The Platonic Solids & the Nine Concentric Circles – “The Circles of Form”
In this brief article we will delve deeper into the following diagram by Robert Lawlor by reviewing the new discoveries of Charlie Ziese from the Pyramid Science Foundation.
See page 107 in Robert Lawlor’s Sacred Geometry: Philosophy & Practice
Lawlor writes, “In this demonstration the regular polyhedra are determined by nine concentric circles whose pattern gives all the necessary information for the construction of these forms. Each volume is in a simple harmonic relationship to the others, and it is the same transcendental function, √2, √φ, and φ that make up these patterns of relationships. As in the previous drawing, all the volumes emerges simultaneously. But in this case if one of the concentric circles is removed then the pattern cannot yield the remaining volumes. This is an image of the great Buddhist idea of the co-dependent origination of the archetypal principles of creation.”
These nine circles can also be seen as the form of nucleus and atom. Robert Lawlor explains in Homage to Pythagoras: “The two [innermost] circles mark the end of one octave of form-genesis and the beginning of a second. These two circles being the coinciding of beginning and end become analogous to the nucleus or seed, thereby leaving us with seven circles surrounding a dualized nucleus as is imaged by the structure of the atom.
The inner circle and intercircle of the innermost form, the octahedron, represent the reappearance of the icosahedron, and thus the overlapping of the beginning and ending of the cycle. In nature this coincidence of beginning and ending is the seed or nucleus. The nucleus is the perfect continuance of polarity: the androgyne. It is root/germ, neutron/proton, etc. Therefore the Circles of Form are analogous to a nucleus sustaining a seven-fold orbital field of polarized interactivity. This is the same basic cosmological model as that of the Kabala, both Greek and Hebrew, and it is also found in Hindu and other cultures. It is also central organizational pattern of light and sound differentiation: the atom and the solar system. Thus traditional cosmological unifying models can be associated with the generation of volumes.”
Lawlor continues: “The seven circles can be metaphorically linked with the seven colors. Just as each frequency level of light evokes a new quality (color) so each concentric circle in turn evokes a new quality or genus of form/organization, or a new electron orb evokes a new family of substance in the Periodic Table. All the circles are co-dependent: the loss of one dissolves the entire encodement. The inner black circle with the floating white circle represents the continence of the nucleus, yet still having its polarity in potential.
Substance and light are of the same electromagnetic energy; they are fields of force whose movement/form is detectable as wave phenomena. Substance varies from radiated light in that it has been organized into relatively stable geometric vortices by the three primary principles of organization, the protonic, the neutronic and the electronic: the movement towards centrality, centrality and the movement away from centrality. The varying proportions of these three powers determine the geometry of the substance.”
The above paragraph explains that the structure of the atom itself is a torus. It consists of three principles: the movement towards centrality, centrality and the movement away from centrality. These combined movements form the atom.
New Discoveries by Charlie Ziese
Watch his video series on rumble here. And YouTube here.
Ziese states, “Lawlor’s diagram is a two-dimensional depiction of a dynamic 3D model of Platonic Form progression that incorporates Russian Pyramid/Phi Scaling Angle/Torus geometry and 12-tone equal temperament phi-based scaling. The resulting dynamic model provides new and unique insights into the steps inherent in the progression of the Platonic forms. It is an integration of the ‘process’ with the ‘pathway’.”
Robert Lawlor lays out the specific side length dimensions of the nested Platonic Forms, as shown above. This results in a ratio of the side length of the outer icosahedron to the inner icosahedron of phi3, which perfectly matches the slant height to base length of the Russian Pyramid/Phi Scaling Angle.
Russian Pyramid diagram
Each lower circle diameter is divided by phi to get the diameter of the circle above it (shown below).
It continues in this progression. This is the Phi Scaling Angle and it represents a 3D spiral vortex.
This means that if you looked at the above diagram as a 3D drawing and you were gazing up at the image from the South Pole upwards to the North Pole (from larger circle at the bottom to smaller circle at the top), the circumferences of the nine circles would create the exact slant height of the Russian Pyramid/Phi Scaling Angle, (shown above on left).
As stated, the Lawlor diagram of the ‘Circles of Form’ is actually a two-dimensional depiction of a dynamic 3D model of progression.
The nine concentric circles designate specific radii lengths associated with the progression of the Platonic forms (shown above). However, there are significant variations in the dimensions calculated from the diagram versus those calculated from his nesting ratios.
Missing Definitions to 9 Concentric circles Diagram Key:
R = Circumscribing Sphere
p = interior sphere
r = radius of Platonic form
a = side length of Platonic form
To repeat: Lawlor’s Dimensions of Nested Platonic Forms
| Central Icosahedron | 1/phi2 |
| Octahedron | 1/√2 |
| Star Tetrahedron | √2 |
| Cube | 1 |
| Dodecahedron | 1/phi |
| Icosahedron | phi |
The Ratio of the side length of outer icosahedron to side lengths of central icosahedron = 4.236 = phi3 = slant height of Russian Pyramid.
Multiple Octaves of the Progression – scaling by 4.236
Lawlor’s diagram is actually a view from the bottom, looking upwards at the rings/spheres as they would appear vertically in 3 dimensions. This 3D model could possibly integrate the ‘process’ with the ‘pathway’.
Each of the nine circles/spheres fit perfectly within the 76.345° Russian pyramid geometry.
Using phi3 as the “octave” in the scaling process results in the creation of a 12-tone equal temperament scale, which is perfect for phi-based scaling. We have now developed a ‘pathway’ that matches the geometry of the Torus/Russian Pyramid/Phi Scaling Angle with 12-tone Equal Temperament harmonic scaling.
There are significant variations in the dimensions calculated from the diagram versus those calculated from his nesting ratios.
The Differences between the “Nested” Dimensions and the “Diagram” Dimensions
The upper and lower icosahedra, as well as the octahedron are the same. The 3rd sphere (containing the star tetrahedron, cube & dodecahedron) are different by a factor of √2
The diameter, radius and side length of each Platonic Form are all increased by 1.414 or sq rt.2, versus the corresponding nested dimensions.
The Russian Pyramid Scaling matches the upper and lower icosahedra of the nested Platonic solids, but not the 2 inner spheres. These icosahedra are the anchors. This leaves us with:
- The icosahedron – in a single sphere
- Octahedron – in a single sphere
- Star Tetrahedron/Cube/Dodecahedron – all 3 together in a single sphere
- Icosahedron – in a single sphere
- 4 spheres total
The interior sphere of the icosahedron also matches with the interior sphere of the cube and tetrahedron.
Seven total unique geometric proportions and perfectly matching midpoints – this could not happen except in the Russian pyramid (76.345°)
The apex of the interior sphere of the dodecahedron and the base of the circumscribing sphere of the octahedron come together at exactly the same vertical point. The fact that these two spheres share an intersecting base and apex is not apparent from Lawlor’s two dimensional diagram because it is drawn in two dimensions. However, it becomes apparent when drawn in three dimensions. This intersection of apex and base could ONLY occur when mapping the spheres inside a pyramid/torus with a 76.345° angle.
Static vs. Dynamic Progression
A good way to demonstrate that the diagram is depicting a dynamic progression of the Platonic forms is to compare the four major circles encompassing the diagram’s ‘octave of progression’ to a similar plotting of the ‘nested’ circles.
When plotted in 3D some important differences become evident.
Major Premises:
The geometrical boundaries of the pyramid are in fact those of the torus/phi scaling angle.
The spiraling torsion field powering the toroidal field is coming up from the bottom, applying pressure to the spheres.
When compressed each sphere will morph into a new sphere/form to fill the ‘space’ available to it within the limitations of the torus/pyramid geometry.
Since we now see that the nested model of progression does not make sense in a dynamic model, it is logical to assume that Lawlor’s diagram is a 2D depiction of the dynamic process.
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