Universal Geometry - The shape of the universe

form emerging out of sound, Color. letter and Number

Sacred Geometry is the Geometry of the Field of Thought Waves.

all Mandalas (images) or Mantras (sounds) are shadow images of geometric solids, bidimensional projections of thoughts. 

Thoughts are three dimensional mental objects. Thoughts are things.

Ancient Alchemy

The Substanceless Universe and the Four elements of Matter


This introduction is very compressed and perhaps difficult to understand for someone who has not been initiated into the new cosmogony. Firstly I will clarify the vocabulary used in the text to avoid confusion about the definitions used:

1.) The four elements of alchemy are, in their symbolic origin, the components that make possible this illusion of the so called Uni-Verse, or at least, the small part that we can observe from it, and the tiny part of it we can interact with :

the AIR




the FIRE



... is the element of empty SPACE

  Which embeds everything and forms the cubic volume of void. It's gravity's pressure *.

... is the element of MOTION

  The omnipresent flow of ideas that circulate and always return to the source.

... is the element of TIME 

  Which gives sequences to the infinite cycles of change and consumes them in its passage,

.... is the element of FORM and MATTER.

  Which separates and concentrates in spheres. It is radiation's unstable pressure *.

2. (Gravity is not a force that pulls from within, but pushes from the outside inward.) There is no attraction in the universe, even more impossible is the attraction of opposites. Whenever two opposites meet, they out cancel each other.)

Gravity is the fulcrum of the lever or the eye of the hurricane, which regulates, controls and balances any expression of opposing movements. It is the stillness of the fulcrum, where all the light of consciousness, the idea, knowledge and energy ** is located. From that stillness it controls the equilibrium between centripetal and centrifugal motion (water) and gives them inertia in time (fire).

3.) The three Dimensions have nothing to do with measures, masses or volumes. They are not related to properties of objects or things. They are the three axes or, in their geometric extension, the three planes of infinite extension at 90° angles between each of them, which define empty space and are the sole reference between an observation and the point from which this observation occurs (the observer).


But .... Maybe all this is an illusion and there is a real universe where none of this exists?

What would remain of the universe without these four elements? ... without opposing pressures and dimensions?

There will remain the only "thing" that can exist without anything that sustains it: Consciousness.

Because she is witness of everything, even of time and space because she conceives them, and nothing can be conceived, testified or observed from within, but only by something external. Consequently she, consciousness, can not be anything. If she were something, this something could be witnessed, ... and who could possibly witness or testify it?


Where there is nothing there is pure consciousness, without place, dimension or extension. This point, infinite, without substance, is the creator and witness of the four elements; Time, space, change and form; And the geometry that provides form to them to create the illusory images that consciousness can perceive without ever forming part of them.

Consciousness is an artist. It creates ideas and reproduces them in simulation of matter; But matter is not the idea it reproduces. The Artist can not be found in his creation. Neither the painter nor the sculptor or composer is part of his work. (In the link: New Cosmogony I will explain the concepts of Walter Russell in more detail).


I will show through Geometry that the singularity of this point in nothingness, consciousness, is the only reality and the true substance, while the form that arises out of its imagination is pure illusion without any substantiality.


"If you want to find the secrets of the universe, think in terms of energy, frequency and vibration."

Nikola Tesla

AIR - the empty space

Consciousness is an infinite point. It is unique.

It is neither infinitely large nor tiny. It lacks volume.

It has no extension, no movement, no space surrounds it. Nor is it part of the flow of time. Lacking past and future, it has no form.


Non of the elements is real.


Consciousness as an artist imagines and shapes his imaginations into a three-dimensional imaginary canvas: the Empty Space.

- Space is a singular illusion. There is only ONE because there is only one consciousness that holds it in its imagination ... in pure state, it still lacks any image. That is why it is infinite. Being the void it does not contain form and only form can have limits. As well as consciousness, space takes never part of the drama. The screen does not change according to the movie projected on it. At the end of the projection, the Space, like the canvas or the screen, is as clear, pure and virgin as if nothing had ever happened...


The element of Air was described from ancient times as the concept of ether or aether, which we must forget ... as we also need to overcome the concept of God. There has been false indoctrination on those terms for centuries ... because the altered mind refuses to accept the fact that space and form are secondary effects of a cause without form, volume, extension in space, nor substance or mass. I avoid using these terms, when I can ...


"All motion is curved - All curvature is spiral"                                                                       W.R. 



water - vibration and motion

All motion is cyclic, repetitive and rhythmic.


Each of the four elements manifests Three-dimensional.

Nothing can exist with less or more than three dimensions. Dimensions are the coordinates that define the space. Height, width and depth. End of story. There can be no more than three axes at 90 ° angle to each other.


All motion manifests itself in Vibration Waves. Vibration is rhythmic variation of pressure. All our senses are electric, Electricity is the liquid element of Water: vibrations that interpret vibrations.


Water is the fulcrum between Air and Fire.

In other words: Vibration waves are the mediator between Time and Space. They are also illusions, supported by their three dimensions:

- the sphere of compression is the axis of depth and equals the visual axis, it creates the illusion called perspective or centripetal motion. It is the focal point.

- The Earth Plane is formed by adding the axis of width. Width and depth create the plane of pressure balance, also called Horizon, the sum of infinite focus points.

- The expansion cube is the result of adding the third dimension, height. It creates the illusion called space or centrifugal motion.

The three dimensions form the Wave Field. The geometric position within the field determines the length-frequency duality, amplitude, and velocity of the wave.


"Burn your life in fire. Look for those who ventilate your flames."


Jalal-al-Din Muhammad Rumi


fire - as Time goes by


The three dimensions of time are past, future and now. Now it is the axis of depth, past the horizontal axis and future the vertical.

All three are inseparable, interdependent and form the illusion of CHANGE among them.

Time is not linear.

Without the illusion of time (fire), there is no shape (earth) nor change or movement because form is vibration and consequently rhythmic motion, Motion is perpetual repetition of wave frequency. Time forms the field of variation, where repetitive motion becomes change or movement.


MOTION NEVER CHANGES - it is constant and eternal. The atom does not decompose, it does not evolve, just like stars and galaxies or the universe. They are vibrations, they are motion. They are eternal because they are timeless.


CHANGE NEVER MOVES - it focuses on static sequences of seeming motion from different points within space-time.


Movement is defined by the distance traveled in a time frame (Wave amplitude), but time is also defined as the movement through distance (wave velocity), and the distance is movement or pulsations by time (frequency and wavelength). The three values are defined through each other. Multiplying two of them gives the value of the third.


The Constant is Rhythmic motion, (Water), wich is male in nature, while time (Fire) and the fraction of space traveled (air) are Variables and female.

T = 1 = f · λ

In a harmonious or balanced system, space is always one, equaling Time (t) by cycles (f) multiplied by the fraction of the path in wavelength (λ) The simplest formula in history. The higher the frequency, the shorter the wave and vice versa).

 This fact has profound implications because it explains the function of the PHI factor, the Golden Ratio or Divine Proportion and its abundant appearance in nature. (On the next page I will explain why.)


All thoughts, ideas, and concepts that emerge from consciousness are three-dimensional static objects, vibrating at a given frequency. They are like slides or frames of a 3D movie. The light projects through them a static image into space, which, instead of a flat canvas, is a three dimensional firmament. The illusion of motion is produced by the rhythmic sequential interchange of frames of thoughts. Each frame or each slide stays, however. Static and motionless forever ... Movement or change in motion, is simulated by this interchange of static thoughts. This sequential change is called "time" and, like all kind of motion, is always rhythmic and periodic as well.


(Talking about light, it is important to forget the misconception of the speed of light.) It is not the light that travels through the slide: It is the opposite: Light is synonymous to space and absolute stillness.


Air is constant, infinite and eternal space. Fire is the rhythm of interchange, instantaneous and momentary Time. Water is the circulation of thought in motion between time and space: the constant flow of concepts and ideas fixed and eternal but seemingly changing, because, once conceived, they circulate omnipresent through the field of space and time in spirals of centripetal and centrifugal movement in infinite repetition, waiting their turn in time when the light of consciousness returns to them.


Form and matter are expressions of thoughts. In order to express themselves they first need to compress. the term causality describes the relationship between causes and effects, it is fundamental in all natural sciences, especially in physics. The uni-verse is a perfect balance between expansion and compression.


Expansion and compression are the opposites that make up the wave of vibration. The balanced rhythmic interchange that builds and destroys the universe in endless sequences.


Actioni contrariam semper & æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales & in partes contrarias dirigi

"To any action there is always an equal and opposite reaction: meaning that the mutual actions of two bodies are always equal and directed in the opposite direction."                                Newton's 3rd law



The  Trinity  Space- Time - Vibration is the one set of singularities. They lack form. There is only one space, one time and one Movement. With their three dimensions they are a single phenomenon. the value of each is ONE. Being inseparable they can not be added or subtracted. They only multiply or divide between them


Form is Dual.


It is the greatest of all illusions. Actually in a UNI-verse where everything is one, form can not exist. It can only seem to exist. It can not be but it can be simulated. It is the idea of separate parts, which part from the inseparable whole.

The three dimensions of form and matter are identical to those of space. Three coordinates intersect at 90 degrees. The difference is that in space the point where the X, Y and Z axes intersect is omnipresent and therefore not localizable, whereas form is the concentration of thought at a particular point with a specific position in space, time and wave. The concentration forms compression and it causes expansion as equal force in the opposite direction: Action and Reaction form polarity. Where the coordinates cross at 90 ° is the point of maximum compression. It is the positive nucleus or pole: The point of minimum volume and Maximum pressure. The field or space that surrounds it, of maximum volume and minimum pressure, is negative. The positive Mono-pole and the negative field are equal in potential, but opposite in volume and always in perfect balance in respect to the Zero of their fulcrum. Between the compression PLUS and the MINUS of expression there is a ZERO that controls and balances the opposites.

In other words: The X, Y and Z axes of width, height and depth, the three-dimensional axes become rulers with measurements parting from zero. The measures are NUMBERS.


Form is duality and duality is expressed in Number.


Every positive number has its opposite negative number, identical in value but opposite in polarity. All polarity is concentration versus expansion in perfect equilibrium. Polarity means the simultaneous existence of one concentated North pole, and one expaded South field. Between any pair of opposite North poles and South fields, there is a zero plane where there is no polarity. The zero plane and the opposite position define the actual position of anything and, consequently, the shape. They are the points of reference. Without them nothing can seem to exist in the universe. They are synonymous with: projection (-), objective (0) and film (+).


Generally we count all numbers wrong because the zero is not only the beginning before the one, but rather there is a zero of stillness ahead and behind each of the numbers: 010203040506070809010 ...

In everyday life we use only half the cycle, and half the numbers ...

the display of a pendulum is the correct way to count: a push is required to move from zero to +1, which is the most unbalanced state. Then it returns to zero, or rather it crosses the zero gaining inertia wich pushes it towards -1 (in fact it is -0,999 due to the friction, resistance to the air, etc.). When the pendulum then returns to zero, a full swing is completed. Any positive number has its negative counterpart and, between the two, is the zero of balanced stillness. That's why economics and maths use to get it wrong. There is no growth. In order to add something to anything you need to subtract it or take it from somewhere else. There is also no multiplication without simultaneous, equal and opposite division.



"Close these eyes to open the other.- Let the center light up your view."                      Jalal-al-Din Rumi



 The geometry of the ONE that forms the trinity of dimensional illusions and that of Space-Motion-Time is the Cube-Sphere (hexahedron). The Cube contains the sphere and vice versa: the sphere also contains the cube. The sphere and the cube are ONE. The sphere is the compressed cube and the cube is the sphere extended or unfolded. The sphere is potential of unity, the cube is potential of multitude. (When a multitude of spheres are compressed, they come together and "pack" into hexahedrons, filling the entire space: The most regular torsion geometry and base of all tessellation).

The cube is the regular geometry with the maximum outer surface in relation to its volume. The sphere is the geometry with the minimum surface.


The cube is Space - Air - Magnetic Field SOUTH-EAST-WEST 

It is the origin of the Gravitational principle yang (陽) that charges and compresses from the cube towards the sphere of centripetal form; The male-female sex *. The positive current (+). Generative.



The sphere is Form - Earth - Magnetic Pole NORTH 

It is the origin of the Radioactive principle - jīn (陰), that discharges and expands from the sphere to the cube centrifugally: the female-male sex *. The negative counter-current (-). Disintegration.



* The Feminine and Masculine genders are the two currents of opposite movement that constitute the Wave. Its function is the simulation of opposition, which is achieved by balanced rhythmic interchange of pressures. Genders are the cause of the illusion of movement in form and time by rhythmic appearance- and disappearance sequences. Form is sex, in the double sense of the feminine seeking the masculine (flow) or the masculine looking for the feminine (fire) in order to annihilate the sexual desire in the sexual act and to become the movement of the opposite sex. * Gender is not static, but movement towards the opposite sex.


Gender is the play between flowing water and flaming fire: motion and time.

The hexahedron is the basis of all tessellation (the complete filling of space by regular geometric solids).

The cube is defined by eight vertices at equal distance in space. The vertices at a time are the points of maximum distance of the central point: the sphere. The center of each of the six sides is the closest point to the sphere. Like the sphere, each of the vertices is defined by their respective XYZ axes of their three dimensions, forming the edges of the cube. Thus the eight vertices form points of concentration, which are perfect mirages of the central sphere. They continue to be one with the central sphere although they may begin to be counted. It is a sphere that at the same time is NINE spheres.

To separate them you have to imagine the fulcrum zero among the nine, forming planes of stillness.

Thus the nine numbers emerge from the cube plus the corresponding zero, which centers all of them and at the same time creates the illusion of separation between them.

(The image shows the number arrangement according to the Lo Chi magic square).

 The cube is the geometry of eight vertices at equal distance and a central point: in total nine points, which are also Fulcrums, spheres, nuclei, stars or suns.

The hexahedron, including the cube, can also be defined by only two points. It is the only geometric solid that is defined by two points, each of them forming the fulcrum of its three dimensional XYZ axes that cross at a 90 degree angle. Each pair of two axes define a plane. In the illustration on the left a third point was added in the precise middle of the two, crossing the central sun, forming a total of eight cubes. It is seen how the cube composed of eight cubes is defined through nine planes: Red, green, blue, forming three spheres whose nuclei intersect at right angles, centered by three suns, forming a total of three horizontal planes and six vertical planes; Each triplet of them parallel and equidistant. Each sun or core is the North Magnetic Pole. The yellow "Y" axis describes the South, upon its horizontal and blue magnetic field, "X" & "Z" are the colors cyan and magenta and form the east and west, green and red magnetic fields of vertical orientation . Magnetism is unipolar. The north pole is the quiet center.


"If you only recognized the importance of Three, Six and Nine, you would have the key to the Universe"

Nikola Tesla

They are three dimensional planes - six colors of simulated light - nine numbers that define the space cube.

The eight vertices form perfect clones of the sphere because they are the sphere. They are the numbers as points of maximum compression in the cube of maximum expansion. In the center of the cube simulating expansion is the zero sphere "0" whose diameter is ONE equal to the edges of the cube.

The whole universe fits into this CUBE that is one. It has six sides that are mirrors reflecting its content and thus creating the illusion of the infinity of Space.

The whole universe fits into this SPHERE that is one. It has a single side that is curved, the intersection of curves forms lenses, thus creating the illusion of Volume and Measure (large vs. small .. Low vs high, far vs. near, expansion vs. compression, dark vs. light .. .).

Here are marked in green, the eight intersecting convex lenses. In this constellation of nine cubes with their equivalent spheres, there are eight zones of intersection between the spheres of zero, forming convex lenses where each of the spheres of compression of the eight vertices touch the centering sphere. The lenses are at an angle of 109.47122 ° between them. They coincide with the sides of the inverse Platonic solid to the Cube, its dual: the Octahedron.

It is the octahedron that has its twelve edges of the same length as those of the central cube: 1.

The lenses are also right in the middle between the central sun and their respective clones at the vertices of the space cube. The suns of the eight vertices are projections of the sphere (or central sun) through each of the lenses.

The intersection of the Cube of space with the Octahedron that defines the phase between the lenses, forms the most complex tessellating geometry that can be repeated to fill space with identical solids and at the same time to have the minimum surface of contact: the Catalan solid  called Truncated Octahedron . It has fourteen sides: eight of them hexagons forming the lenses and six squares forming the mirrors (and also the concave lenses): the reference of the XYZ planes of the dimensions of the space-motion-time unit.

In the image below left are marked in red, green and blue the planes X, Y, Z through the sun.

All five platonic solids can be drawn from this geometry. The image shows in green the icosahedron, The image of the center shows the dodecahedron

In the image to the right the tessellation of the Truncated Octahedron is shown.

It is the geometry of the "close packing of spheres" called body-centered cubic, because there is a sphere in the center of a cube formed by the vertices of eight sphere-centered cubes.


Here is a schematic image of the position of the 14 light lenses within the cubic wave field:


- eight convex lenses (green) and

- six concave lenses (yellow)


The lenses naturally form in this constellation in the body-centered packing of spheres.

The six concave lenses project and expand the sphere through the faces of the cube towards the neighboring cubic fields, forming eccentric rings on the dimensional planes that traverse the central points of those cubes.


The eight convex lenses project and compress the concentric rings that surround the central sun to the vertices of the cube, forming eight perfect clones of the central sphere

If we continue to expand the cubes in the same way, that is to say by the geometry of body centered packing of each of the eight cubes from the first sequence, we arrive at a larger cube composed of 27 cube-spheres. Three on each side. The middle cube is the same we had at the beginning, it means that there is an initial cube plus eight cubes projected towards its vertices (seen in the previous images), plus 26 reflected cubes: a total of 35 interlaced cubes.


It follows an implosion sequence of the original space cube of:

1 - 8 - 26 - 56 - 98 - 152 - 218 - 296 - 386 ....

Each volume being the additional volume or number of cubes added in each reflection-projection sequence.

The reflection sequence (or projection through concave lenses) on the six faces of the cube is:

1 - 26 - 98 - 218 - 368 - etc. Based on the odd natural numbers cubed.

Odd numbers are odd, because they include the central cube.

The projection sequence through convex lenses on the eight faces of the octahedron is:

8 - 56 - 152 - 296 - 488 - etc. Based on the natural even numbers cubed.

Even numbers are even, because they exclude a central cube, the vertices of eight cubes joining at the center point.


Each number corresponds to a larger cube, which includes in its center all smaller cubes. The relation between this volume difference forms the octave. The octave of colors and the octave of sound. The following image shows how the geometries are formed by rotating and folding the triangles of the DOdecahedron that wraps the outer cube towards the inner Tetrahedron:

tone      value    related solid                color       reflexion/projection

TI         1        tetrahedron                  yellow          no     /     yes

- LA        3        interior cube                 light blue      yes    /     no

- SOL      5        octahedron cube dual    red               no     /     yes

- FA        7        icosahedron                   violet            yes    /     yes 

- MI        8       cub-octaedron external blue              yes    /     yes

- RE        10      exterior cube                 light blue      yes    /     no

- DO        12       dodecahedron                green           yes    /     yes


Read more here: Close Packing of Spheres