STELLA! (octangula)

[MythMath]

Not too very long ago, I found myself compulsively
constructing various forms of paper polyhedra...

Primarily stellated octa- and dodeca-hedra...

During the process of gluing one together one day,
I flashed back to a nearly-forgotten practice in my past:

In 6th grade, I ran a modest pyramid building business...

For some reason, my teacher allowed me to design, construct
and sell (.25/each) personalized paper pyramids in class...

I displayed my wares on the windowsill next to my desk...

My enterprise lasted several weeks before the 'novelty' wore
off and my potential customer base became saturated...:(
_______________________________________

The following from Wikipedia:

http://en.wikipedia.org/wiki/Merkaba

In modern esoteric (http://en.wikipedia.org/wiki/Esoteric) teachings, it is taught that the MerKaBa is an interdimensional vehicle (http://en.wikipedia.org/wiki/Vehicle) consisting of two equally sized, interlocked tetrahedra (http://en.wikipedia.org/wiki/Tetrahedron) of light with a common center, where one tetrahedron points up and the other down. This point symmetric (http://en.wikipedia.org/wiki/Point_symmetry) form is called a stella octangula (http://en.wikipedia.org/wiki/Stella_octangula) or stellated octahedron which can also be obtained by extending the faces of a regular octahedron (http://en.wikipedia.org/wiki/Octahedron) until they intersect again.
In his books, researcher and physicist Drunvalo Melchizedek describes this figure as a "Star Tetrahedron", since it can be viewed as a three dimensional Star of David (http://en.wikipedia.org/wiki/Star_of_David). By imagining two superimposed "Star Tetrahedrons" as counterrotating, along with specific "prana (http://en.wikipedia.org/wiki/Prana)" breathing techniques, certain eye movements and mudras (http://en.wikipedia.org/wiki/Mudras), it is taught that one can activate a non-visible 'saucer' shaped energy field around the human body that is anchored at the base of the spine. Depending on the height of the person doing the exercise, this field is about 55 feet across. Once activated, this 'saucer' shaped field is capable of carrying ones consciousness directly to higher dimensions.
_______________________________________

Does anyone here have any tales of the Merkaba...?

[Anibis]

Does anyone here have any tales of the Merkaba...?

I do, though I always found Melchizedech to be off-puttingly flaky. This may simply be translated into my being a grouch who has spent too much time in academic philosophy.

In any account however I have contemplated this figure alot. Clearly one can take a layout such as the abrahadabra grid and consider it as a 'side' of a given tetrahedron. The various excercises and such that m1thr0s gives (or that one may design oneself, considering these techniques) are pretty solid material for constructing such tetrahedri. then it's just a matter of counterspining two of them. Sounds basically like a 3-d version of the effect of putting two opposite trangular grids together to form a Magen star("Star of David")... So, the no brainer is that the Merkaba is a 3rd dimensional Magen star ! okay.

The historical Merkabi, not to be confused with Drunvalo's methods, were vehicles or chariots built, as far as I can tell, out of the names of God. While I am no expert on these matters, am told that the Sepher Yetzirah is basically an instruction manual for the construction of such a chariot. "Merkabah Mysticism" was Proto-Qabalistic Hebrew mysticism which flourished in the first Millenium of the Christianized Era. The mystics would build these chariots and then use them to explore altered states of being, traveling through 7 heavens called Hechalot... the objective was to witness God seated upon his throne. DOC HOLIDAY is the man to tell us about this in more detail, I suspect...
In any account we can also link the Merkabah to the Tarot trump, the Chariot (for obvious reasons). This gives us so many options it would be impossible to play them all out in this post. Firstly we should notice that as the 7th trump, it draws our attention to the Magen star again: 6 points and a centre. Moreover, since it is associated to 8, through 'Cheth' (which can be expanded to 418 easily, since Cheth, by Hebrew Gematria= Ch+I+Th, or 8+10+400) it is linked to the octahedron, which Mythmath mentioned (Please mythmath, show me how I can extend the sides of the octahedron to produce the two interlaced tetrahedri, I'm not seeing it completely).

The Octahedron can do tons of stuff. It was the first figure I really got into. I generally would build it by conjoining an upwards and a downwards pentacle (which have been rendered as pyramids), though now I simply build it by interlacing two twinstars (which actually produces a sideways Octahedron). One of the coolest things about it is that you can actually map the entire tarot of 22 trumps onto it. This is only one of the countless ways that 22 is related to 418, but it is a powerful one. I know I have mentioned it alot, but in this respect, have another look at the Abrahadabra Key (http://forums.abrahadabra.com/showthread.php?t=167), since it is the powerhouse of my work.Here are the two methods:

http://Ibisis.zoints.com/image/36013-Pentacle-pyramid

http://Ibisis.zoints.com/image/36011-Twinstarmagenstar

I will leave off the specifics of the Trump attributions for this post, but basically, check out all the points and lines on the constructed octahedron. There are 7 points, and 15 lines. The points correspond to teh Hebrew 'double' letters and I attribute them as per the central Hexagram on the Tree of life. The lines are divides as follows. There are 3 inside the figure, which correspond to the mother letters (this includes the axis of the Octahedron, which while it does not get automatically generated by the pyramid method(you gotta just assume it), does indeed if you use the TwinStar). There are also twelve outer lines, which correspond to the simple letters (the Zodiac). Conveniently these are grouped into three sets: those which rise to the Zenith, those which hold the central square, and those which descend towards the Nadir. These divide along the same lines as the cardinal, mutable and fixed signs.

It's neat also that the TwinStar method actually encloses this octahedron inside a magen star: is this perhaps a way of rendering the Stella Octangulata?

Well, that's it for now...
-Ibisis-

[MythMath]

I do, though I always found Melchizedech to be off-puttingly flaky. Yeah, I didn't really feel that he needed to be name-dropped in the Wiki article...

In any account however I have contemplated this figure alot.
Clearly one can take a layout such as the abrahadabra grid
and consider it as a 'side' of a given tetrahedron.
I recently made one with the Abrahadabra grid printed on the sides...:rolleyes:

Please mythmath, show me how I can extend the sides of the octahedron
to produce the two interlaced tetrahedri, I'm not seeing it completely.
http://upload.wikimedia.org/wikipedia/commons/1/19/Stella_octangula.png

The stella octangula (eight-pointed star),
also known as the stellated octahedron,
is the polyhedral compound (http://en.wikipedia.org/wiki/Polyhedral_compound) of two tetrahedra (http://en.wikipedia.org/wiki/Tetrahedron).

It is both the simplest regular polyhedral compound
and the simplest non-convex uniform polyhedron (http://en.wikipedia.org/wiki/Polyhedron).

Thus it is the first (and only) stellation (http://en.wikipedia.org/wiki/Stellation) of the octahedron.


http://Ibisis.zoints.com/image/36013-Pentacle-pyramid

http://Ibisis.zoints.com/image/36011-Twinstarmagenstar

It's neat also that the TwinStar method actually
encloses this octahedron inside a magen star:
is this perhaps a way of rendering the Stella Octangulata?

I followed most of what you wrote regarding the points,
paths and construction methods from your graphs,
but I don't actually see the result as an octahedron...
______________________

Pre.S. - I have been examining your Abrahadabra Key with interest
(for use as a future kymotrope design) and using it to help me
tackle some of the intricacies of adapting the TwinStar system...

[Anibis]

I followed most of what you wrote regarding the points,
paths and construction methods from your graphs,
but I don't actually see the result as an octahedron...


It's definitely there. Take a look at the Pyramid method. Just imagine those two pentacles as five sided Cheops style pyramids, then put the two together. It should 'pop out' at you then. By the way, thanks SO much for the lovely Stellated Octahedron. It seems to relate somehow more to the TwinStar method, which produces the octahedron sideways inside of a Magen star than to the pure octahedron. As for the Abrahadabra Key, I will be returning to that article soo, I think, and re-animating it. Plus that article is years old, I think i could elucidate it a little further now, in light of the discussions we have all been having here. Cheers;
-Ibisis-

[MythMath]

Am I looking for a Regular Octahedron?

Like this:
http://upload.wikimedia.org/wikipedia/en/thumb/2/27/Octahedron.jpg/240px-Octahedron.jpg
______________________________________

I'm having trouble even seeing your 3D pyramid with a 5-sided base...

Do you have any other renderings that could help my perception...?

[m1thr0s]

http://abrahadabra.com/images/merkabah.sm.gif

It is certainly possible to look at the whole Abrahadabra formula as a form of the Merkabah, though it has been my impression that this winds up being a way of depreciating its actual value. This may be because its traditional properties have been too narrowly defined to begin with. I'm not real keen on traditional Judaism anyway and I'm not about to spend my whole life locked inside the dead-ended debates I find there, but the parallel is a fairly clear one, so far as it goes.

I'll return to this a bit later...it's a very important discussion I think.

m1thr0s

[MythMath]

Oh, look what I just found:

http://upload.wikimedia.org/wikipedia/en/thumb/f/fe/Cell16-4dpolytope.svg/310px-Cell16-4dpolytope.svg.png

Are you talking 3- or 4-D...?

(The above are apparently 4-D polytope images)

I sort of see it...my brain hurts...:o

[Anibis]

Well, it's the same figure as you drew, but I made it a little abstract, sorry. I'll see what I can do, but for now, Find the square in the top pentacle of the 'Pentacle/pyramid' diagram. Then note the x that crosses it. that x'd square is the flat base of the pyramid. Then look up to the top point. That's the apex. Note that it has lines that connect to all four corners of the square? There's your Cheops pyramid. Then note that the lower one is exactly the same, only inverted. Then put them together.... If you still can't see it, I'll try to make another, but trust me, it's there....
-Ibisis-

[MythMath]

Ibisis,

Got it...!

I see it/them now...

Thanks for the walkthrough...
_____________________

m1thr0s,

Looking forward to more details...

MM

[m1thr0s]

One of the problems I run into when dealing with any "traditional" Hebrew construct of any kind is we almost never see Hebrew scholars crediting anybody else besides other Hebrew scholars for their origins, something I find disingenuous to say the least. All rational appearances are that the mathematics underscoring the Merkabah actually originate with the Tetractys, yet the so-called Star of David (which actually has no historical links to King David that we know of) gets most of the popular credit for this construct generally. For me this creates a real problem as when we are dealing in Hebrew constructs we are typically dealing in an elitest and uncompromising set of ideas that will not own up to its own syncretic nature...yet imagines itself justified in accusing all the world of taking its ideas and profaning them...

So I would rather not talk in terms of the Merkabah at all but mainly look to the language of the Chariot as typlified in the Book of Thoth. Here we would have to be blind in both eyes not to see the signature of the Tetractys:

http://abrahadabra.com/images/chariot01.jpg

While not perfect in its symmetry, the symbolism is plain as day with the monad at the crest of the helmut, two points at shoulders, three points spanning hub-shield-hub, and four cheribum at the base. Why is this symbolism so pronounced here? Whether consciously or unconsciously, my feeling is that the Tetractys itself is inherently the core principle behind the Chariot.

So why would this be the case? For one thing the Tetractys was always heralded as Logos to the Greeks and there have arisen certain ideas relating to flight linked to this, as well as other ideas linked to the Body of Man in general. "Soul" is essentially the manifestation of Spirit and is therefor the Body portion of the equation in strict relation. I have very little doubt in studying this and other iconographic images that the Tetractys is somehow implicit in the idea of the Chariot. But what I don't know is why. When I say that, I don't mean that I don't personally know why because I do...but that I do not know why this would have been arrived at historically.

In terms of Abrahadabra itself, there can be little doubt remaining (once all the facts are observed) that the Tetractys is very much a key player in that particular magickal formula which, since it carries the Body of Light itself in a kind of vehicular modality of some kind, can very easily be identified as an exalted form of The Chariot.

So...if all of this was known already, why the hell hasn't anybody said anything about it...particularly in relation to Abrahadabra? This I do not know. It is possible that certain ideas have been connected artistically that have somehow not found their way to logical explanations.

There is more to say of this but I will leave it there for now...

m1thr0s

[Kain]

Wow...the connection is plain as day indeed! That is a very interesting thing you bring up m1thr0s, and even though this is something I think we have never discussed in the past, I have always approached this subject in the same way and I deeply feel the Tetractys to be the "technological core" concerning the concept of the Chariot. In fact, I have been working upon this premise myself for some time now, even though I have not widely employed the Tetractys symbol itself so much as I have it's ramifications. It's interesting to know you see things the same way though.

Kain

[m1thr0s]

There are many mysteries to be sorted out regarding history...some of which we may never get to the root of. We do know that the Book of Thoth is very old and many of its underscoring symbolisms take us all the way to Thebes and perhaps back even further than this. Owing to the Egyptians fondness for triangles in general, it is not a great stretch of imagination to consider that they may have been aware of the Tetractys and held it in high esteem as did Pythagoras and others but we can't really be sure of this on the basis of any known historical documents. Sometimes it doesn't even matter in that there are some things that can be resolved at the level of geometry and mathematics itself and we needn't extrapolate anything historical at all...

Yet certain questions tend to linger and perhaps this is as it should be. I don't really know just how "pure" the symbolism of the Chariot really is from a historical perspective but as to the here and now, we have every good reason to assert that the Tetractys is the heir-apparent underscoring principle behind its "force" and it would not be surprizing to discover that its symbolism is very old and pretty much the same today as it was in the time of Thebes...

If I had a couple thousand years to live I would certainly set this as a research project for the Abrahadabra Institute, along with the entire Book of Thoth in general, as it would be extremely useful to us in many cases to know just what symbols have remained intact from antiquity and which others have been added on in route...but it might actually take nearly that long to sort it all out, particularly owing to the loss of the great library at Alexandria...

edit: along these same lines, you should examine the symbolism of the shield ensignias of both the Emperor and Empress...which also contain the Tetractys and even allude fairly clearly to the TwinStar itself! How can this be? It is difficult sometimes to know if we are dealing in a lost knowledge or have simply crystalized a recurrent theme which has always been visually prominent but has virtually never been openly addressed.

m1thr0s

[MythMath]

I've been working on the design for the
next kymotrope which is being based
on many of the ideas presented here...

i.e. Stella Octangula/Chariot/Tetractys, etc...
__________________________

I'm intending to represent these
contrarily-spinning twin tetrahedra
as a sonic structure built of sinewaves...

The resultant audio recording would then be
processed and filmed in the usual fashion that
has been described elsewhere in this forum...

Please offer any more thoughts and/or links
that could yield other details to be examined...

Thanks,

[MythMath]

http://abrahadabra.com/images/merkabah.sm.gif

Construction of the Chariot kymotrope

I'm intending to represent these
contrarily-spinning twin tetrahedra
as a sonic structure built of sinewaves...

I had communicated with fellow forum member Alisa
about using the numbers 11, 22, 33, 44, 55, 66, etc.
for a kymotrope that could have a triangular structure...

I thought that these numbers (bumped up into audible
range by multiplying by 10), would be good for the short
Merkaba/Chariot kymotrope design I'd been pondering...
____________________________

After consigning the up-pointing tetrahedron as odd, I
assigned the following frequencies respectively to each point:
110, 330, 550, 770 (all Hz - see attachment for details)...

And similarly assigned to the points of the inverted
tetra, were these frequencies: 220, 440, 660, 880...
_________________________

By manipulated the L/R panning of the various
appropriate tones, I was able to convey the
sound of one tetra spinning counter to the other...

I wanted to have the thing to 'appear' to start out spinning
slowly and then to gradually speed up to a steady state
for a couple of minutes, then ramp back down in speed...

So I worked out the timing that allowed
the Fibonacci-derived RPM ratio of the two
pyramids to remain relatively constant...
______________________________

I also wanted to somehow imply that the
various tones were eminating from specific
(moving) points at specific, respective heights...

That effect was achieved by playing back the appropriate tones
through a speaker array that could be adjusted in height...

The sounds were then re-recorded through a fixed-height
stereo mic setup that incorporated a Jecklin disc that replicates
HRTF (Head Related Transfer Function) for binaural spacial localization cues...

http://www.josephson.com/tn5.html

The results sound/feel pretty 3-D through headphones,
but are very subtle when monitored on speakers...
___________________________

The actual visual images that are produced by the O-scope do
not really resemble a "Merkabah" per se, but the video does
accurately reveal the sounds isomorphically translated into light...
.

[m1thr0s]

fascinating stuff...wish I could say I understood it well enough to suggest anything. Your package arrived however which I intend to study...thank you very much for that...

m1thr0s

[Naomi]

Hmm, actually I thought that you were trying to analyze and also learn to control the forces behind the merkaba itself in the Abrahadabra research...funny I missed this until now.

Like....I noticed how mithras is flanked by a couple of winged leopards who look like some sort of cosmic taxi service...the chariot. That doesn't tell us anything about that mithras guy and how he does all of that work....you know?

Hey MythMath, are you going to post a cool video when it's finished?

Anyways....merkaba rocks make great caltrops....

[fr.novumorganum]

http://www.cs.utk.edu/~mclennan/BA/PT/M8-image.gif

here is the chariot from the pythagorean tarot. Besides the two pyramids, there seems to be alot of symbolism relevant to this board.

[imagenerator]

A quick note on the octahedron: it is on of the 5 platonic solids. (http://en.wikipedia.org/wiki/Platonic_solid)