Platonic Solids and the Tree of Life

JMD, it has certainly captured my imagination, here are some thoughts, [thinking out loud in a way], before I go away and think about for winterJ

An equilateral triangle can be seen to contain the, Tetrahedron, Octahedron and Icosahedron in that these three solids all have equilateral triangle surface and line dimensions. It’s an interesting point I think, that there can only be 5 regular polyhedra, 3 of them can be made with an equilateral tri matrix. The two left out are the cube and the dodecahedron.

The problem with this is that the equilateral triangle only has 2 dimensions, and building with them, would form a hollow structure…a vessel?
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My take on what you said-
Almost in a manner of cell division, an equilateral triangle could be seen to grow, divide 3 new cells, which fold into the tetrahedron. Within/along side (?), the tetrahedron (womb?), a separate entity, one again growing from equilateral triangles could grow, the Octahedron… and again within the Octahedron comes the Icosahedron. Within/out, this cocoon, the tetrahedron could be seen as the first cell, higher spiritual beings being the motivators. Within the Octahedron, at the same time, forces developing the soul, and within the Icosahedron, our essence, our higher being. This is birth of physical life.

After the fall, daath sinks within the higher being, at this moment a solid connection runs through the system , the ray in a straight line hits tiphareth, then continues straight until yesod.(The Octahedron which resembles a pyramid and its refection), the it takes the tetrahedrons edge down to malkuth, uniting it into one, and a new life form, being starts to develop from the sacrifice of Daath, and the immediate rebirth of Daath [restoration]. A new rose is born.

At death, the tetrahedron folds into the Octahedron [soul], which then itself folds [assimilates] itself into Icosahedron [higher being]. The system then repeats.

triangular solids only...

jmd said:

I'm glad it has caught your imagination too, AmounrA.

Here is a somewhat brief description of some of my work:

Prior to incarnation, the Tree is folded upon itself, but in the following manner: the Tetrahedron (which I consider of pure Spirit) contains the octahedron and icosahedron

*** from the mathematical discoveries of r buckminster fuller:

there is a figure called the cuboctahedron. this figure can be thought of as a cube with the corners cut off. it is also represented by a sphere surrounded by other close packed spheres. 12 spheres about 1. when the center sphere is removed, it looses stability and starts to collapse. it will then stablize as one of the triangular solids (a process fuller calls 'jitterbugging') the cuboctahedron might be considered what you call your folded tree.

fuller calls the cuboctahedron 'the face of god'. i consider figure to represent the wand level-- pure potential.

as the face collapses it can form two different figures.

if it spins on the way 'down' it forms the tetrahedron-- the basic unit of energy. this is the world where creation begins. i consider this the cup level.

if there is no spin, it collapses into the the octahedron. a funny thing here-- this is the sword level, the level of form. if you connect the midpoints of the octahedron, the smaller figure is the cuboctahedron; but now it is frozen in place. so the octahedron 'captures' the face of god. form is the result.

to release the face, the octahedron is 'blown up'. in it's expansion, it reaches the icosohedron phase. i see this as the world we know of... ****

ravenswing

Click to expand...

Thanks for that input Ravenswing - I have only read one of B. Fuller's books, and that was many years ago. I'll have to carefully consider this 'cuboctahedron' - though it isn't what I was describing in the folded process, as these remain the perfect (or 'platonic') solids.

AmounrA, I have been away for a few days, and should have made a response to your post earlier - but these things are at times put off, and then semi-forgotten.

I agree with you that taking the (equilateral) triangle as a basic unit can lead to a very informative growth process. Instead of a duplication in the growth, however, a natural tetrahedron results as each vertex (ie, its furthest points) seek to unite - they thereby fold upon themselves and create this most incredible of forms, whose simplicity, with which I can only presume both you and Ravenswing would also agree, belies its hidden strength and potential.

With regards to a cube (otherwise also called an hexahedron) and its corners (ie, vertices) chopped, this, if continued deeper, results in the cube's transformation into an octahedron. In its earlier stages, it is wonderfully represented in Dürer's Melancholi I - a woodcut worthy, in my opinion, of as many reflections as words written upon it.

Thanks for the various commentaries and reflections - it is the kind of thread which demands even more careful thought than when working with more widely accepted and written about views.

""Instead of a duplication in the growth, however, a natural tetrahedron results as each vertex (ie, its furthest points) seek to unite - they thereby fold upon themselves and create this most incredible of forms, whose simplicity, with which I can only presume both you and Ravenswing would also agree, belies its hidden strength and potential.""

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Yes, folding would make more sense, the growth from point to plane in the 3 steps from kether to binah. Then the folding of the plane, into a tetrahedron.

At each point on the plane, the direction of the line takes a 60 degree turn. I wonder why?

If I had 3 spheres of equal size, all with the same gravity, they would attract each other . Drawing a line from each centre would form an equalateral triangle. {Two spheres would create a line from centre to centre}

Perhaps without the solid spheres , but rather 3 points of equaly attracting energy, they would form the plane, filling the centre with an energy film.. however, trying to visualise this folding is not so easy. It is perhaps easier to see another point of energy born out of the centre 'energy film'?

Your reflections remind me of some meditative visualisations I did a number of years ago with regards to what it would take to construct the simplest perpetual motion 'machine' (I would rather call it 'thought machine', for there are always other constrainst in the physical world).

My reflections lead me to consider placing repelling forces (like little 'magnetic' balls) within the entrails of a hollow sphere, and see what would happen.

If one is placed, its only cause for motion would be an external force - which I precluded in this thought experiment.

If two balls are therein placed, they would maintain their distance along a diametric line within the hollow sphere.

With three, an equilateral triangle would form (with, therefore, internal angles of 60 degrees - but other reasons come to mind for the 60 degrees you mention above).

With four balls, a tetrahedron would form.

With five, we have the first instance of non-equilibrium (interesting, I thought, given how the fives of the minor arcana are generally viewed) - and hence, incidentally, a highly dynamic perpetual motion ensues.

From here on, only four other numbers generate static equilibrial forms, corresponding to the platonic solids (six generates the vertices of an octahedron, eight of a cube, twelve of an icosahedron, and twenty of a dodecahedron). Other static shapes are also generated, but with internal anomalous forces - such as with 60 points, producing the shape of combined hexagons and pentagons reminiscent of a soccer ball (football, for Europeans)... I must admit that I didn't carry, in visualised form, the thought experiment much past this number.

Anyhow - this probably moves away from the thread, but I couldn't help remember such musings reading AmounrA's post.

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With regards to the 60 degrees, if two arms of equal length, being a distance apart of their length, swing out, their extremities but meet at sixty degrees on the plane.

I think this brings the Archimedean solids into bat. A football is a truncated Icosahedron. Do you think the early formation of structures from point dot would splinter into such solids?

I wonder what the effect would be if the magnetic balls where different sizes?


The relation to the 5 disrupting the balance is most apt to the tarot . 5 is a facinating number in the sense of the golden geometry with Phi contained within not just the pentagram, but each arm. This type of magick contained within 'flat' geometry, does make you think about the fractal nature that may lie within 'solids'.