THE DODECAHEDRON
From man or angel the great Architect
Did wisely to conceal and not divulge
His secrets to be scann’d by them who ought
Rather admire; or, if they list not to try
Conjecture, he his fabric of the heavens
Hath left to their disputes, perhaps to move
His laughter at their quaint opinions wide
Hereafter; when they come to model heaven
And calculate the stars, how they will wield
The mighty frame; how build, unbuild, contrive
To save appearances; how gird the sphere
With centric and eccentric scribbled o’er,
Cycle and epicycle, orb in orb.John Milton, Paradise Lost
The ancient Greeks honoured the twelve signs of the zodiac in the sacred host of the Dodecatheoi, the twelve gods whose temples were placed in the twelve equally divided sections which radiated out from the centre of the city of Athens. Their popular worship shrouded the secret correspondences of sets of twelves observed in a multitude of natural and cultural phenomena. There were twelve hours of the day and night, twelve months in the year, twelve units in various measurements and weights, twelve labours, columns of sacred temples, and the twelve days between the winter solstice and the first day of the new year which marked a return to chaos and the subsequent rebirth of order. The many derivatives of the basic term dodecatheoi in the Greek suggest a fundamental twelve-part division discernible in many facets of human life. The number twelve itself was seen as symbolic of cosmic order, archetypally represented for much of the ancient world by the twelve points through which the zodiac revolves.
Such correspondences were based upon arcane philosophical tenets as well as upon actual observations of natural cycles. Plato spoke of the twelve signs (gods or theoi) of the zodiac as modes of manifestation of the single creative force which governs the universe, calling them the Gates of Heaven. The zodiac itself was associated with the Demiurge and the primordial Eros or the will to create. This is rather similar to the theme found in many cultures of the twelve fruits borne on the Tree of Life or the twelve tribal progenitors. Metaphysically, the twelve divisions through which the sun seems to orbit have been seen for millennia as corresponding to the twelve degrees or stages in the continuous action of the active principle upon the passive. This cosmic creation, within the division of twelve, involves vital combinations of numbers such as twice five plus two and three times four. It also involves depth and breadth of action on three and more dimensions, yielding the fifth and final of Plato’s regular solids, the dodecahedron. Just as the symbolism of each sign in the zodiac springs from the number it bears in the series, so the twelve pentagonal faces of the dodecahedron express the point, the line, the plane and, in their totality, all the geometric solids. Thus the dodecahedron, which Plato called the supreme spiritual metaphor for the One and the many, is a paradigmatic model to serve as the archetypal framework for every possible manifestation.
The Highest and most Good Creator in the creations of this mobile world and the arrangement of the heavens had his eye on those five regular bodies, which have been most celebrated from the time of Pythagoras and Plato right down to our own day, and that to this nature he accommodated the number of heavenly spheres, their proportions, and the system of their motions.
Johann Kepler
Confined by the theocentric language of his time, the bold statement of Kepler showed a vision which extended far beyond the truncated notions associated with the unique creation of an anthropomorphic god that persisted in the seventeenth century. The Platonic concept that the manifest cosmos was gestated through Divine Ideation is clearly traceable in Kepler, as it is now in the few daring contemporary physicists like Fritjof Capra, who invokes “metabolic mentation” from cells to the higher levels of conscious intelligence, culminating in the Cosmic Mind. He suggests that “both life and mind are manifestations of the same set of systemic properties”, thus arriving, despite the limitations of the language of systems theory, at the threshold of Pythagorean-Platonic cosmology. In conveying the majestic grandeur of cosmic manifestation, the lofty prose of The Secret Doctrine enables us to explore the subtle correspondences and textures of meaning lying in and around words capable of intimating that which lies beyond and also precedes the visible cosmos. H. P. Blavatsky declared that the visible universe “was built on the model of the first DIVINE IDEA”, which existed from eternity in a latent state. Reiterating the teachings of the initiated Plato, she taught that, just as the animating soul of the invisible universe is the Central Spiritual Sun, so also the sun is the soul of the visible which is built by the first-begotten of the One, who constructed it “on the geometrical figure of the dodecahedron”. This first-born is the aggregate of the Host of Builders or first constructive forces, the Tetragrammaton at the head of the seven lower Sephiroth and the triad at the top of the Pythagorean decad.
That there are distinct orders of Angels, assuredly I believe; but what they are, I cannot tell. Dicant qui possunt; si tamen probare possum quod dicunt, saies that Father. Let them tell you that can, so they be able to prove, that they tell you true. They are Creatures, that have not so much of a Body as flesh is, as froth is, as a vapour is, as a sigh is, and yet with a touch they shall moulder a rock into lesse Atomes, then the sand that it stands upon; and a milstone in smaller flower, then it grinds.
John Donne
In the magical unfolding of cosmogenesis a vast hierarchy of spirits is involved, led by the Divine Fire of Daiviprakriti given direction and force by the mysterious magical potency of Fohat. From this primordial motion the Fire and Aether, which constitute the Atma-Buddhi prototype of incarnating monads, come into being and give life to the Triads (the Atma-Buddhi-Manas prototypes) who work through the sacred matrix of human consciousness (the Rupa Angels), in which lies the vital germ that will fall into incarnation. From this springs the fifth group of Dhyanis connected with the microcosm expressed in the pentagon and the five-pointed figure of man. In arcane philosophy the hierarchy of creative powers is divided into seven, whose components four and three, when multiplied, equal twelve: the four bodies and three faculties of Brahma (the four elements and three gunas), thus yielding the twelve orders of the zodiac expressed three-dimensionally in the dodecahedron.
Each descending level of this hierarchy is marked by increased differentiation which unfolds according to law. At the beginning of a period of activity this law, resting in a latent state of concealed wisdom (Chitshakti), awakens and begins to act in the pre-cosmic Mind. Fohat then commences to form the universe “in accordance with the conceptions generated in the universal mind out of the differentiated principle of Cosmic matter”. Cosmic ideation continues ceaselessly as long as there exists a manifest world. If it ceased, even for a fraction of a moment in time, the process of differentiation would stop and the night of pralaya begin. Owing to a deep and lasting comprehension of this fact, especially as it is expressed through sound vibrations, the tradition persists that to utter the sacred Word is to join one’s voice with a vibratory current that can be traced back to the very genesis of Being. In the mundane language of systems theory, this idea can be traced in terms of interdependent, living organisms which are always at work, renewing themselves within their stable patterns of organization and dying only when the continuous exchange of energy and matter with their environment ceases.
The latent design exists in the one unborn eternal atom, the centre which exists everywhere and nowhere.
T. Subba Row
Conceptions of latency and of primordial beginnings evoke questions about whether the universe is infinite or bounded in time. Is it closed or open? Is it evolving or in a steady state of equilibrium? Does the creative and destructive dance of Shiva Nataraj continue endlessly or does it too have periods of rest? Is it contained within the twelve faces of the dodecahedron or is it beginningless and without limit or order? Contemporary cosmological theories engaging the minds of astrophysicists tend to swing between the notion of the universe as a steady state and the so-called Big Bang theory. Proponents of the steady state theory envision the universe as endlessly expanding, evolving new radiation in compensation for that lost through expansion, whilst those focussed upon beginnings assume that an exceedingly simple matter exploded out of a super-dense kernel. Followers of the latter theory believe that this matter was initially composed of photons, protons, electrons and neutrons, and that after only seconds the universe cooled enough to permit their aggregation into larger units from deuterons to heavier elements. In the early aeons of its expansion, light-energy predominated, subjugating, so to speak, the expanding matter in a sort of ‘reign of radiation’. When the temperature dropped (as a result of expansion) below the threshold of thermonuclear reactions producing photons, the ‘density’ of radiant matter decreased more rapidly than that of dark matter, until the density of the latter exceeded that of the former, ushering in the ‘reign of matter’. According to this model, during the predominance of light-energy, matter spread uniformly as a ‘thin’ gas until, with its increased density, it broke up into gas balls which slowly drifted apart to become eventually the galaxies of our universe.
The problem with this model lies in its slavish acceptance of a dualistic reality wherein the term ‘matter’ is muddled and pushed around to accommodate everything that is acted upon by something. In addressing itself to primeval beginnings, it places the same mechanically conceived muddle at the threshold of the infinite. The steady state theory has the merit of leaving the question of causation alone. As a few modern thinkers (often borrowing freely from the ideas inherent in Taoist, Buddhist and Hindu metaphysics) have pointed out, mass is not matter (substance) necessarily, but a form of energy. What we call objects are really patterns in a unified cosmic process. Things are events or happenings and only secondarily ‘things’. The teaching of Nagarjuna that “things derive their being and nature by mutual dependence and are nothing in themselves” is echoed by the atomic physicist Henry Stapp when he asserts that “an elementary particle is not an independently existing unanalyzable entity. It is, in essence, a set of relationships that reach outward to other things.”
The energy patterns of the subatomic world build up stable atomic and molecular structures whose aggregation presents the ‘solid’ appearance we call ‘matter’. At the macrocosmic level this translates usefully into the idea of substance, but at the atomic level the idea loses its meaning. The dynamic relationships of the sub-organic world describe patterns (rather than substance) like a dance of energy, and the answer to the question whether the creation and destruction in the cosmic dance endure in a steady state is contingent upon the relationship between the existence of patterns in the manifest cosmos and the pre-cosmic Mind. Considering these ideas from the standpoint of relative cycles within cycles, it becomes apparent that the steady state and Big Bang theories are alike partially correct and inadequate. Hampered in their expression by mechanistic language and the intellectual polarization of spirit and matter that has crippled the thinking of philosophers and scientists for the past two thousand years, they do, nonetheless, as theories manage to touch the garment hem of a greater cosmological truth.
The interesting idea here involves the notion of relationship within the whole manifested as a pattern, a noumenal basis for seeing form in terms of archetypal designs rather than simply aggregations of matter. In considering the process of the coming into being of form or morphogenesis, modern physics is coming to realize that DNA alone does not suffice as an explanation. This realization led, as early as the 1930s, to a consideration of morphogenetic fields which are spatial dispositions rather than material structures. In them is preserved a design body that is causal and guides the development of form, remaining associated with it and restoring it if necessary. Some investigators point to the regenerative capability of certain plants and animals as indicating the presence of such a purposeful form-fulfilling potential. Such fields are physical in the sense that physics can explain them but they are not material structures. They cannot normally be seen or touched, but any member of a species of any of the kingdoms of life taps into such a field and is thus affected (even prior to birth) by developments and adjustments experienced by that species throughout its history. The DNA code is thus necessary merely for tuning to the right frequency and participating in patterns contained timelessly in the right field.
Such a reaffirmation of arcane metaphysics opens doors through which the fresh air of archetypal ideation can flow and begin to sweep away the creaking structure of Cartesian thought, which itself has become an imprisoning design in the collective ‘morphogenetic’ field of the human mind. It has been suggested that hierarchies of morphogenetic fields work upon each other, the more archetypal ordering and designing the lesser: some responsible for the forms of chemical systems, others for organisms or crystals, etc. New compounds, lacking a morphogenetic field, are not strongly influenced (for example in the case of a crystal) to assume a particular form. But once they are crystallized a first time, each subsequent crystallization becomes more automatic. Precisely in this way learned behaviour amongst members of higher species spreads without any physical communication. It would seem to follow that the more generalized and universal the form, the greater its ability to tap into the higher archetypal morphogenetic fields and express their designs through form, behaviour and even thought. Here, the theosophical Teachings concerning the levels of the astral light related to the sthula, linga and karana shariras as well as Akasha are needed in order to carry the discussion further. The main point in the concept of a morphogenetic field is that it indicates a continuous medium in which causation can work through archetypal forms.
Another central fact about the universe, revealing something fundamental concerning the geometrical form upon which it was constructed, is that it maintains an isotropic state. There is an isotropic uniformity with respect to the direction of arrival of radiant energy, and cosmic expansion as a whole takes place isotropically. No matter where a galaxy is found, its recessional velocity is related to distance by the same proportionality. This means that the universe is remarkably symmetrical, and it would seem from these observations that we happen to be at the very centre of it. But this is deceptive, as the same would be true if we were observing and measuring from the standpoint of any other galaxy. In such an expansion every point is its own centre and there is no preferred centre. One could say that our galaxy is indeed at the centre of the universe – but so is every other galaxy.
The creation of the world is the combined work of necessity and mind. Mind, the ruling power, persuaded necessity to bring the greater part of created things to perfection, and thus after this manner in the beginning, through necessity made subject to reason, this universe was created.
Plato, Timaeus
In the orderly development of forms, a criterion of spatial and structural economy involving the least expenditure of energy or movement to accomplish ends is always observed. If the universe is symmetrically constructed and its faces are indeed pentagonal, then they will be regular pentagons and the figure of the universe will necessarily be a dodecahedron. Put differently, the dodecahedron is the necessary representative or expansion of the pentagon in three-dimensional space. As a projection of the pentagon, Plato considered the dodecahedron to be the culmination of the hierarchy of five solids, alluding to a growth or development associated with the four elements plus Aether. Thus the dodecahedron contains all the other elements, framing, as Timaeus described, “one visible animal comprehending within itself all other animals” while remaining more fiery than anything else. The ancient Kabbalists put it in terms of “the Dodecahedron [which] lies concealed in the perfect Cube”, suggesting that the earthy body of the world contains within itself the archetypal cosmic design which reveals itself, however, only to the eyes of one who understands the mysterious process whereby the One becomes the many through divine geometry.
In the development of solid forms, the icosahedron precedes the dodecahedron and symbolizes the realm of the astral light. Thus, despite its fiery triangular faces, it is a form associated with water and carries within it the seed of the design yet to be born. In terms of the hierarchy of spirits, the icosahedron would correspond with the Rupa Angels who follow the Triads and represent the matrix of human consciousness, in which lies the germ that will fall into incarnation. Thus the Atma–Buddhi–Manas prototype (of the Triads) passes into that subtle and watery pre-cosmic realm of anticipated form before manifesting as the fifth group of Dhyanis, the Pentagons or Kumaras who sacrifice themselves in the ‘fall’ of spirit into a gathering density of matter. In the physicist’s description of the shift from the ‘reign of light’ to the ‘reign of matter’, one can recognize an echo of this conversion. One can also illustrate it by describing a sphere around the icosahedron, from the centre of which perpendiculars are drawn through its faces to meet the surface of the sphere. If the points of these intersections are joined together, the pentagonal faces of the dodecahedron will be formed. Thus, points become lines and lines define the perimeters of the next level of geometrical complexity, leading ultimately once again back to the sphere, the circle and the point.
The pentagon is the shape of supreme sacrifice. This is symbolized by the fact that it is the only face of a regular solid having angles wider than a right angle. Its outspread arms at each corner seem to illustrate an open acceptance and willingness to accommodate. Its five sides answer to the Sanskrit ma-karam, the name of the twice five or tenth sign of the zodiac and an anagram for the sons of Rudra-Shiva, the Kumaras. The number five itself signifies this willingness to uplift matter by bringing the fiery triad of spirit to bear upon the duad of the Mother substance in the embodiment of the Manasic principle. As a figure, five is comprised of the two Greek accents over vowels which indicate whether they are aspirated or not. The higher, aspirated mark signifies the “strong spirit” of God, whereas the lower, unaspirated mark is that of the secondary “Spirit of Love” reflected in the world. Together these describe the five mystic vowels uttered by Brahma at creation and are expressed in the spiritual and terrestrial human compound.
Following the criterion of numerical and structural economy inherent in intelligent Nature, the logical elegance and beauty of the dodecahedron presents itself as a perfect expression of the twelve transformations of spirit into matter that are said to have taken place during the four great ages of the first Maha Yuga. Thus the three of spiritual fire and the four of the earth gave depth and breadth to that which is represented in the ten points of the Pythagorean decad. One can imagine the perfect economy of growth involved in this in terms of sphere-points describing the Platonic solids ultimately contained within the dodecahedron. Four equal spheres are the greatest number that can be in simultaneous contact. They represent the first regular pattern, which is the tetrahedron. Six equal spheres form the next regular pattern, with each sphere touching four neighbours in the cube, which is the ‘dual’ of the octahedron. Twelve equal spheres may surround and touch, not one another, but a nucleus of equal size. When this occurs, the form contracts so that each sphere touches its five neighbours, completing a threefold transformation referred to as the “twelve degrees of freedom”. The linear and turning movements required in this process thereby draw together the tetrahedron (fire), the octahedron (air), the icosahedron (water) and the cube (earth) into the dodecahedron containing all, plus the Aether of the heavens.
This numerical and structural economy is further demonstrated by the golden ratio which presents itself diagonally on each of the pentagonal faces of this cosmic form. Within it the centroids of the twelve faces are divisible into three coplanar groups of four, which quadrads lie at the corners of three mutually perpendicular and symmetrically placed golden rectangles, their one common point being the centroid of the dodecahedron itself. This perfect structural economy results from a gnomic growth, from inside outward, as opposed to an agglutinative growth involving a simple addition from the outside of identical elements. It is a more basic, subtle, internal growth which begins on the unseen planes of the Cosmic Mind and slowly takes on the logically unfolded expression of fully manifested life. It is an ideational growth involving archetypal relationships that yield patterns capable of echoing the One in the many. The beauty of the dodecahedron swells in the mind with the growing understanding of this idea. It combines so perfectly the wholeness and oneness of the sphere (which is its constant reference point) with the great sacrificial presence of the Triads in the quaternary (represented in each of its pentagonal faces) that its form could easily become the focus of one’s deepest reverence and gratitude.
In the dodecahedron one can see the outline of the unmanifested ideal, the manifesting cosmic ideal fathered by sacrifice, and the human microcosm capable of centering itself and focussing – like one of the twelve disciples – upon the central nucleus which isotropically informs the whole. Thus each human soul can fulfil the potential symbolized by the pentagon and become a Gate of Heaven through whose five-limbed vehicle the undimmed Light of the fiery Triads streams. Each can do this by taking the perspective of the whole made up of galactic centres everywhere, realizing that each true disciple of Krishna experiences himself or herself as one with the Lord at the centre of the universe. There can be no exclusivist element in this experience. Every pentagonal face worships and has its being in that centre, and each must come to know that in this centre lies its indivisible unity with all the other faces. Only thus is the macrocosm made manifest in the microcosm and the disciple made worthy of entering the perfect cosmic symmetry reflected in the twelve-gated city of the Lord.
The cosmic dance is fiery,
Yet it moves within a sphere;
Pulsating with the drum of time
Around the centre there.
The radiant flames encircle
The moon on Shiva's brow,
And the mixtured glow intones
The sacrificial vow.
"I, Shiv, bring forth my sons,
A youthful virgin race,
That all creatures yet to be
May come to see their face."
And so saying, the Fiery Lord
From point and sphere produced
The Triads and the Pentagons,
Their forms with light infused.
Thus did the Cosmic Plan unfold
In twelve-fold symmetry,
And thus did man obtain the form
To match Divinity.
Published by permission of theosophytrust.org.