Platonic Solids

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The Formula for the Five Platonic Solids

Metaphysical Platonic Form & the Ultimate Ontological Statement

The five platonic solids are the crown jewels of geometry, perfect in symmetry and a unique group of objects, to this or any possible universe. So it is of some importance when it is understood that these five perfect objects can be seen in the sum of Exodus 3:14, one of most important verses in the theology of the Bible.

These are the surface points of these figures and are in fact more improbable than the solid variety, being that they must conform to each specific geometry on both the inside and the out.

Exodus 3:14

And God said unto Moses, I AM THAT I AM: and he said,

Thus shalt thou say unto the children of Israel,

I AM hath sent me unto you.

ויאמר אלהים אל־משה אהיה אשר אהיה

ויאמר כה תאמר לבני ישראל

אהיה שלחני אליכם

Exodus 3:14 = 3338

9^th Tetrahedron Surface (A005893 (2n² + 2)) = 130

9^th Hexahedron Surface (A005897 (6n² + 2)) = 386

9^th Octahedron Surface (A005899 (4n² + 2)) = 258

9^th Dodecahedron Surface (A005903 (30n² + 2)) = 1922

9^th Icosahedron Surface (A005901(10n² + 2)) = 642

130 + 386 + 258 + 1922 + 642 = 3338

The formulas for all five are identical except for their coefficients. Collectively they can be reformulated via 4*(13n² + 2) + 2. This looks like, but is not the average of the coefficients, rather it is the prime factors of the sum of the coefficients.

2n + 6n + 4n + 30n + 10n = 52n

2 x 2 x 13 = 52

This pattern has endless applications and is overflowing with theological implications (see below), but it is mathematically indicating an exact specificity to the number nine. This would seem to be a reference to the nine cardinal numbers that produce our modern decimal system.

Looking to the platonic solids we find a similar reference to the cardinal number nine in their terminal repeat cycles.

20-Digit Tetrahedral Repeat Cycle: Digital Sum = 55

10-Digit Cubic Repeat Cycle: Digital Sum = 45

10-Digit Octahedral Repeat Cycle: Digit Sum = 45

20-Digit Dodecahedral Repeat Cycle: Digital Sum = 55

20-Digit Icosahedral Repeat Cycle: Digital Sum = 85

55 + 45 + 45 + 55 + 85 = 285

The sum of all five infinite repeat cycles produce a square pyramid or the nine cardinal numbers squared.

1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² = 285

This sum 285 coordinates with the Three-Seven code in the 37th pyramid, being its frame.

1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² = 285

Further examination of the larger repeat cycles shows a pattern that cannot be overlooked. The infinite layers of the octahedral repeat cycles, repeats a digital sum coordinated with the cardinal number nine.

This is perhaps the finest evidence yet found that the universe does indeed have a preferred number system based on the nine cardinal numbers. This is because the octahedron series and the digital sum of its infinite layers of repeat-cycles are real objects that produce real and tangible objects of universal geometry (the diamond and the triangle). These objects are real and significant in any number system and to any culture, time or age, yet they are infinitely logically married to the decimal system.

The Greek Septuagint translation of Exodus 3:14 is confirmatory that this verse in both Hebrew and Greek has to do with platonic shapes:

Exodus 3:14 (Septuagint)

καὶ εἶπεν ὁ θεὸς πρὸς Μωυσῆν ἐγώ εἰμι ὁ ὤν

καὶ εἶπεν οὕτως ἐρεῗς τοῗς υἱοῗς Ισραηλ

ὁ ὢν ἀπέσταλκέν με πρὸς ὑμᾶς

= 10,914

17 x 642 = 10,914

9^th Icosahedron Surface (A005901(10n² + 2)) = 642

The cube of the series is also of due biblical importance, being the sum of the modern day Hebrew name for Jesus (Yeshua).

The captured squares number to 1412, the sum of the Greek for Alpha and Omega

Alpha and Omega

Number series that are created by formula very often contain repeat cycles, typically the terminal or last digit of each number in the series repeats every ten or twenty iterations. In fact many such series are nothing but endless layers of repeat cycles, starting with the terminal digit then moving on the to the last two digits (typically either a 100 or 200 iteration cycle) and moving on down to a three digit which most often iterates every 1000 or 2000 numbers.

As seen in 'Fibonacci-60' these cycles can be graphed into a repeating curve. Fibonacci-60 shows that these repeating graphs cannot be considered trivial and appear to constitute a new form of digital analysis that is one of the many new digital frontiers of modern mathematics. The Australian mathematician Jain-108 discovered this form of analys

Most of the repeated curves I've seen so far are either 'Walkers' or 'Quarter-Curve. A walker will continue in single direction forever, while a quarter-curve will repeat in a loop ever four cycles. Since walkers don't loop there is nothing to analyze, and although quarter-curves are very common they do offer two bits of data, a 'Hold' the size of the rectangle that contains them and a 'Capture' the number of squares the loop encapsulates. The only other two types of repeating curves are the double-curves, curves that unexpectedly loop every two cycles and the most rare mono-curve that loops in one cycle. The Fibonacci-60 mono-curve is the only significant mono-curve so far discovered.

By scrolling below one can see that all five of the Platonic Solid series produce quarter curve cycles. This is somewhat unusual but wholly surprising considering they share are very similar similar formula. All five cycles line up one after another don't produce anything novel or interesting, but when we merged the 5 into a four rowed table something magical happens 9See animation above). Because two of the cycles are 10-digits long and the other three are 20-digits long merging them into the table not only fits right but aligns their numbers in a most certain and significant way.

The summed columns of the table then produce an unexpected double-curve.

Another surprising double-curve can be constructed from the sum of the iterations of the 5 Platonic Solids, here necessarily employing centered cubes, since the rest of the configurations are centered. By adding all these polygonal series together we find a 20 digit repeat terminal cycle whose sum is 115, the 37th semi-prime and the number of the Hebrew, Jesus the Messiah (Christ).

The sum of the quasi-super-shape of the 5 Platonic Solids

The rectangular 'Hold' of this configuration is 18 x 23 or 414 the ordinal sum of Latin Genesis 1:1. The 'Capture' the number of squares encapsulated by the repeating curve is 206 the sum of the Hebrew for the 'Word' Dabar.

The simplest curve is a square curve, made from a single repetition. The reciprocal of the prime number 89, the 11th Fibonacci number, creates just such a square curve but in a tricky way, by folding over its 44 repeating digits into four rows of eleven.

Other important patterns can be found in the study of these repeat cycles.

The prime factors of this infinitely repeating sum (9250 = 2 x 5 x 5 x 5 x 37) shows us that when we cube the number we can reformulate architecture based on the name Jesus-74. Since this number repeats endlessly, this reformulation happens a lot, what I mean by that is — infinitely a lot.

If we keep repeating this cycle again and again, every time we hit a cube the above pattern of the Jesus-74 will reappear. For instance, twenty-seven repeats of the cycle produce a Jesus-74 configuration based on the blocks of the Fountain of the Water of Life.

The third cube reformulates in a Jesus-74 cube with 15^3 blocks. All this coordinates with the 16,650 sum by making a triangle of triangles (based in 15) that matches this sum.

9250 x 27 = 249,750 = 2 x 3 x 3 x 3 x 5 x 5 x 5 x 37

16,650 x 15 = 249,750

In this light, its possible that the reference from Revelation 21:6 (The Fountain of the Water of Life) is another way of saying the Tree of Life, or the platonic form of all things.

The quarter curves of the five repeat cycles produce another geometry in that of the tetrahedron

Infinite Platonic Cycles

By plotting each of the five terminal repeat cycles on a square graph we find that each repeats in a quarter curve. These sort of quadrilateral repeating curves are common enough, but since all five repeat in the same fashion they may show a shared identity. As seen in the picture above, the sum of the five repeat after completing one circuit of the graphing curve and sum to 1140 (285 x 4) a significant geometry in that of the 18th tetrahedron.

Matthew 1:23 ordinal = 1140

A virgin shall be with child and shall bring forth a son,

and they shall call his name Emmanuel,

which being interpreted is, God with us.

Each individual repeat cycle can be enumerated in several ways. Based on the evidence of the 60-digit Fibonacci repeat cycle, the most significant is the 'Capture' number, that is the number of squares the repeating curve encapsulates. Secondary figures are the number chambers to the configuration and the 'Hold' which is the maximum extent of the square that the graphing curve repeats in. The graphing curves of the five platonic repeat cycles are as follows:

Tetrahedron

Capture: 173

Chambers: 25

Hold: 19 x 19

The cubic repeat cycle has a connection to of-all-things Noah's Ark!

Certain repeat cycles are very regular and easily calculated. The powers of any given number is a basic form of mathematical operation, which is why powers (squares and cubes) are so fundamental to mathematics in general. Almost all the repeat cycles I've studied come in two varieties, a 10, 100, 1000 and a 20, 200, 2000. The equation for these cycles is:

(Σ: 1-9)*10ⁿ

The cube's repeat cycles sum to:

Terminal 10 cycle = 45

Terminal 100 cycle = 4500

Terminal 1000 cycle = 450,000

The last here is the exact cubic volume of Noah's Ark, which can fit exactly 24,000 Ark of the Covenants.

Ark of the Covenant = 1.5 x 2.5 x 5 = 18.75 cubic cubits. Noah's Ark = 30 x 50 x 300 = 450,000 450,000 ÷ 18.75 = 24,000

Cube (Hexahedron)

Capture: 65

Chambers: 41

Hold: 13 x 13

Octahedron

Capture: 113

Chambers: 29

Hold: 17 x 17

Dodecahedron

Capture: 145

Chambers: 17

Hold: 15 x 15

Icosahedron

Capture: 217

Chambers: 49

Hold: 21 x 21

By repeating all five we can show they largely occupy the same space, the largest and all encompassing hold being a significant number to biblical mathematics, 3 x 7 x 7 x 3 (441).

The footprint then, of all five overlaid atop one another gives a consolidated capture number of 233, a Fibonacci number and suggestively the sum of the Hebrew for the Tree of Life.

Genesis 3:22

And the LORD God said, Behold, the man is become as one of us,

to know good and evil: and now, lest he put forth his hand,

and take also of the tree of life, and eat, and live for ever:

This connection is further affirmed by looking at the binary 25-cycle of the sum of the surface of the five Platonic forms, or the product of the equation 4*(13n^2 + 2) + 2:

Platonic Binary Cycle = 1050

1050 x 3 = 3150 = Genesis 3:22

Another series of repeat cycles is the binary 50-cycle of the last two digits of the surface points of the five platonic forms. Here the top two rows (tetrahedrons & cubes) produce the 50-cycle and the octahedrons produce a complimenting 25-cycle and the twin forms of the dodecahedron and icosahedron repeat in a 10-cycle. If we compare them side by side to the longest cycle, we find that the average of all 50 faces of all five platonic forms has a perfect average of 113, the capture of the octahedron's repeating graph. It is also the sum of this all important phrase from the heart of the Shema: The Lord Your God is One, Ord. (אחד יהוה אלהינו יהוה) = 113.

Sum = 11,300

50 x 113 = 11,300

Octahedron Capture: 113

אהיה אשר אהיה

I AM that I AM

In Exodus chapter three Moses asks God for his name. In verse 3:14 God responds, telling Moses to tell his people that I AM sent him. This name in Hebrew אהיה Ehehyeh is one of the cornerstones of the Three-Seven Code, as its sum is 21 or 3 x 7. This name has been intensively studied for many years and has produced a great many marvelous mathematical coordinations with the rest of biblical math.

The sum of the verse itself, however, has remained a mystery, until now.

It should be noted just how important this verse is, historically, religiously and culturally. It is the supreme being giving his name to the world. Jews and Christians alike, famous theologians and philosophers both, have long pondered this name and why God should name himself so. The name itself has long been recognized as the wellspring of ontology (the study of being), being the source of all 'being'. Its nature then, is the fundamental basis of universal being.

You can't get bigger than that.

With this in mind, it would seem that the verse should yield some cosmic mathematical pattern to reflect the universal nature of its theology. And so it does. But its secret was buried well, hidden within layers of complexity and the many masks of culture. For its secret was not so much Christian nor Jewish, but found in the mathematical philosophies of the Greeks.

Whole books and whole series of books could be written on this connection in this one verse alone. What it means for philosophy, metaphysics and theology we can only begin to guess at, but its estimation grows the more one considers its depth. Mathematically, there is an obvious connection with the number nine.

So what's the big deal about the number nine?

Far and away the most pertinent meaning of the number is the nine cardinal numbers (1,2,3,4,5,6,7,8,9) the basis of the world's de facto decimal number system. The word decimal comes from the Greek word for ten deka, but the decimal system is composed of nine fundamental (cardinal) numbers, the number ten is the number of eclipse, the beginning of the cosmic return.

However....

Science and math does not admit or claim that the universe has a definitive number system. Most experts claim that we employ the decimal system simply because the human being has ten fingers. This common collective conceit, is a pseudo-intellectual gloss, used by many to sound smart and well informed. Unfortunately, not only is it not true it has no historical merit.

The world has had many different number systems. The Babylonians used a 60-digit number system, but no one is arguing that the Babylonians had sixty fingers. There is far more evidence that the Greeks chose the number ten because of their infatuation with the ten point triangle called the tetraktys than any evidence for finger counting.

So is their a universal number system? Does the universe prefer one number system over another?

Modular mathematics is all about the wide variety of different numbers systems and how to convert one to another. This conversion is so easy and universal, that it's is generally assumed that there is no one perfect universal number system.

Enter the repeat cycle... .

Mathematical formula and equations are recipes for an infinite series of numerical bodies. These bodies are repeated and grow larger with each new iteration. In the process, this engine of math runs through a series of cycles based on which number system is being employed. The most famous of these is perhaps the 60-digit Fibonacci, which has shown itself to be positively pregnant with biblical mathematical patterns.

What is less understood about repeat cycles, is that if there is one, then there will be an infinity of others. Most mathematicians are well aware of the terminal repeat cycle, where the final digit in the series is repeated forever and ever. But where there is one cycle there will be more. The study of these cycles, is, at best, a fringe element of modern mathematics. They are considered insignificant, footnotes at best to the larger mathematics that create them.

Yet in my short study of these cycles, what I have discovered is something like a mathematical microscope into a miniature world where the echoes of the mathematics sound on and on forever. A great example of this is how the repeat cycles of the tetrahedron and the dodecahedron share the same digital summation. This is no accident for when one examines the various numbers in these repeat cycles, we find the exact same integers, but rearranged. This would indicate an undiscovered mathematical connection between these two objects.

A standard collection of D&D dice

includes all five of the Platonic Solids

Greek Philosophy

Very few people today read Greek philosophy and even less read Greek mathematical philosophy and only a few erudite mathematicians know that both are exactly the same thing, and are the fundamental metaphysical metric for science, physics and the very 'being' of the universe. That being said, let's talk about the roleplaying game Dungeons and Dragons!

D&D (as aficionados know the game) is an imaginative storytelling game that employs a variety of strangely shaped dice to resolve conflict and determine the fate of the characters in the story. These dice have long been a mainstay of the game ever since Gary Gygax invented the game nearly fifty years ago. These dice are also the closest most anybody gets to the pinnacle of Greek mathematical philosophy in the shape of the five platonic forms.

Greek philosophy and Greek thought has largely been forgotten by the modern man or forced to wear a funny hat, instead of its proper golden crown. When we think of the Greeks (if we think of the Greeks) we probably think about old men in robes droning on about things that seemed to be smart once-upon-a-time but have no relevance in this modern technological world we now live in. This is of course an absurd fantasy, and if it were true, no one would have bothered with Greek thought in the first place.

So what is Greek thought?

It revolves largely around two figures, teacher and pupil, Plato and Aristotle, the two titans of classical thought and the leaders of the dual poles of philosophy that has forever divided the thinking of mankind ever since; from Plato came came Neo-Platonic thought and most of modern philosophy and from Aristotle came what eventually was called 'science.' That sounds like a pretty big deal, but in a way, it's unimportant, because what really is important is what preceded or what gave birth to that thought, and what that was, was the math and geometry of Pythagoras.

What is so often (and infuriatingly) left out of the Greek philosophy conversation is the underlying science that gave birth to it. Plato's great Academy in the golden age of Athens, was not a school for philosophy. It was a math school, which is why this (μηδείς άγεωµέτρητος είσίτω µον τήν στέγην) was written on the entrance, which meant: "Let no-one ignorant of geometry enter here." Plato became known as the 'Maker of Mathematicians' and some of his students were the finest mathematicians of the ancient world, such as Eudoxus, Theaetetus and Archytas.

So what really drove Greek philosophy was not really... philosophy as we now know it. It was math. So what's this got to do with Exodus 3:14, the Platonic solids and D&D dice? The answer is everything. One of Plato's big ideas, was that of the forms, super-physical ideal constructs that were the basis of the physical universe, aka everything. Plato relates this idea in the story of the cave of shadows, in which a bound man watches a play of shadows cast by torchlight on a wall, and since this is all this man has ever seen, this is to him reality. But Plato says, it is but shadows of the real. What was Plato talking about? It sounds silly today and most philosophy class teach it all wrong, and often use the example of a chair, i.e. that there is some ideal chair in heaven by which all other chairs are based.

Let me be clear. Plato wasn't talking about chairs. Plato was talking about math.

Of all the ideas of the ancient world, of all the philosophies of the Greeks, one idea has survived and is more true than all the others put together. That idea is in fact, Plato's theory of the forms, but known in another way, perhaps it should be called the theory of numbers, or better yet the proof of math. Simply stated it is: that the universe operates according to mathematical principles and the relationships and ratios (the logos) between numbers. That idea was the most important idea of the Greeks and is itself the very basis of science itself. Put another way, if there wasn't math, there would be no science.

This is why at the very highest levels of science you see all those numbers, mathematical operators and Greek letters.

The quintessential form to which to the forms refer, are the five Platonic forms, the only known and only possible five shapes that have perfect rotational symmetry. The Greeks of old thought these were the basic units (atoms) of the universe and that all things were made up of them. This was something of an overreach, but it was thousands of years before the invention of just the basic microscope, so we must not throw out the baby with the bath water. These five shapes are the crown jewels of geometry, but they aren't the atomic basis of all things, and besides being useful D&D determinators they don't have a lot of application these days.