Atomic Elements in the Geocubic Model

by Tom Gilmore
Copyright 2017
All graphics by Tom Gilmore
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Introduction to the Geocubic Model

Octave Periodicity

The 3-D Periodic Table (2-8-5)

 (2) The periodic table begins with a pair (2) of Elements (Hydrogen and Helium) that exhibit the duality of active and inert. 

(2-8): Following this are (2) octaves (8) of Elements that exhibit an expanded duality of active and inert (7 active and 1 inert). 

(2-8-5): Following this are 2 sets of 2 more of the same octaves as the first 2 octaves except that after the second (2) Element in each octave (8), additional Elements in sub-groups of (5) are inserted.  These sets of 5 occur as 3 groups of 10 (2x5), and 2 groups of 15 (3x5), both adding to 30 each, except that at Element 57 the first group of 15 intercepts and replaces the first Element of the third group of 10, reducing the third group of 10 down to 9.  To show this pattern correctly requires a 3 dimensional approach to the periodic table, as shown below.

The first intercepting group of 15 (Elements 57 to 71) are called the Lanthanides, and are centered on Element 64 (4x4x4).  The second set of 15 is centered on 96 (3/2 of 64).

Bias Forms

The Protons in an Element are encased individually in spherical force surfaces.  Only certain Atomic Numbers can arrange the Spheres to meet the Order and Symmetry Laws, and those that don’t meet the requirements must bond with other atoms to reach a number of Spheres that does meet the requirement (of 2-dimensional symmetry, but not 3-dimensional symmetry).  The valid Sphere arrangements will form internal force planes if sufficient Sphere centers align on that plane (called the Bias), and the Element will be a solid, subject to crystal forces, and also subject to any atomic bonding that reduces the internal Bias energy (the law of Lesser Energy).  When there are no Bias planes the Element is inert, meaning it is a gas, and it is not subject to atomic bonding. 

Sphere Arrangements

The conventional academic model of the atom involves a central Nucleus of Protons and Neutrons being orbited by Electrons organized in “Shells”.  This is in direct contradiction with the Geocubic Model (refer to the article on Electrons).

In the Geocubic Model the Sphere arrangements fall into groups by atomic number, and these correspond loosely with the “Quantum Mechanical” shells of the first 28 Elements.  As detailed in the appendix of the Electron article, the first 3 “shells” number 2, 8, and 18 (adding to 28).  The Geocubic Model shows that not all Elements have valid arrangements, and consequently do not exist outside of molecules.  This treatise presents graphics showing the Elements currently determined to have allowed arrangements, along with the Bias of that Element.  The Elements are grouped by common arrangement characteristics, beginning with the 2-Sphere-Diagonal, but the Bias forms are variable in the groups..

2 Sphere Diagonal

2 Sphere Perpendicular

With Neon(10) the 2 large Spheres change from being diagonal to being perpendicular (as in the inert form depicted below the energized form). 

When Neon(10) is energized by electric current, a diagonal Bias of 6 Spheres forms as shown below, however when the current is withdrawn the inert arrangement of Spheres takes over (due to the Law of Lesser Energy), and the energy of the Bias converts to light.  The Tron changes from Electron to Photon.  By pulsing the electric current a rapidly flickering conversion form electricity to light is produced.

The perpendicular pair of Spheres in Neon persists through Silicon(14), with the exception of Aluminum(13) that has an early 3-layer arrangement.

3 Layers

With Argon(18) the law of order dictates that the Spheres shift to taking on 3 layers.  With 3 layers (an odd number), both even and odd atomic numbers have valid arrangements (all the way to Cube/26).

Chromium(24) forms compressed double-crossing planes, and this is responsible for its deep shine.

3 Layers Magnetic

With 3 layers, a layer cannot take 10 or 11 Spheres (without 4 Spheres lining up), and the next layer-form possible is 12, where 4 rows of 3 are offset (see layer of 12 below).  Iron(26) has a magnetized allotrope shown below where a layer of 12 is sandwiched between layers of 7.  The Spheres on the Iron Bias plane are more compressed than on the 2 outer planes, and this creates a local 2-dimensional gravitational distortion (a magnetic field), and the same applies to Nickel, but the Iron Bias ratio of 12 to 14 (6/7) is beyond the 3/4 ratio limit, while the Nickel Bias ratio is 12 to 16 (right on the 3/4 ratio limit), but producing a weaker magnetic field than Iron.


Cube/27 is 3x3x3 and as such is symmetrical in all three dimensions, violating the Law of Symmetry’s precluded order.  There is no 3-layer distribution of Spheres that is symmetrical in 2 dimensions, so (59)Cobalt(27) is absent order with no available nearby Element-form (with less energy) to emulate in a bond.  (With a limit of 4 bonds the available Element-forms for Cube/27 range from Cube/23 to Cube31).


Copper(29), Silver(47) and Gold (79) align on the periodic table, and are of an odd atomic number that lends itself to a malleable arrangement (Silver being the hardest).   Copper(29) forms a diagonal of 13, while at the same time forming a perpendicular of 13, where 5 Spheres are shared by both planes.  The combination of both planes gives copper a warm color in reflecting light, and a malleable crystal linkage.


With 30 Spheres, Zinc(30) could take 3 layers of 9-12-9, but the greater area of the diagonal plane overrides the more compressed perpendicular plane, and the 12 Spheres expand to the diagonal.  The ratio of 12 to 18 is 2/3 (due to symmetry, a bias ratio of 2/3 means the ratio of the Spheres on each side to the Bias (9/12) is 3/4). 
This Bias ratio of 2/3 is the preferred Bias proportion.

Zink(30, Zirconium(40) and Tin(50) have similar forms.  Refer to the Decimal (/10’s) Group following the Element diagrams.

Multiple Offset Layers

At 32 Spheres the layering changes to multiple offset layers.  The main layers consist of 8 Spheres arranged in a diagonal cross, with offset groups nestled between the 3 main layers. 

Krypton(36) forms 4 offset layers of 9 and is inert.

Yttrium(39) does not take on 3 layers of 13 because the layers of 13 are too thin, instead forming offset multiple layers, but with main layers a diagonal cross of 9 Spheres.

There is an imbalance in Yttrium because of the 6 layers, and a layering of 8 and 5 is only slightly more unbalanced than 9 and 4 (due to a very small central Sphere in the layers of 5). 

Cube/40 is another 2/3 Bias ratio Element.  Refer to the Decimal (/10’s) Group following the Element diagrams.

Cube/42 is another 2/3 Bias ratio Element.  Refer to the Refractory Group following the Element diagrams.

4 Main Layers

At 44 Spheres, Ruthenium(44) is the first Element with 4 main layers.

4 Layer Offset Layered-Cross

Silver(47) and Cadmium(48) take on 4 crossing layers of offset alternating rows of 3 and 4.  Silver starts the cross with rows of 3 at the edges (for a total of 31)  and Cadmium starts with rows of 4 (for a total of 32).  The first fully 4 Layered-Cross Bias occurs with the brittle allotrope of Cadmium(48)

Tellurium(52) and Polonium(84) are a symmetry group.

The Cadmium(48) layered-cross is X8 (with layers of 12), and the Tellurium(52) layered-cross is X9 (with layers of 13).  Since there are 4 layers, the axis ratio of the layer to the 4-deep compression is the square-root of the Sphere count of the layer.  For Cadmium the layer ratio is 3.46/4, and for Tellurium it is 3.61/4.

Cube/50 is another 2/3 Bias ratio Element.  Refer to the Decimal (/10’s) Group following the Element diagrams.

Layered-Cross Elements

The 4-deep layered-cross Bias is shown above in the 3 possible spatial orientations.  Each layer has a crossing group of 9 Spheres, and 4 partitioned wedge-shaped empty areas where fillers are forced to fit into.  There are 5 allowable layer-forms, at 13, 15, 17, 19, and 21 Spheres, as diagrammed below.  The numbers in parenthesis following the layer count are the square root.  Since the number of layers is 4, the most stable layer-forms are 15 and 17, with the square roots closest to 4. 

Below the 5 diagrams of layer-forms, the layers of the even-numbered Lanthanides are listed.  Cube/60 is known as the “True Lanthanide”.  This is due to the rotated layering of 15, where between layers, the spaces with two spheres alternate with the spaces with one sphere, allowing ideal packing of the fillers.

The Heavy Elements

Cube/73-74 average a 2/3 Bias ratio.  Refer to the Refractory Group following the Element diagrams.

Osmium(76), the heaviest Element, has an efficient packing similar to Neodymium(60), using exclusively layer-form 19 and alternating fillers of 2 and 3.


Platinum(78) uses 4 layers of 17 alternating with two offset layers of 4 and a central layer of 2.


Like Copper(29) (which has a single diagonal and a single perpendicular Bias plane), Gold(79) forms both diagonal and perpendicular Bias planes, but double the planes (crossing planes) and the planes are parallel (as shown below).  The combination of both crossing planes gives Gold a glowing warm color in reflecting light, and a very malleable crystal linkage.

Liquid Metal

Mercury is midway between 4 layers and 5 layers. The Bias is similar to Chromium(24) with double-crossing planes, but angled to 3/5 of the cube face and spaced 1/5 apart, leaving a 1/5 gap at one of the faces.  This gap is produced by a 4x(4x5) offset layering, and can shift to other faces, making the crystal a liquid.  The double crossing planes give Mercury(80) a deep shine similar to Chromium(24).  Seen from the opposite face (the cube below to the right that is flipped over from the cube on the left), there are 8 offset layers of 10. 

Lead (Semi-Shield)

When a layer reaches 25, the Bias Plane is highly energized by the aligned Protons, and this force will reflect x-rays, where lesser-count layers will not (this is why lead is used to shield x-ray technicians from exposure).  Lead(82) is the first Element where a Shield plane is supported. 

Shield-Layer Radioactive Elements

Lead is the final stable Element, as those following are radioactive due to what is termed “Shield Intervention”.  What this intervention means is that a Shield plane tries to form but is unsupported and collapses, only to instantly try to form again

Polonium (Cube 84) is 21,21,21,21 with a layer square-root of 4.58, making it unstable toward 5 layers (Shield Intervention), and consequently is radioactive.  Tellurium (Cube/52) is 13,13,13,13 with a layer square-root of 3.61.  The similarity of fully symmetrical fillers is why Polonium is also called “Radio-Tellurium”  With Polonium the 21-Sphere layers, with 9 Spheres on the Bias and 12 fillers per layer, has reached 9/12 or 3/4.  Polonium(84) and Radon(86) are the only Elements to utilize the 21-layer form.

At Uranium(92) there is an unstable arrangement that avoids Shield plane formation, so it is much less radioactive that the Elements surrounding it.

Shield (Sh)

The Geocubic Model predicts that at “Shield”(105), all six cube faces support a Shield plane.

Although each face of Shield(105) has 25 Spheres, it only takes 98 spheres to fill all six cube faces with Shield planes because the spheres at the face edges are shared.  For Cube/105 there are 7 spheres interior to the 98 spheres on the exterior (105-98=7), and this allows for the 6 Shield faces to each be supported at the face centers, with a central Sphere supporting the 6 supporting Spheres, as diagrammed below.

The law of precluded 3-dimensional order is not violated by the 6-face Shield surface because of the shared Spheres of the faces.  The Sphere force only applies as a whole integer.  Each face is guaranteed the force of 16 spheres, because (98/6=16.333).  Since 98-(16x6)=2, two of the faces must take on the force of an extra Sphere (and symmetry demands they be opposite faces). These 6 faces could be expressed as (17,16,16,16,16,17).  This inequality of Shield strength constitutes a 3-dimensional asymmetry.

Elements with valid arrangements are also predicted at 107 and 109.

The Special Groups

There are clear periodic relationships of valences (and some physical properties) between some Elements aligned on the periodic table, in particular the 3 columns of inert (zero valence) at far-right, halogen (-1 valence) at second column from right, and alkali (+1 valence) at far-left.

A – The “Stair-Step” separates the metals (left) from the non-metals (right).
B – The magnetic group.  Iron(26) is the most magnetic, followed by Nickel(28).
C – The “Coinage Group”.  Copper(29), Silver((47), and Gold(79).
D – The Platinum Group are “noble” metals, meaning that in bulk they resist oxidation.
E – The Refractory Group resist infusion from other metals.

The Refractory Group

The internal arrangement of the compressed spheres of Element 41 and 42 are diagrammed below (with the central diagonal layer isolated).  There is a similar diagonal layering in both Elements 41 and 42, with diagonal layers of 3,9,(17 or 18),9,3.  The central diagonal layers alternate 5 rows of 3 and 4 spheres, the difference being starting with a row of 3 (Cube/41) or a row of 4 (Cube/42).  This offset layering of rows acts to compact the spheres, as they nestle between rows. 

There is an exact mathematical ratio in Cube/42, (18/24=3/4), between 18 Spheres in the central diagonal layer and the 24 “fillers”.
There are 12 fillers on either side of the central diagonal layer, so there is an exact ratio (12/18=2/3) of the 12 fillers per side to the 18 Bias Spheres.

This mathematical ratio is repeated at a larger scale in the average of the two refractory Elements of Cube/73 and Cube/74, as illustrated above.  The central diagonal layers alternate 7 rows of 4 and 5 spheres, the difference being starting with a row of 4 (Cube/73) or a row of 5 (Cube/74).  In this case the same exact ratios involve the averaged diagonal Bias layers of the two elements ((31+32)/2=31.5).  There are 21 spheres on each side of the diagonal Bias layers, so the ratio of the averaged diagonal layer (31.5) to the total fillers is (31.5/42=3/4), and the ratio of the 21 fillers of each side to the averaged diagonal layer of 31.5 is (21/31.5=2/3).

The Decimal (/x10’s) Group

In the case of Neon (Cube/10) the layered form results from being electrically energized, and results in a diagonal Bias plane that emits light when the atom de-energizes (neon light).

In the case of Calcium (Cube/20) the layered form is an unstable allotrope.  An allotrope is an alternate internal arrangement available to an Element.

The /10 Series ends at Cube/50 because at Cube/57 a 4-layer crossing structure takes over.

Notice that all Elements of the /10 series have outer diagonal rows of 3 spheres.  The diagonal layering of Elements 30, 40, and 50 are stable.  Notice that the central (Bias-diagonal) layer progresses from 4 to 6 to 12 to 16 to 20, which is generally an increase of 4 except with Cube/20, where it is 6 rather than 8, and this reveals why the allotrope is unstable.  With the exception of Cube/20, these Elements have the same ratios as the refractory group, but inverted to 2/3 & 3/4.

Except at Calcium(20), the ratio can be seen in the split-up of each step of adding 10, where 4 go to the central diagonal and 6 to the fillers (4/6=2/3).  Since the fillers are split 3 to each side, the ratio of added spheres to each side of the 4 added to the central diagonal is (3/4=3/4).

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