Platonic Solids

Because the purpose of the Magic of L.V.X. is primarily to develop in the magician a vivid realization of his place in the cosmic order, whatever will tend to deepen or broaden one’s mental grasp of the fact that this is truly an orderly cosmos, wherein nothing whatever happens by chance, helps to strengthen the magical consciousness. As you have read in other lessons of this series, ceremonials are of little avail unless they are backed up by knowledge, will and courage. The more, then, you know about the cosmic order, the better will you be able to discern your relation to it.¶

The purpose of this lesson, therefore, is not merely to make you familiar with the ancient esoteric meaning of the five Platonic solids. We hope, by setting these facts and some of their meanings before you, to intensify your magical consciousness.¶

The following description of the Platonic solids is taken from Nature’s Harmonic Unity by Samuel Colman, N.A. (pp. 14 to 17).¶

“The Greeks, long before the Christian era, discovered that there could be but five regular solid bodies, or polyhedra, three of these formed by the use of the equilateral triangle, one based upon the square of 90°, and one upon the regular pentagon, which forms we shall now analyze as set forth by Euclid.¶

“The simplest regular polygon is the equilateral triangle, and since each apex of an equilateral triangle is an angle of 60°, three such triangles can be combined to form a polyhedral angle. It is seen, then, that a regular polyhedron can be formed, bounded by equilateral triangles and having three at each vertex. This has four faces, and is called a tetrahedron. (See fig. A) Since four angles of 60° are less than four right angles, four equilateral triangles can be combined to form a polyhedral angle and it is seen, then, that a regular polyhedron can be formed, bounded by equilateral triangles, and having four at each vertex. There is such a regular polyhedron. It has eight faces and is called a regular octahedron. (Fig. B) Since five angles of 60° are less than four right angles, five equilateral triangles can be combined to form a polyhedral angle, and it is seen then that a regular polyhedron can be formed, bounded by equilateral triangles and having five each vertex. There is such a regular polyhedron. It has twenty faces and is called the regular icosahedron. (Fig. C) No regular polyhedron bounded by equilateral triangles had having more than five at each vertex is possible, for six or more angles of 60° are equal to or exceed four right angles, and cannot form a polyhedral angle.¶

‘The regular polyhedron next in order of simplicity to those formed by the equilateral triangle is the polyhedron formed by the square, each of whose angles is a right angle. Three right angles can be combined to form a polyhedral angle. It is seen then that a regular polyhedron can be formed, bounded by squares, three at each vertex. There is such a polyhedron. It has six faces, and is called a cube or regular hexahedron. (Fig. D) No regular polyhedron bounded by squares and having more than three at each vertex is possible, for four or more right angles cannot form a polyhedral angle.¶

¶

“The next regular polyhedron is that formed by the use of the pentagon, each of whose angles contains 108°. Three angles of 108° each can be combined to form a polyhedral angle. It is seen then that a regular polyhedron can be formed, bounded by regular pentagons and having three at each vertex. There is such a regular polyhedron. It has twelve faces and is called the dodecahedron. (Fig. E) No regular polyhedron having more than three angles of 108° at each vertex is possible. These five polyhedra, the tetrahedron, the octahedron, the icosahedron, the hexahedron, and the dodecahedron are the only ones possible.¶

“It would be well for the serious student to construct models of these five figures in order fully to comprehend their meaning. This can be done easily and with perfect accuracy by drawing on cardboard the following outlines, cutting them out and gluing the edges. It may easily be seen by examination that the square, the pentagon, and the hexagon by its equilateral triangle, are all that appear to the eye in regarding them. This trinity of forms is now disclosed to be harmonic with all five of the polyhedra and they are therefore all that are necessary in an analysis of proportional spaces, excepting the Egyptian triangle with the angles of 38° 30’ and 50° 30’ and the ideal angles of 42° and 48° which will be considered later.”¶

The patterns referred to in this quotation will be found on the next page. They should be somewhat enlarged for convenience in construction, and the student who succeeds in making good models of the polyhedra will find himself amply repaid for his trouble.¶

¶

Assuming that the boundary lines of these patterns are all composed of units of the same length (although they are not so represented in the patterns given below), the pattern of the tetrahedron will have a perimeter of 6 units, that of the cube 14 units, that of the octahedron 10 units, that of the dodecahedron 38 units, and that of the icosahedron 22 units. Each of these numbers is significant to students of the Ageless Wisdom. We need not elaborate upon the significance of 6, 10, 14 or 22. 38 refers by Gematria to אזל, moving one thing through another, spinning; גלה, to uncover, to lay a thing open, to reveal; חל, wall, rampart; לח, new, unused. These meanings are particularly related to the esoteric meaning of the dodecahedron, and we shall explain them presently.¶

The sum of the numbers 6, 10, 14, 22 and 38 is 90, and its Gematria is given in Lesson 9 of Section A.¶

Pythagoras, and Plato after him, together with the Neo-Platonic and Neo-Pythagorean schools (to which we are indebted for so much of our knowledge of the Ageless Wisdom), ascribed special properties to each of the regular polyhedra. In these schools it was taught that the dodecahedron corresponds to ETHER, the octahedron to AIR, the tetrahedron to FIRE, the icosahedron to WATER and the cube or hexahedron to EARTH.¶

The order in which they are mentioned in the preceding paragraph is the order of the evolution of the Tattvas, as given in the Science of Breath, the Sanskrit work quoted in Lesson 3 of Section A. Ether, or the Quintessence is the Akasha, Air is Vayu, Fire is Tejas, Water is Apas, and Earth is Prithivi. (See Figure 4A)¶

We know that Pythagoras studied in India, and it is equally certain that the Neo-Platonists and Neo-Pythagoreans were influenced by Hindu philosophy. Thus it is not surprising to find that when we tabulate the various properties of the regular polyhedra, keeping them in the order of the evolution of the Tattvas, we find some striking symmetries which will, if we take the hints they give, lead to valuable practical conclusions.¶

Hereafter, for convenience, we shall designate the dodecahedron by the capital letter “D”, the octahedron by “O”, the tetrahedron by “T”, the icosahedron by “I”, and the cube by “C”.¶

Now, bearing in mind that the pentagon represents 5, the triangle 3 and the square 4, let us consider one aspect of the meaning of the polyhedra.¶

D. has 12 pentagonal faces = 12 x 5 = 60¶

O. has 8 triangular faces = 8 x 3 = 24¶

T. has 4 triangular faces = 4 x 3 = 12¶

I. has 20 triangular faces = 20 x 3 = 60¶

C. has 6 square faces = 6 x 4 = 24¶

Observe the symmetry of this arrangement. The tetrahedron is the central point. Above it is a pair of numbers identical with the pair below. This reminds us of the Hermetic axiom, “That which is above is as that which is below.” The pair above (D and O) totals 84, and so does the pair below (I and C). Again, the extremes (D and C) also total 84, and so do the opposites (O and I).¶

The symmetry of the arrangement is striking, but it also points to some very extraordinary conclusions, if we apply the mathematical rule that “things equal to the same thing are equal to each other.” For then, since D and I, which represent Akasha and Apas, or the Quintessence and Water, or the Unmanifest and Subconsciousness, are both represented by the number 60, the implication is that Akasha and Apas, Ether and Water, the Unmanifest and Subconsciousness are aspects of the same thing. We may sum this up by saying that the universal, unmanifested reality is identical with the cosmic subconsciousness, and this is a direct echo of Hindu teaching, for we read in Sanskrit works numerous passages like the following:¶

“She who is pure, eternal Mulaprakriti (root-matter) is Parabrahman itself and the Devata We (the supreme triad of Hinduism, Brahma, Vishnu and Shiva) worship.”

¶

Thus it is that we find the unmanifested Reality compared over and over again to a great ocean, implying that its nature is like Water.¶

In like manner, because both the octahedron and the cube are represented by the number 24, we may look for an identity between Vayu and Prithivi, Air and Earth, superconsciousness and “matter manifested.” This identity is hinted at by the Western symbols for Air and Earth, which are identical in form, but opposite in position. It is also suggested by this passage from the Sepher Yetzirah:¶

“He created from the formless and made the non-existent exist; and he formed large columns out of intangible air.” (Chapter 2, paragraph 6).

¶

At first this may seem difficult to grasp, but it is scientifically true. The property of Vayu, say the Hindus, is motion, and that of Prithivi is cohesion. Cohesion is the result of motion, and just as the root-substance of air is electrons, since the atmosphere is made of molecules of gases composed of atoms, so are electrons the basis of all the solider forms that we call earth.¶

In like manner, that which we experience through the senses as matter is identical with that which we know in superconsciousness. And here we are very close to the knowledge which becomes fully unfolded in the magical consciousness, the knowledge which overcomes the illusions of appearance, and makes it possible for us to perform works of power firmly established upon our knowledge of reality.¶

The tetrahedron corresponds to the number 12, which is one-seventh of 84. This suggests that a seven-fold expression of the universal FIRE or Fohat or Astral Light, is represented by all the pairs of elements whose combinations, as represented by the polyhedra, give the total of 84. These combinations are: ETHER and AIR (D and O), ETHER and EARTH (D and C), AIR and WATER (O and I), and WATER and EARTH (I and C), four in all. 4 x 84 = 336, and 336 = 3 x 7 x 16. The sum of these factors of 336 is 3 + 7 + 16 = 26, the number of יהוה.¶

Since ETHER and WATER are both represented by 60, or 5 times the number of FIRE, we may regard ETHER and WATER as being in some sense a fivefold manifestation of FIRE.¶

Since AIR and EARTH are represented by 24, or 2 x 12, we may regard them as corresponding to each other, and as being each a duplication, or twofold manifestation of FIRE.¶

Another table shows the same correspondences, but based on different facts.¶

D. (ETHER) has 30 edges O. (AIR) has 12 edges T. (FIRE) has 6 edges I. (WATER) has 30 edges C. (EARTH) has 12 edges¶

Again, the points of the dodecahedron are the same in number as the faces of the icosahedron. Similarly, the points of the octahedron are the same in number as the faces of the cube. Vice versa, the faces of the dodecahedron are equal to the points of the icosahedron, while the faces of the octahedron are equal in number to the points of the cube.¶

Here is another table, showing the same correspondences, but enabling us to compare the solids by means of the numbers derived from adding together the numbers of the points, lines and faces of each figure:¶

TABLE 4A¶

Here the solids representing ETHER and AIR, AIR and WATER, WATER and EARTH, and EARTH and ETHER give 88 as the sum of the numbers representing each pair. The number 88 is connected with the Pi-proportion and with the Great Pyramid. It is the number representing the circumference of a circle having a radius of 14, because 14 radius = 28 diameter, and 28 x 3 1/7 = 88, which is the circumference number of the circle of Assiah, as explained in Lesson 2 of this Section. 88 is also the number of units around the base of the Great Pyramid, if the height of that structure be reckoned as 14, the number which corresponds to the tetrahedron, or FIRE in the table above.¶

Note also that in this table 62 and 26 are not only complementary, as being the component numbers of 88, but they are formed by the same digits, so that one is the reflection, as it were, of the other.¶

By reducing the numbers shown in the preceding table, we arrive at the following:¶

D = 62 = 6 + 2 = 8¶

O = 26 = 2 + 6 = 8¶

T = 14 = 1 + 4 = 5¶

I = 62 = 6 + 2 = 8¶

C = 26 = 2 + 6 = 8¶

8 + 8 + 5 + 8 + 8 = 37¶

¶

Thus the number 37 is the sum of the least numbers of the five numbers which represent the geometrical properties of the Pythagorean solids. The digits of 37 are the digits which particularly correspond to the Tree of Life, which has 3 Supernal and 7 Inferior Sephiroth.¶

Now, if we represent the cube of 4 x 4 x 4, which is built up from 64 small cubes, by a series of points showing the symmetric aspect of that cube in flat projection, the resulting diagram will be what is shown here.¶

Each point represents one of the 64 constituent cubes in the great cube, and none of these lesser cubes 37 are visible. No more than 37 can be seen at any one time.¶

The whole 64 stand for Truth, because the Greek word ΑΛΗΘΕΙΑ=64, and thus 37 may be taken to symbolize the revealed or manifested truth.¶

The reason that this is important is that the Gnosis of the New Testament books indicates, beyond reasonable doubt, that their writers understood the significance of the cube in question. Frederick Bligh Bond, after years of investigation, has made lists of the names, epithets and types of Christ which are multiples of 37. In one of the books written by him in conjunction with T.S. Lea, (their names are given in Lesson 1 of this Section) he gives more than a hundred examples. In another book he gives more than 500 Greek words and phrases, used in the New Testament, which correspond by Gematria to 2368, or 37 x 64, which is the number of ΙΗΣΟΥΣ ΧΡΙΣΤΟΣ, Jesus Christ. By the mere operation of the law of averages, something like three percent of all the words or phrases in the New Testament would be multiples of 37, but as Dr. Lea says, “when a large collection exhibits peculiarities for which the doctrine of Chance cannot wholly account, then other causes must be looked for and will probably be discovered.’¶

The root-word from which all these New Testament appellations of Jesus Christ are derived is Hebrew, the proper name H B L, Abel, which is derived from a verb spelt with the same letters, meaning, ‘to breathe, to wave.’ Thus the root-meaning is that of the rhythmic motion of the life-breath.¶

The same noun is used again and again in Ecclesiastes, being translated “vanity” in our English Bibles. The real meaning is “transientness,” or “transitoriness.” Thus when the Preacher says, “Vanity of vanities, all is vanity,” he is saying just what Omar puts thus:¶

‘The worldly hope men set their hearts upon
Turns ashes—or it prospers; and anon,
Like snow upon the desert’s dusty face,
Lighting a little hour or two—is gone.’

¶

These are not the accents of despair. They are the wise man’s recognition of the fact that all external conditions are fluid, that everything as Heracleitus said, “is becoming, so that a man cannot bathe twice in the same stream.” The idea is ominous and sorrowful for those who have believed in the permanence of things, in the importance of the world’s standards of success, in the reality of appearances.¶

They tell us, indeed, that we shall find no permanent happiness in the world of transient forms, in the phantasmagoria of the appearances of the One Reality. We must find THAT which is behind these appearances if we would have a treasure that nothing can destroy. But there is another aspect of this truth. When it is understood that every condition is impermanent, that the external world is plastic and fluidic, that the law of transition is at work in every detail of our environment, the first step has been taken on the path which leads finally to absolute and magical mastery. It is when the imagination is set free from the belief in the permanence of Name and Form that the ground is made ready for the mustard-seed of conviction which develops into the great tree of confident expectation. So long as you believe in the permanence of mountains, you cannot have faith to move them; but when you see that they are mere temporary waves upon the ocean of ETHER, perhaps your belief that they may be moved will take form as the invention of a new high explosive.¶

But there is an esoteric meaning to this word HBL, behind the dictionary definition. “H” or Heh is the Hebrew definite article ‘the.’ בל is a combination of letters which has several meanings. BL is the negative adverb, NOT, equivalent in meaning to LA, which you will remember as the metathesis of AL, strength. It refers to the truth that all things are transitory expressions of the STRENGTH אל which is NOT-anything. בל, again, is the Aramaic word for “heart”, and originally it meant, ‘courage, or strength.’ בל is also a contraction for BOL, meaning master or Lord. Thus הבל may be read as the (H) No-thing, the Lord, whose strength is the heart or core of all things בל. Again, בל is 32, so that הבל may be read Qabalistically as ‘The Thirty-two’ referring to the complete manifestation of the 32 paths of the Tree of Life.¶

Now, the fact that the key-number to all the dimensions of the polyhedra is 37, coupled with the fact that this is the key-number of hundreds of names and epithets of Jesus in the New Testament means that liberation from bondage to conditions is the outcome of the realization that all things are transitory, that whatever exists is the temporary self-expression of the power of THAT which is No-Thing. For we must remember always that the very name “Jesus” means “liberation,” that it is synonymous in significance with the Hindu word “mukti,” and that the whole purport of the teaching of the New Testament is completely misunderstood if we lose sight of the fact that it aims to develop in those who grasp and apply it a truly magical consciousness.¶

Priestcraft has done its best to conceal the truth. Yet at Christmas-time we read again the story of the visit of the Wise Men, guided by their knowledge of astrology to the birth-place of the Liberator. And not even the effrontery of priestcraft, despite all its false teaching that man is a worm of the dust, has been equal to the suppression of the words which definitely establish the magical quality of the Master’s teaching:¶

“And these signs shall follow them that believe: in my name shall they cast out devils; they shall speak with new tongues; they shall take up serpents, and if they drink any deadly thing, it shall in no wise hurt them; they shall lay hands on the sick, and they shall recover.”

¶

The belief, the conviction, which finally leads to such mighty works has its roots in the knowledge that all the conditions of human environment are expressions of an invisible, impalpable Reality, which can only be designated by negatives. The “miracles” of this One Thing which is No-Thing are partially interpreted by materialistic science. But our laboratory researchers cannot get at the heart of the phenomena they observe so patiently and accurately. What is missing? They do not see that all these transformations of electro-magnetic energy which they are so busy cataloguing and reducing to formulae are brought about by the mental activity of the One Power whose outward vesture is that same energy. They do not perceive that the whole cosmos is the IDEATION of the Life-Power.¶

The last few pages may seem to you to have been a long digression from the subject of the Lesson. What has all this to do with the polyhedra? Quite a good deal. For in the symbolism of the Ageless Wisdom one of these figures is a constantly recurring type of the perfection of the cosmic order. The cube furnished the pattern for the Holy of Holies in the Jewish Tabernacle and Temple, is the New Testament symbol of the New Jerusalem, and was the symbol of Hermes among the Greeks. We are now familiar with the fact that this figure represents יהוה by the sum of its points, lines and faces (as does also the Octahedron). In Hebrew tradition, moreover, it is said that Solomon’s Temple was built of cubical blocks, measuring nine units every way, just as does the cube which is the basis of construction for the Vault of Brother C. R. in the Rosicrucian allegory which describes that Vault as “a compendium of the universe.” Thus we know that one of the polyhedra, at least, is widely employed to symbolize the perfection of the manifestation of that cosmic order which, in greater detail, is summed up in the properties of all five regular solids.¶

Now, in a work of Rhabanus Maurus ‘de laudibus Sanctae Crucis’, there is a plate wherein the Nimbus of Jesus has the letters A. M. Ω., signifying the beginning, Middle and End. These letters, written in their primitive forms give us the outlines of the tetrahedron, the octahedron and the cube, thus:¶

¶

Thus, it is evident that behind the esoteric doctrines of Christianity there is hidden an esoteric doctrine, for when we find New Testament titles of the Liberator repeating over and over again the number which synthesizes the properties of the polyhedra, when we find an old Christian writer using symbols that represent FIRE (tetrahedron) as the ALPHA or Beginning, AIR (Spirit) as the mediating principle (Octahedron), and EARTH (cube) as the End, or manifestation, and when, too, we find the opening words of the Fourth Gospel repeating Platonic and Pythagorean philosophy, we must be blind if we do not see that the real Christianity is inseparable from the stream of the Ageless Wisdom which preceded it. It is a truly magical doctrine, aiming at magical results, and accomplishing them (as was said in the first of these Lessons) by the employment of magical words of power.¶

See now the agreement between the association of the letter ALPHA with the tetrahedron and FIRE, and the older Qabalistic doctrine you have learned from previous lessons. The Sepher Yetzirah says that FIRE corresponds to the Holy Letter, Shin, which is called “holy” because its number, 300, is the value of the words רוח אלהים, Ruach Elohim, the Life-Breath of the Gods. The Sepher Yetzirah assigns this Ruach also to Aleph, and Aleph is identical with ALPHA. Thus in Hebrew as in Christian symbolism the Beginning of manifestation is associated with FIRE, symbolized by the tetrahedron.¶

From the Table 4A, it is evident that the number 14 is the key-number of the tetrahedron, and to a Qabalist this immediately suggests the name דוד, David, or LOVE, and thus links up the ideas of Beginning and Creative FIRE with that of the attraction between complements which pervades all existence. But this is an aspect we may pass for the time. We shall pass, too, all the interesting deductions which might be drawn from the fact that 14 is the diameter number of the Creative World, as explained in Lesson 2 of this Section. What we wish now to emphasize is that 14 is a numerical representation of the movement of the cosmic Life-Breath.¶

Traditionally the Elohim אלהים are the seven spirits of God. Thus Ruach Elohim may be understood as “Life-Breath of the Seven.” (Incidentally, this fact as well as tradition, for the cosmic breath has seven aspects). Therefore, because breathing consists of two movements, inspiration and exhalation (with a pause between them, which is not a movement, but a cessation of motion), the idea of breathing is numerically represented by 2. Hence the motion of the sevenfold Cosmic Breath may be represented as 2 x 7 = 14.¶

The Cosmic Fire-breath is dual, Outbreathing or manifestation, and Inbreathing or return to the unmanifest. The Outbreathing involves (winds up) the Fire-Breath in the conditions of Name and Form. The Inbreathing involves (unfolds or unwinds) that same Breath from the complexities and limitations of name and form, and brings itself back to the Unmanifest.¶

All states of ETHER, AIR, WATER and EARTH are states of name and form embodying the FIRE of the Life-Breath. All states of ETHER, AIR, WATER and EARTH are states either of Involution or of Evolution, and at any given period, states of Involution exist simultaneously with states of Evolution. In other words, the Life-Breath is involving itself at one point at the very moment it is evolving itself at another.¶

The symbol of this is the turning wheel or ROTA, and in previous lessons you have learnt that R.O.T.A. in Hebrew letters adds up to 671, (another 14), which may be represented in our alphabet by A.O.M. (reckoning final M as 600). Of this A.O.M. the Hindu Pranava AUM is a variant, and so is the A.M.O. (mega), that has been studied in this lesson.¶

It will not escape you, either, that A.M.O. is the spelling of LOVE in Latin¹, so that the word which makes 671=14 in Hebrew utilizes the letters that spell LOVE in the later tongue of science, but has a numeral value which is the number of LOVE (DVD) in Hebrew, and the number also of the tetrahedron.¶

The name Elohim also points at the same thing. Its total numeration is 86 = 8 + 6 = 14. This 14 also reduces to 5, the number of the polyhedra, and of the elements and Tattvas. (Note, too, that 14 expresses numerally the idea of the manifestation of ORDER (4) through unity (1)). And each letter of ALHIM corresponds to one of the elements, thus:¶

• A: letter of Ruach, really ETHER (D)¶
• L: letter of Libra, therefore AIR (O)
• H: letter of Aries, therefore FIRE (T)
• I: letter of Virgo, therefore EARTH (C)
• M: letter of the element of WATER (I)

The order of the elements in this word is the order of the evolution of the Tattvas, except that the last two are reversed. FIRE is central, ETHER and AIR are above, and WATER and EARTH are below. The purport is evident.¶

Nor should we overlook the significance of the number 86, which is the value of Elohim. It represents the expression of RECIPROCATION, interchange, and the like (6) through the RHYTHM, periodicity, and alternation represented by 8. Thus, from another angle we arrive at the very same idea that the Life-Breath is a rhythmic pulsation of Evolution and Involution.¶

There is another detail about the polyhedra which we must take into consideration. Three have faces formed from equilateral triangles, one has faces formed from the square, and one has pentagonal faces. The triangle is the number 3, the square the number 4 and the pentagon the number 5, so that in the construction of the polyhedra we find once more the familiar numbers of the old Egyptian triangle of Osiris (3), Isis (4) and Horus (5). The sum of the squares on the three sides of this triangle is 50 (3² + 4² + 5²) and 50 is the number of the faces of the polyhedra and also the number of their points or vertices. Thus we find the basic numbers of the triangle in the construction of these Platonic solids. Furthermore, the angle formed by the lines of Osiris and Isis is the angle of 90°, and this angle’s numeral value is represented by the total number of edges in the polyhedra, which is also 90.¶

The polyhedra with triangular faces represent AIR, FIRE and WATER, and they correspond to Osiris, or 3. That which represents EARTH corresponds to ISIS, or 4. That which typifies ETHER corresponds to Horus, or 5. Osiris is a sun-god (Fire), a Nile-god (Water), and, as careful examination of Egyptian myth will show, an atmosphere god also (Air). Isis typifies Mother Earth. Horus, son of Osiris and Isis, represents the Ruach, or ETHER, which is the Quintessence, or fifth essence, of the alchemists.¶

We hardly expect you to see the force of some of these details at first reading. The reason that this lesson on the polyhedra has been introduced at this point is to show that there is a thread of connection between the mystery symbols of Egypt, India, the Neo-Platonists and Christianity. In these days when the land is filled with the disputes of jarring sects, the fact seems to be forgotten that Christianity is essentially a magical religion, that its aims are precisely the same as those of the older faiths which preceded it.¶

One of our aims in the B.O.T.A. is to revive this fundamental aspect of Christianity. And although all this explanation of numbers and geometry may seem to be very complex (and to many readers, perhaps, more or less far-fetched) we know from experience that the contemplation of these mathematical truths will lead the mind at last to a deeper perception of the hidden symmetries of the cosmic plan. The real meaning of what lies behind all this strange symbolism is simple enough. Everything that exists is an appearance of a single reality. All the appearances are transitory. None has permanence. For the knower of Self, therefore, no obstacle is insuperable, no condition unalterable, no limitation so fixed that it cannot be overcome.¶

But the mere assertion of this truth is not enough. The Emerald Table advises us to separate the subtle from the gross, the fixed from the volatile with great ingenuity. That is, we must devise as many means as we can to help us in the work of distinguishing the Permanent or Real from the Impermanent or Apparent.¶

The study of the mathematical properties and correspondences of the polyhedra is one such application of ingenuity. Many others are required in order to overcome the hypnotism of those volatile, ephemeral conditions of Name and Form which seem to us so fixed and unyielding. It is not that these manifold symbols have any magical power of their own. That is not why you are asked to become familiar with their esoteric meaning. The value of this kind of study is that it exercises a power of the mind which is not properly developed by our modern methods of schooling. From the perception of the symbolic correspondences between the letters of the alphabet of nature the mind is led to the realization of the unity which is veiled behind the multiplicity of appearances.¶

This is the important thing to grasp, and this is the really valuable result of the study of comparative symbology. At first one seems to be lost in a maze of strange signs and emblems, but finally comes the realization which Eckhartshausen expresses in The Cloud Upon the Sanctuary, when he writes:¶

‘As infinity in numbers loses itself in the unit which is their basis, and as the innumerable rays of a circle are united in a single centre, so it is also with the Mysteries; their hieroglyphics and infinitude of emblems have the object of exemplifying but one single truth. He who knows this has found the key to understand everything, and all at once… He who has discovered this way possesses everything therein; all wisdom in one book alone, all strength in one force, every beauty in a single object, all riches in one treasure only, every happiness in one perfect felicity.’

¶

Footnotes

1. Ed. note: AMO = “I love”, “Love” = AMOR (noun) or AME (imperative). ↩