The pentagram has been a significant sign throughout man's history, and I wonder if it is because in some secret way it has a hidden function of being a template for an arcane and mysterious purpose. The television media and fiction have always implied this and produced their nondescript versions of its usage but without qualification and why. The pentagram is a sign, and a sign will always point to something, and here I hope to show what it is pointing to and unhide its true meaning.
Imagine the encircling of a sphere, which unlike a great circle which travels from pole to pole, it is bifurcated by being split away from rejoining and continues its path around the globe, many times until it finally re-meets its origin. I have discovered that this path circumnavigates the sphere a minimum of five times before it rejoins with itself, and when looked at from one angle, it forms a perfect pentagram. The interactive 3D model below illustrates this path:
The pentagram's usage is as a template for performing this 3 dimensional encircling. This means that the pentagram is the signature for the revolution around a sphere, and this is not what it is normally known for. If it is not being kept a secret it is possible that this knowledge has been lost, or at the least very well hidden, and the Latin word for hidden is occult.
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Upon investigating the history of the pentagram, I found the earliest depictions coming from the Sumerian’s more than 3,000 years ago, but I have found no references to its spherical function, anywhere yet. Not even Pythagoras — who adopted the symbol for his system — seemed to know that it is a map for the encircling of a sphere, and it would seem neither did Eliphas Levy in his Transcendental Magic 2,000 years later. Indeed I have yet to find any esoterical mention that the pentagram has association with this divine geometry, which I find strange.
The pentagram symbol drawn with straight sides is the orthographic 3D view, which is the view you would have from a position of infinity — a divine perspective. It is this divine perspective that has been used as a symbol by people in their ceremonies and observances for centuries or millenia, while the 3D perspective is something which might only be known from computer aided design 3D models, and is a possible excuse for why it has only ever be drawn in orthographic view throughout history. It is an extraordinarily difficult thing to construct in 3D.
The 3D construction consists of 5 circles, and I wonder if the pentacle — with its circle around the pentagram — is the symbol for this object. It is interesting that there is a pentacle but no hexacle! The hexagon can have a circle drawn around it too, but it is not given a special name, and you cannot create a 3D path with 6 circles that circumnavigates a sphere from it. The pentacle (in my opinion) is the declaration of secret knowledge which it would seem no one has been able to decode until now.
So, despite the lack of evidence, I still believe that the pentagram's pre-eminence as a sacred symbol throughout history might be because it is the sign of the perfect encircling of a sphere, and the pentacle the symol to allude to this. The perfect path around the perfect form. This is why the pentagram should be important, though I think this aspect of it might have been lost in modern occult usage. If things are hidden, it is hardly surprising.
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The pentagram is pivotal to Pentegraph, underlying all the formations that circles use to division a sphere. Tracing this 3D circle with your hand is a technique I call the Esokirkos or Aster, and is the performance of sacred geometry; it is a fundamental pattern of the universe, and is significant for that reason. In Megâk, the sign can be used as a key to unlock the universe for you, and in my book ‘One Turning’ it is the sign I use to represent the universe.
You have no chance at all of ever being able to perform the technique of the Esokirkos without using the pentagram as a template, and you might never be able to prove its geometric authenticity without computer models. I think the reason for why there are not any models of this structure preserved in man's history is due to the difficulty in being able to create it. I have only been able to do it because I live in the age of computers. Surprisingly, I also have not seen it demonstrated in any occult or science fiction productions in cinema or TV.
There are 2 ways the pentagram is discovered in the Pentegraph Orb. One is from the crossing paths of rotation of eights within the Ikosakirkos Penter, the other is from the joining of the circles in the Dodekakirkos Orb, which encase these Penters. The performance of the Esokirkos (Inner Circle), can take place within the Orb where there are 12 of them produced by the ways described above.
Below shows the Aster performed within the Penter.
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It is tempting to use geometrical forms to provide a framework of presentation for philosophy, but they will inevitably become a constriction to explaining what is in actuality unbounded, and may hinder the traveller on their journey if used as a map. Man is drawn to using these methods as history shows us, but each one ends up with the method being confused for the message, and signs and symbols given importance beyond their true function. The pentagram is typical of this. I have a theory about the Taijitu too.
Pentegraph does not use its symbols as a presentation method of parameters and associations like other systems do. There is no air, earth, fire and water here being attached to pictogrammatic points; they are old, confused and redundant ways of understanding the universe, though their pure spiritual hearkening to nature can still be useful in certain circumstances.
But why is this function of the pentagram not in any of the basic literature? What would be the point of concealing it? Without the help of 3D computer programs, I would not have been able to work it out, so perhaps this is something that gets discovered now, though I find it hard to believe that others have not done it before me, and I do not believe that this is new. My discovery of it has been with the feeling that this is very ancient indeed; even preceding civilization.