Geo-Quantum Mechanics (GQM) is an extension to the field of Atomic Geometry. Whilst Atomic Geometry focuses on the S,  P, D, and F orbitals, produced from the Hydrogen atom, GQM examines the nature of the electron cloud for the entire periodic table. It presents a more advanced geometric model of the atom that takes into account the addition of neutrons and protons in the nucleus of each element.

The result is the worlds most accurate atomic model in terms of atomic radii, that supersedes the Bohr Radius and the Van-Da-Waal Radius by over 100% in some cases.



Geo-Quantum Mechanics explores the electron configuration, and size of the atomic radii in relation to the structure of Platonic and Archimedean Solids outline in our concept of Atomic Geometry.

At first appearance the  radii of the atoms distributed throughout the stable element appears to be random and unpredictable, failing our current theoretical models. Yet through the lens of geometry, a pattern begins to emerge that can explain many of the deep mysteries of traditional quantum physics

Geoquantum Mechanical blueprint

In the above image we outline the geo-mechanical blueprint which is used to produce an accurate model of the atomic radii for all stable elements on the periodic table. The result when compared to the standard model, which uses the Bohr and Van-da-Waal Constance, we find the Geo-Quantum Mechanics provides a far more accurate description.

Geoquantum Mechanics mapping the first  elements

In the above image we see the radii for the first 18 elements on the periodic table. The solid blue line represents the results of experimental measurements. The dotted green line that in appears to superimpose the blue line is the model generated by the Geo-Quantum model. With the exception of element 14 (where there is a small discrepancy, the rest of the elements appear as an almost perfect match. Compared to the Red and yellow line that are the predictions made by our present scientific models, we can see that Geo-quantum Mechanics offers a far more accurate description.

Key Points

  • Geoquantum Mechanics is the worlds most accurate modle of the atom in terms of atomic radii
  • It is based on a simple to understand geometric template
  • It offer new explainations for many phenomina found in the quantum world

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Explore the concepts of Atomic Geometry and Geo-Quantum Mechanics.

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Geometric mapping the Atomic Radii

Geo-Quantum mechanics is an extension of the field of Atomic Geometry, that examines the nature of the Electron Cloud for the complete set of stable element on the periodic table.
based on simple geometric principle of the regular polyhedra and their transformation, we can map the expansion and contraction of each type of atom, to produce the worlds most accurate model of the atom in terms of atomic radii.
To achieve this result, we present an extension of Buckminster Fuller’s Jitterbug, that include the Snub Cube and Rhombic-Cuboctahedron.

The cube of space

Physical phenomena is measured within the Cubic nature of space. The Cube is the only Regular Space-filling Platonic Solid, which provides an X, Y and Z axis. This allows us to qualify distance measurements in terms of length, breadth, and depth.

All solids exhibit an In-sphere, Mid-sphere, and Out-sphere, (or circumsphere). We prefer to use the words IN, OUT and MID to maintain clarity. Let us take the example of a Cube with a side length of 1. The diagonal of its side length will measure √2, and the distance between opposite corners will be √3. therefore, a sphere placed inside of the cube will have a diameter of 1, the IN-sphere. By increasing the size of the sphere, it will touch the centre of each side, producing a MID-sphere of √2. Finally the OUT sphere encompasses the Cube.

In Mid and Out spheres of a Cube

The cube of space

In the concept of Atomic Geometry we show that electron can fill specific places within a cube.

We can compare this concept to the average size of each atomic orbital and find that almost every block exhibits points structure where a sequential series of elements share exactly the same radii.

P D and F orbitals electrons mapped to a cube of space

Putting aside the the P1 and P3 orbitals for a moment and turning attention to the other orbitals, we notice there seems to be a specific radius where each set levels off. P2 elements level off at around 100 pm, whereas P4, all the D-block elements level off at around 140pm. The first half of the F-block elements have radii of about 185 pm, falling to 175pm at around the halfway point.

If we imagine a cube with a side length of 200 then we find that each type of orbital radii roughly falls over the point where the IN, MID and OUT sphere are located.

Whilst this is just a rough overview it a good starting point for scaling our atomic model the the values of the radii. Not only do the orbitals fall at around the correct radius, that also fall into the cube in the exact configuration we have allocated for each orbital type.

rough sketch of atomic radii mapped to a Cube

These values are only a rough guide, and in reality there is a tremendous variation in size for each type of atom. However, by using the principles that transform Platonic into Archimedean Solids, we are able to generate a far more accurate match. So accurate in fact, that it supersedes all other existing predictions.

Geometric Functions

We are not the first people to suggest that the atom follow a geometric structure. A similar idea of the atom was conceived of by Buckminster Fuller. He discovered that by collapsing the square faces of a Cuboctahedron into two triangles will create an Icosahedron. Continuing this process produces an Octahedron at the final stage. This transformation was termed the ‘Jitterbug’ and was suggested by Fuller to be in operation within the atomic structure.

Both the Octahedron and Cuboctahedron are 2 forms we have identified from the orbital geometries.

Within the theory of Geo-Quantum Mechanics we extend the jitterbug concept to include two new forms, the Snub Cube and Rhombic-Cuboctahedron. The ‘Extended Jitterbug’ contains five polyhedra, with the Cuboctahedron located at the centre of the set. With the exception of the Snub Cube, all of these geometries have been identified as having a particular relationship to the different orbital types, that we believe is enough to prove that validity of Atomic Geometry.


The second important geometric transformation used in Geo-Quantum mechanics is ‘Truncation’. This is enacted by the division of the side length of a Platonic Solid into two or three. By dividing the side of a Cube or Octahedron in half, the Cuboctahedron is formed. By dividing the sides into three, the corners of each polyhedra can be removed, forming the truncated Cube or Octahedron.

We can place these objects in a row, with the Octahedron at one end and the Cube at the other. Comparing this to the ‘Extended Jitterbug’ both begin with an Octahedron (P-orbital). The truncated series collapses the Octahedron into a Cuboctahedron, whereas the Jitterbug expands into the Cuboctahedron. The first diminishes in size and the latter grows in size, meaning that the two Cub-octahedra exhibit side lengths that are double in size.

InInfinity Theory AtomicGeometry TruncationofOctahedronandCubeintoArchimedeanSolids

Geo-Quantum Blueprint

We can combine the three previous geometric concepts, the Jitterbug, Truncation, and Compounds, to produce the ‘Geoquantum Blueprint’ that we can use to map the atomic structure.

The compound of the Cube and Octahedron, share the same mid-sphere, which each defines a Cuboctahedron at its center. Both the Octahedron and Cube can have a portion of their corners removed to produce their truncated versions.

The Octahedron can explode through the Jitterbug process, to create a larger Icosahedron and Cuboctahedron (double in size), and then on to create the Snub Cube and Rhombi-Cuboctahedron.

The Cuboctahedron in the centre of the cube/octahedron compound can also expand and shrink through the same jitterbug process. As the Cuboctahedron collapses into a smaller octahedron, so new compounds can be formed, firstly from the Icosahedron/dodecahedron pair and then another Octahedron/Cube. This can also be truncated and als contains a smaller Cuboctahedron as its centre. Again it can expand and contact in size, through the extended jitterbug process.

Each of these polyhedra has an IN, MID, and OUT sphere, most of which exhibit different sizes. However, some of these spheres do fall in exactly the same space. The mid-sphere of the Cube/Octahedron compound, which also form the out-sphere of the Cuboctahedron, for example.

This Geo-mechanical scaling is what we believe structures, the not just the radii of the atomic shells, but more incredibly, the variation of atomic radii for every element on the periodic table.

Predicting Atomic Radii

When we think of an atom, we often imagine that the size must be increasing in incremental steps as more electrons begin to fill each shell. However, this is far from the truth. The atomic radius seems to vary widely for each type of atom. Additionally the different sizes seem not to follow any kind of predictable pattern. Sometime we see noble gases like Helium (2) and Neon (10) expand in size, whereas others, such a Argon (18), contract in size. At the same time we find certain element exhibiting the exact same radius. Why?

Using the Geoquantum Mechanical model we are able to explain this large variation, whilst maintaining a logical geometrical process. In this way we can produce a curvature that almost exactly matches the experimentally measured values for all the atomic radii on the periodic table.

Currently, there are two sets of data that are used to try and calculate the atomic radii. The first is the Bohr Radius, which is a theoretical value based on an infinitely dense atomic nucleus. The second is the Van da Waal radius, which considers the atom as a hard shelled sphere.

However, for the majority of elements we see that the predicted values do not even come close to the data extrapolated by experimental results, that are accurate within a tolerance of about 5 picometers.

The table below shows the results generated for each atomic radii for the first 18 elements. The blue line provides the results generated by experimental data. the dotted green line might be hard to see, as it is so close to the measured data, whereas the red dotted line depicted the data derived from the Bohr radius, and the Yellow line from the Van da Waal radius. Clearly Geoquantum mechanics is a more accurate representation of experimental results

All of these radii are derived from the Geoquantum Blueprint. Two Cube/Octahedron Compounds are scaled through the extended jitterbug, so that the fist exhibits a mid-sphere radius of 50pm and the second a radius 100pm

In the graph above the green sections produce radii based on the Cube, Truncated Cube, Snub Cube, or Rhombi-Cuboctahedron, the red section is based solely on the Octahedron, and the blue section is based on the Icosahedron/dodecahedron compound.

From this we can see that the first 3 element expand through a Cube and then an Octahedron, after which the 4th element collapses back onto a truncated version of the cube. The atoms diminish in size, until 50pm, which is the mid-sphere of the first compound. Then Neon (10) grows dramatically in size, filling the pentagonal mid-sphere of the Icosahedron. The 10 electrons of this noble gas, are a perfect fit for the rotation midsection of an icosahedron.

As more electrons are added, the radii decreases through an Icosahedron, compound with a Dodecahedron, before collapsing into the Snub Cube. The atom continues to decrease in size, levelling out at element number 15-17. This occurs in the mid-sphere of the second Cube/Octahedron compound, which also happens to contain a third polyhedra, the Cuboctahedron. Having fill each of these forms that occupy the same space, the atom suddenly collapses in size by a factor of √2, as it falls into the in-sphere of the Cube or onto the out-sphere of an octahedron nested inside. this completed octahedra now forms the 3rd noble gas. Argon (18).

This explains why Argon (18) has a radius of around 71pm, whereas Helium (2) has a much larger radius of 120pm. It all follows a logical geometric progression. In this way we are able, not just to construct the most accurate model of the Atomic radii so far produced by any atomic theory. We are also able to show the logic that produces it.

The implication it that the space around the atom is geometric, and that is why the electrons are held in such stable ‘orbits’. This insight sheds a completely new light on the functioning of the atom, which validates the theory of Atomic Geometry, and introduces another new field of science to the world. Geo-Quantum Mechanics.

Data Sheet

Comparison between the Borh Van da Waal and Geo Qauntum Mechanics predicted radii to experimental data



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What does this tell us about the Atom?

The suggestion of Geo-Quantum mechanics is the is it the space surrounding the Nucleaus, that quantises the electron cloud, that accounts for the quantisation of each shell at a specific energy level.

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Geo-Quantum Mechanics: The most accurate model of the atom to date.

Current atomic theory is unable to account for the difference in size between the first two atoms on the periodic table. Geo-quantum Mechanics can define the whole set of stable element to an almost exact degree, which for most cases, is in within the range that accounts for experimental error.

Carry On Learning

This article is part of our new theory, Atomic Geometry
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Got a Question? Then leave a comment below.

john hammond
JOHN - Engineer

I thought quantum theory was accurate of billionths of a degree of accuracy?


This might be true for the hydrogen atom (1), however, it is not the case for the other elements. Often traditional QM looks inside the atom to discover information about sub atomic particles. The Muon is one example where QM fails in its predictions. If we begin to examine atoms that contain Neutron (all atoms above hydrogen) we see the QM struggels to maintain its predictions.


Is this model of the atom applicable to all the elements on the periodic table?


There are 81 stable elements on the periodic table. We have found that all can be mapped by the Quantum Geo-Mechanical Model.

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