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In this article we will finish our discussion of the Tetrad before we move into a 12-part series on the Platonic solids.


The Tetrad is the first number to achieve solidity as it is associated with volume.

We have moved from the point (Monad) to the line (Dyad) to the plane (Triad). Now we will look at volume – the Tetrad.

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Infinite Potential is Volumized in Order for Creation to Begin

“The perspective of volume offers yet another metaphor for the original and ever continuing creative act of the materialization of Spirit and the creation of form. The very ancient creation myth coming from Heliopolis in Egypt gives an example of this mode of envisioning. Nun, the Cosmic Ocean, represents pure, undifferentiated spirit-space, without limit or form. It is prior to any extensive, any specificity, any god. It is pure potentiality. By the seed or will of the Creator, who is implicit within this Nun, the undifferentiated space is impelled to contract or coagulate itself into volume. Thus Atum, the creator, first creates himself or distinguishes himself from the indefinable Nun by volumizing, in order that creation might begin.”1

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Plane to Volume

The movement of plane to volume builds off the three ‘ways’ of a line seen in Article 22.

3 ways of a line


Plane to Volume uses:

  • Rotation – circular movement of an object around a center
  • Movement of a vertex – movement of a vertex in a straight line
  • Translation of an object – moves an object a certain distance; it is not rotated, reflected or re-sized. In this case every point of the object must be moved in the same direction for the same distance.


Circle to Sphere

The circle spins to become a sphere. (Rotation)

point to sphere


Triangle to Tetrahedron

The triangle produces a fourth point at an equal distance from the other three to produce the tetrahedron. (Movement of a vertex)

One equilateral triangle produces three more.

point to tetrahedron


Square to Cube

A square lifts away from itself until another four squares are formed to create a cube. (Translation of a square)

point to cube


Volume Ratios

The following volume ratios are from the work of Archimedes.
cone sphere cylinder


The ratio of the volumes of the cone : sphere : cylinder are 1 : 2 : 3.

Volume of a cone = (1/3)πr2h (1/3 of a cylinder)

Volume of a sphere = (4/3)πr3 (2/3 of a cylinder)

Volume of a cylinder = 2πr3


We can see from the above diagram that the volume of a sphere plus the volume of a cone equals the volume of a cylinder.



Creation of the Platonic Solids – The Most Essential Volumetric Forms

“In the electromagnetic field, the spiraling, massless photons thicken into tiny opposite spinning whorls of protons and electrons that braid into massive atoms. The precipitating atoms are tied in Borromean knots along the archetypal lines of force like threads in a carpet or beads on a loom.

Atoms, the basis for the elements, precipitate in precise geometric patterns, like lace embroidery or Islamic tiles, along these lines of force. The geometries of nature’s forms reveal the pattern of their energy fields.

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stucco ceiling 1627013 1920


We can perceive the invisible lines of force by looking at the geometry of nature’s forms.

The archetypal field where the patterns first appear is a sphere, a Monad. The geometry that arises within this sphere is obliged to manifest the Monad’s principles of equality in all directions.

sphere 1984021 1920


Nature’s first expressions in three dimensions are such forms that fit perfectly within the sphere and present us with an identical view in all directions, no matter how you turn it. These forms, or volumes, are based on surfaces with the same shape, either square, triangle, or pentagon.”2


These are the five Platonic solids.

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The Four Earthly Elements

Recall that one of the most important symbolic aspects of the Tetrad is the Four Elements.

These include: Fire, Air, Earth, and Water.

4 elements platonic


What is most important to know about the Four Elements is that they are each related to a Platonic Solid. Therefore the symbolism of the Elements represents the basic building blocks of all reality: The Platonic Solids.

Tetrahedron – Fire Triangle

Octahedron – Air Triangle

Cube – Earth Square

Icosahedron – Water Triangle


The dodecahedron represents the “Fifth Element”. This fifth element is Consciousness or Spirit – the director of the other four elements, as consciousness creates and forms matter.



Brief Overview of the Platonic Solids

We review the Platonic solids in many articles. This information is always worth repeating as everything in Cosmic Core revolves around these five solids.

The Platonic solids are the only possible convex regular polyhedra.

Platonic solids in a row lo


A regular polygon has equal sides and equal lengths.

A regular polyhedron has equal regular polygon faces and identical vertices.

The Platonic solids are the only shapes:

  • with equal side lengths
  • with equal interior angles
  • that look the same from each vertex (corner point)
  • with faces made of the same regular shape (triangle, square, pentagon) 3, 4, 5
  • all fit perfectly in a sphere (circumsphere) with all points resting on the circumference


Plato Volume Shape of Face Faces Edges Corners Sum of Angles Dual
“Heaven” or Aether Dodecahedron pentagon 12 30 20 6480 Icosahedron
Fire Tetrahedron triangle 4 6 4 720 Tetrahedron
Air Octahedron triangle 8 12 6 1440 Cube
Water Icosahedron triangle 20 30 12 3600 Dodecahedron
Earth Cube square 6 12 8 2160 Octahedron


7920 = the sums of the angles of the tetrahedron, octahedron, cube and icosahedron, the Four Elements.

4 elements platonic2


The Earth’s polar diameter in 2013 (NASA): 7899.86 miles

The equatorial diameter of Earth: 7926.33 miles

The diameter from tropic of Cancer to tropic of Capricorn: 7920 miles

Note that these numbers are always in flux due to seasonal, lunar, meteorological and geological changes.




7920 protons and neutrons are used by 64 codons that make up our DNA (from Anthony Morris).

7920 = the number of inches in a mile and a half.

7920 inches = 1 furlong (from Randall Carlson).

7,920,000 = diameter of New Jerusalem (the establishment of “heaven” or harmony and unity on Earth).



Frank Chester, the Chestahedron & Earth Measure

See Article #67 for more information on the Chestahedron.

7920 = the total surface degrees of the Chestahedron (7 faces) and its dual, the Decatria (13 faces).

The Chestahedron = 1800º

Chesahedron transparent


The Decatria = 6120º



1800 + 6120 = 7920

Remember, 7920 is also the mean diameter of Earth in statute miles to 99.97% accuracy (NASA 2014).

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  1. Lawlor, Robert, Sacred Geometry: Philosophy & Practice, Thames & Hudson, 1982
  2. Schneider, Michael, A Beginner’s Guide to Constructing the Universe, Harper Perennial, 1994

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