetrahedron. What is interesting about this form is that it contains an Octahedron at its centre. By adding 8 tetrahedra to each face of an Octahedron, the StarTetrahedron is created. Just as the Porbitals begin the atomic structure with an Octahedron, the Forbitals terminate at the StarTetrahedron.
Key point
Just as the Porbitals begin the atomic structure with an Octahedron, the Forbitals terminate at the StarTetrahedron.
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DOrbital Torus and the RhombiCuboctahedron
Forbital torus and the Icosahedron
There is one last orbital left that we have yet to discuss. Whilst Dorbitals exhibit a torus orbital, within the Forbital configurations we find a double torus. This can be viewed as a 5D hypersphere, which we have assigned the Icosahedron to.
Just as the RhombicCuboctahedron is only one Archimedean Solid that exhibits a ‘rotational’ property, the same can be said of the Icosahedron from the set of 5 Platonic Solids. Deconstructed into three sections reveals a pentagonal middle prism.
The pentagon contains the Golden Ratio (1:1.618), a particular proportion found throughout nature which relates to √5. Whilst many people have heard about the Golden Ratio, the Silver Ratio, is not so well recognised. The Silver Ratio is related to the Octagon, based on √2.
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.
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.
THE
Conclusion
What does this tell us about the Atom?
Unlike other models of the atom, Atomic Geometry provides a clear description, that can be modelled using simple geometry. This makes understanding the suborbit structure far more simple than any other model of the atom.
Atomic Geometry: a fresh perspective.
Atomic geometry is applicable to the electron cloud that surrounds the hydrogen atom, from which the scientific data of the S, P D and F orbitals have been collated. It offers a clear view of the fractal nature of space. The same structures can also be seen to organise other physical phenomena too, such as the planets of our solar system. This in turn lends us to a new geometric model of the universe that begins to solve some of the most perplexing problems facing traditional atomic modles.
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YOUR QUESTIONS ANSWERED
Got a Question? Then leave a comment below.
Question?
This post seem quite striaght forwards, but why hasn’t science recognised this geometric nature?
ANSWER?
We have tried to approach the scientific community with our ideas. Unfortunately, we have not had much success. This might be because QM is generally involved with quite complicated mathematics, and so the geometric model, and its simplicity, may not be taken seriously, simple bacause it is so easy to grasp
Question?
Is this model of the atom applicable to all the lement on the periodic table?
ANSWER?
Data about the S, P, D, F orbital shells has been gathered by ‘pumping’ energy into a hydrogen atom. Science uses hydrogen as it is the simplest atom to work with. However, as it does not exhibit a neutron, like all other atoms, the atomic radii changes as we move through the periodic table. We have a more advanced model of the atom called geoquantum mechanics that produces the most worlds accurate description of all stable elements in terms of atomic radii.
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