THE SACRED GEOMETRYOFDODECAHEDRON
The Dodecahedron has been a source of metaphysical interest for at least 2000 years. Like a crystal or gem, its facets and symmetries compel our eyes and hearts
to observe life more deeply. Some have believed that the Dodecahedron represents an idealized form of Divine thought, will, or idea. To contemplate this symbol
was to engage in meditation upon the Divine. Today many people believe there is a lost knowledge residing in the past, slowly being rediscovered. It is known that
figures like Pythagoras, Kepler, and Leonardo, among many, were educated in these Sacred Geometries, and held many beliefs about them and their role in the
Universe.

The polyhedron represents a regular division of  3-dimensional space, equilaterally and equiangularly.

The Tetrahedron represents the concept of system.  It has been associated with the element Fire.

The Hexahedron or Cube represents the three-dimensional, physical, manifest world, with its four directions angles, right angles, and polarities.  It has been
associated with the element Earth.

The Octahedron has a dual relationship to the Cube. It has been associated with the element Air.

PROGRESSION OF THE SHAPES, SYMBOLS

Presented as a symbolic journey through the process of manifestation.

1,     The Circle represents Unity and Totality. All points from the center radiate equally. It also symbolizes the void; the pre-manifest
seed or germinal idea, expanding and asserting itself by will. It is the first, primordial, state of all things. The Beginning.

2.    The first step in manifestation is differentiation. So, the circle will split and divide by two at the center, bilaterally. The Cosmic idea
is preparing to self-replicate. This is Logos.

3.    As the splitting has begun, new radiating points are formed, and new tangents created. The area of the two inner circles equals
one-half of the outer one, yet the circumference of them both is identical to the latter. Thus the paradox where the two and one
are united. There cannot be two without first, the One. This synthesis and interplay of opposites-as-unity is also revealed in the
Chinese Yin-Yang symbol:

4.    We next draw tangential arcs from the top and bottom points as centers, creating a vesica, which is also expressed when two
circles each touch another at the center, like this (at 90 degrees):  this vesica has slightly different proportions

This is Unity becoming Duality. The relationship created between these two circles can yield all regular polygons and in particular the geometric solution for squaring
the circle, which is the most elegant geometric analogy of the infinite becoming manifest.

A variant of this symbol is in the zodiac, namely Pisces:

*There is an extensive correlation between Pisces, the vesica, and Christ, which is beyond the scope of this exposition, but quite worthy of pursuit.

Represents the creative idea, represents the first duality, is the creative idea, manifested.

It can be seen that the first regular divisions of 2-dimensional space emerge as the Triangle, Square and Pentagon.

Then come the hexagon, octagon, decagon, and dodecagon...the Ten-Thousand things.

5.    In this closed system of radiation, differentiation is a constant impulse, and each circle tangentially presses against another, pushing the envelope of the totality
of the surrounding universe. One circle might begin at an open center, until it reaches the other radiating circles.

6.    Here we see the first organic system, and thus pentagonal symmetry, as is often evident in many forms of life. The points created by the intersections of these
basic radiations within a circular area yield the five-fold relation symbol known as the Pentagon.

7.    Like all regular polygons, the Pentagon is filled with many internal correlations. Each side is opposite a point, every diagonal that unites two sides, internally, has
a Golden ratio to either of the sides it unites. The instances of groups of fives and pentagonal symmetry in everyday life are many-fold.

8.   This shape is known as the Pentagram. It represents the first harmonic division, again, by differentiation. Over the course of history, it has come to be associated
with images of Black Magic or the Occult. Although it may indeed be an order of "secret", "forbidden", or "ancient" knowledge, it is by no means malevolent. It simply
expresses archetypal geometries and relationships that are infinitely exposed all around us, by virtue of the interactivity of radiating points, which then beget infinite
forms. As stated earlier, each internal diagonal line has a Golden ratio to an outer side. The Golden proportion is one of the constant,
incommensurate ratios that govern manifestation. So, too, is PI.

9.    This represents the second order of differentiation, the second harmonic division. Each side has been bisected, and every  resulting internal point connected.
Symmetry yields symmetry. A smaller, fractal child has been generated from the parent.  This is also known as recursion. This process can occur at any scale and
size, and still retain the same inter-relationships and  proportions. This shape also reveals many regular and semi-regular polyhedra at various views. It is among my
favorite as a meditative device, like a Mandala. Additionally it contains 30 scalene triangles of varying scale, which symbolize the 30° of each of the 12 houses of the
zodiac, as well as the idealized circular sequence of 30 days in each of the 12 months.

10.   One of at least two possible resultant 3d projections of polyhedra, namely the Dodecahedron. 2-dimensional differentiation yields 3-dimensional manifestation.

11.   Here, removed from the grid, is the Dodecahedron. Historically it has symbolized the concept of a fifth element, Ether (Aether) or Universe. It represents the
perfect mediation of the infinite and the finite, the sphere and the cube, analogous to the circle and the square. It is reciprocal with the Icosahedron; whereas the
Icosahedron has 20 faces and 12 vertices, the Dodecahedron has 12 faces and 20 vertices. Each shape can easily be transformed into the other by truncation or
stellation.

Humanity is represented by the Dodecahedron and the Pentagon:

Gurdjieff is the best resource for a deeper understanding of this symbol.
Any whole number divided by 7 will contain the following numeric progression, usually after the decimal: 142857...

The Dodecahedron is associated with visual harmonic division and proportion with music and sound, music in particular being something of an aural geometry.

Kepler tried to associate the polyhedra with the relative orbits of the planets known at that time (planet Earth was related to the Dodecahedron), and in turn to
correlate these to rather sweeping musical frequencies, the sound of which create a harmony, into which we are born, always hearing, indeed a part of it. Likewise,
many have believed that the soul or spirit essence of the material body exuded a harmony, much like the notion of a visual aura, and this harmony resulted from the
harmonic vibrations of energy patterns, holding the molecules of the material in place to manifest in the form of structure.

Quantum Physics and many Eastern mystical religions hold apparently similar views about the existence of energy fields which harness molecules (matter) by
vibrating them, bestowing manifest shape, all sharing one common source. To observe things in this way can inspire reverence for all of reality, as the totality of the
Universe may appear to be a collection of dormant molecules, woven together like a vast matrix, shaken and vibrated by energy fields which give them cohesion and
consistency, namely mass, a medium for energy to travel by, like a wave upon the ocean, illuminated in time-space by light.

The unity of all things becomes revealed.
Terahedron
Cube
Octahedron
Dodecahedron
Icosahedron
Logos
Unity and Totality
 Opposites-as-unityThere cannot be two without the one.
Yin-Yang Symbol
Unity becoming Duality
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