1. Cube and Triangle

The most simple symbol for the septenary in man is the division by Sinnett into the lower quaternary represented by a square and the higher triad represented by the triangle,(alchemical symbol )as follows:

7. Atma

6. Buddhi

5. Manas

4. Ego (Kama Rupa)

3. Astral (Linga Sartha)

2. Etheric (Prana)

1. Physical Body

Again, we see our factors of the three and the four, now this time as the number seven as a compound of the three and four. The reason for this correspondence is because the Law of Seven is the factor element in nature and the occultists recognizing this principle made it also the factor element in every ancient religion and culture, including the Hindu, Chaldean, Babylonian, Persian, Egyptian, Hebrew, and Pythagorean.

Thus, the triangle as three represents the triple aspect of Deity, the unmanifested cosmos, and in man, the future evolution of the three higher aspects of spirit. The square as four, represents the manifested world of matter and in man, the product of earth evolution of the ancient four elements of fire, air, water and earth as well as the earth's evolution of the mineral, plant, animal and man kingdoms of nature. Every man is a quaternary representing the earth elements and earth evolution of the four kingdoms. Man number five, either as a result of his own efforts or the future evolution of mankind as a whole, is represented with the triangle resting congruent on the top of the square as this is why in our present fifth (Ayran) root race, man is called a pentagon or five pointed star. This represents the goal of our present evolutionary epoch as the incorporation of the fifth principle (Manas) into the lower man. In the sixth epoch, the sixth root race will conquer the sixth principle and after the evolution the seventh root race, mankind having the higher triad inside him will be symbolized as, with the triangle wholly inside the square.


The most ancient symbol for the septenary in man is the Tau cross or T. It was formed from the figure of 7 affixed to the Greek letter (Gamma) as a double glyph. The letter gamma is the symbol of earth life or Gaia and the figure 7 is the symbol of the divine life taught by Pythagoras as the perfect divine number known as Telesphoros. Together as a double glyph, they represent earth life and divine life linked together eternally. In addition, the horizontal line represents the Female or matter and the vertical line the Male or spirit.

The Egyptians added to the prefect Tau a mundane circle (above) as an attribute of Isis which has come to be known as Ankh (life) or ansated cross as their symbol of eternal

life. The Madam H.P.B. relates that the Ankh cross symbol is another form of Venus as Isis as . It represented esoterically that mid-point in the third root race when the separation of the sexes occurred, when human procreation descended from androgynous Adam and separated into man and woman and procreation of the species through sexual union. Thus, the first "fall" is mankind and all animal life dropping out of the divine spiritual circle and fallen into male and female generation. Symbolically, the divine becomes , then

and finally .

However, the Ankh cross of the Egyptians has a much deeper symbolic meaning. We saw before that the forth Sephiroth HESED represented the Sephiroth of construction as the six dimensions of matter creating the manifested cosmos. It was symbolized by a six-sided cube with the Hebraic script valve of 72. Also, the lower quaternary of man, the first four principles, is represented as square or three dimensional as a cube. This cube of earth-man unfolded represents a very esoteric septenary symbol as union of the three and four. J. Ralston Skinner in The Source of Measures states,

"If it is desired to display the process of the establishment of the co-ordinating unit of measure spoken of, by way of symbol, it would be by the figure of the cube unfolded, in connection with the circle, whose measure is taken off onto the edges of the cube. The cube unfolded becomes, in superficial display, a cross proper, or of the tau form, and the attachment of the circle to this last gives the ansated cross of the Egyptians, with its obvious meaning of the origin of measures."

"It is very observable that, while there are but 6 faces to a cube, the representation of the cross as the cube unfolded, as to the cross-bars, displays one face of the cube as common to two bars, counted as belonging to either; then, while the faces originally represented are but, the use of the two bars counts the square as 4 for the upright and 3 for the cross-bar, making 7 in all. Here we have the famous 4 and 3 and 7."

Thus, on one level and with one key, Skinner shows that the cube unfolded represents the septenary principle in man, the three and four united in a symbol of seven. The Egyptians made the Ankh cross their symbol of man, generation and life and buried their dead with it. But how old is this symbol? Skinner further states that the Aku-aku Cyclopean statues on Easter Isle in the mid-Pacific bear this symbol carved in stone. These islands are the remanent tops of mountain ranges on the ancient submerged continent of Lemuria, the home of the third root race. Madame H.P.B. was right when she said the ansated cross was a third root race symbol, millions of years old.

On another level, using the Hebraic script numbers as a key, Skinner discovered another occult correspondence with the cube unfolded. In Hebrew, one of the word forms for man is ATSH and adding the value of the letters (300 +l0 +l) is 311 or reading from right to left in Hebrew is 113. The Hebrew word for lunar year or SHANAH (50 +5 +300) or 355. As shown in Plat No. , the cube unfolded is an astronomical symbol of the macrocosm and with the circle attached to the tau cross as the head of a man "circling the square", it is a symbol of the microcosm or man. The ratio of 113 to 355 is an ancient value for the ratio of the diameter to the circle or (3.1415).

Thus, the cube unfolded is also an ancient symbol of the primary mathematical relationship of and as Skinner says, an origin of measures reflected in number form in the cross. This Hebrew word for man represented as 113 was probably the "primordial word" of the Hebrew script.

By welding man to the tau cross we also have the concept of the crucifixion in the microcosm and "man crucified in space" in the macrocosm. Skinner says,

"In fact, the Old Testament is rabbinically and kabbalistically familiar with the expression of crucifying a man, or men, before the Lord and the sun. In symbol, the nails of the cross have the shape of the heads thereof a solid pyramid, and a tapering square obeliscal shaft, or phallic emblem, for the nail. Taking the position of the three nails in the man's extremities, and on the cross they form or mark a triangle in shape, one nail being at each corner of the triangle. The wounds, or stigmata, in the extremities are necessarily four, designative of the square; there have been two used as one, or rather one used as tow, in the connection of the three nails with the four extremities. The three nails with the three wounds are in number 6, which denotes the 6 faces of the cube unfolded, on which the man is placed; and this in turn points to the circular measure transferred onto the edges of the cube. The one wound of the feet separates into two when the feet are separated, making three together for all, and four when separated, or 7 in all-another and most holy feminine base number.

In the macrocosm, Plato adopted the decussate cross in space (the X) as the second god who impressed himself on the universe in the form of the cross and astronomically this is represented in the Southern Cross Constellation.

In the microcosm, the fact of Christ crucified on the cross is an ancient idea acted out in the mysteries of initiation for thousands of years prior to the birth of Christ.

The first part of the mystery lay in the coffin. R. Steiner described the candidate for admission being placed in a coffin for three days and nights, during which time his atral body and ego traveled with his master on the astral plane. Upon being "raised" from the coffin, the candidate, after experiencing the spirit world, becomes a fully initiated adept. The druids used subterranean caves or temple crypts in lieu of the coffin. The coffin ritual is still preserved in the third degree of a master mason which still occurs thousands of times a year to this day. Even in black magic this ritual is preserved where the Haitian voo-doo priest drugs his candidate and places him in a coffin for three days, after which he is raised as a zombie slave. Whether placed in an underground crypt or coffin, the symbolism is in all ancient mysteries the same. The three days in the coffin for the candidate is correspondent to the three days Christ spent in the crypt after his crucifixion, both the candidate and Christ are raised or resurrected to a new spiritual life.

The second part of the mystery lies in the crucifixion on the cross as the tree of life. In the Egyptian mysteries, the initiation took place in the kings chamber of the Great Pyramid of Cheops. This room is built entirely of granite, well finished and finely jointed. Positional close to the west wall is a large rectangular granite saneophagus so impressive that the original British surveyors Vyse and Penning remarked (1837) that, "the kings chambers is the principle apartment, and the security of the sarcophagus within it the great object for which the Great Pyramid was erected." So true, the other pyramids were for burying the dead, the Great Pyramid was for initiation of the living and the coming mystery of Golgatha.

The candidate who had passed all his former trials was attached (not nailed) to a wooden cross in the tau shape and afterwards placed in the sarcophagus for the three days during which time his spiritual ego traveled the spirit land. During the night of the approaching third day, the candidate in the sarcophagus was carried to a gallery where at dawn, he was raised to the glory of the rising sun (Osiris), addressing the sun spirit with a newborn spiritual life.

The mystery of Christ, as the Solar logos, crucified on the cross and afterwards his resurrection from three days in the crypt now becomes clear. We know that Plato was initiated in the kings chamber and he is the source of the astronomical cross in space. Likewise, we know Moses and his master JETHRO were Egyptian initiates and they carried this symbolism into the Hebrew Messianic cycle so that the passion and death of Christ was "according to the scriptures" or more accurately " according to the Egyptian mysteries".

Thus, the mystery of the crucifixion dates back to the very establishment of the ancient mysteries where in the candidate becomes reborn after his crucifixion on the tree of life or tau cross. And, so Skinner shows, this mystery is written into the mathematical and geometric symbols of the cube unfolded.


The cube is everywhere the symbol for earth and matter. In the Qabbalah we saw the fourth sephiroth Hesed represent the six dimensions of matter as a six-sided cube. In the Timaeus, Plato described the cube as the corpuscular element of earth and matter. However, there is one fundamental problem with the cube as representative of the building block of the manifested universe, Composed of six square faces, it is inherently unstable.

As B. Fuller says, "Any polygon with more than three sides is unstable. Only the triangle is inherently stable. Any polyhedron bounded by polygonal sides with more than three sides is unstable. Only polyhedra bounded by triangular faces are inherently stable." This can be shown in Plat no. 10 . Therefore, the triangular face of the tetrahedron is more stable than the square face of a cube.

From the Law of Three, we saw that the tetrahedron is the first subdivision of the universe and also the first primary structure. This is not inconsistent with the cube as primary elements of earth-matter, since the cube can be constructed of tetrahedra.

All polyhedra may be subdivided into comparable tetrahedra. Every cube contains two tetrahedra as shown here and here without the cube edges here . This is accomplished by subscribing on every square fact a diagonal which becomes one of the six edges on the tetrahedra. A cube stabilized by one tetrahedra has each of six square faces inscribed by a diagonal. A cube stabilized by two tetrahedra, has each of six square faces inscribed by two diagonals. Obviously, the latter cube with two inscribed tetrahedra is the most stable.

B. Fuller called the alternate pair of tetrahedra, "symmetrically juxtaposed positive and negative " whose centers of volume are congruent with one another and congruent with the center volume of the cube. Thus, every cube can be stabilized with a positive set of six tetra diagonals and a negative set of six tetra diagonals. It is possible to stack cubes in one column containing only positive tetra and a separate column containing only negative tetra.

In conclusion, we have solved the problem of the unstable cube as representative of earth=matter by inserting into the cube either a positive tetra, a negative tetra or both. Thus, our cube unfolded should be re-drawn to show the alternating pair of tetrahedrons inside it as shown above .

Considering the cube as the platonic element of earth-matter with two tetra inside it, some interesting correspondences occur.


First, J.R. Skinner's model of the cube unfolded needs to be reworked. His mathematical and geometrical key for the symbolic coordinating unit of measure discussed on the cube unfolded is based upon, "the figure of the cube unfolded, in connection with the CIRCLE, WHOSE MEASURE IS TAKEN OFF ONTO THE EDGES OF THE CUBE".

His mistake is using the "edge length" of a cube as the primary unit of measure as opposed to using the "diagonal length" of the cube as the primary unit.

From the Law of Three, we observed that the tetrahedron is the primary structural unit of cosmos, and not the cube. Therefore, the edge length of the tetrahedron should also be the primary unit of measure for a coordinating geometry of cosmos. Otherwise, one must always use a conversion factor representing the difference between the edge length of the cube edge as the edge length of the tetra. This is a problem of all modern science which uses the three-dimensional cube as primary unit of measure. For example, volume should be measured not as cubic volume but as tetra volume which is three times more efficient. Also, geometry should not use the 90 degree coordination of the cube but should use the 60 degree coordination of the tetra.

The edge length of the tetra is contained in the cube as the length of the cube face diagonal. Therefore, in the Skinner model of the cube unfolded, the circle or sphere as head of man, should be measured off the diagonal length of the cube and not the edge length of the cube.

Using this new key, synergetic geometry measurement of unity commences with the tetra-edge as prime vector. Unity is not taken from the cube edge, but from one of the two tetra-edge diagonals that structure the cube. MENSURAL UNITY shows the cube structured by the tetra whose unit vector diameter value is two, an the cube edge lengths value is the square root of two, a difference of two - 1.4142 = 0.5858.

For example, the conventional XYZ 90 degrees coordinate volume for a sphere of radius one is 4.1888. To convert that cube edge length value to a sphere whose diameter is equal to the diagonal or tetra-edge length we must multiply by the above mentioned conversion factor of 1.0606. The result for a sphere volume with at tetra-edge length is 4.4429, a difference of 0.2541 primary units of measure.

Second, lets call the Skinner cube now containing two center congruent tetrahedron the " Synergetic Cube Unfolded ."

Reflecting back on the Law of Three and the upper holy triad of the Quabbalah, we saw how the cosmos was divided into the manifest and un-manifest worlds. The unmanifest world showed God as trinity in unity in all ancient wisdom-religion systems. God as trinity also related to the Law of Three as representative of the three forces of active - passive - neutralizing (from Madame HPB and Gurdjieff) and positive - negative - resulting (from B. Fuller).

Taking the volume of the tetra as unity as one, the volume of a tetra-edge length cube is three. The correspondence follows. Contained within the manifest world as cube is the unmanifest world of Deity as three in one unity. Contained with the synergetic cube unfolded, is a positive tetra representing the positive or active face in nature and a negative tetra representing the negative or passive force in nature. A cube stabilized by two tetra is not full in volume, since the cube volume is three and two tetra volume is two. All that remains as space volume in the stabilized cube is represented by the third force as neutralizing - resulting and the holy ghost. The active - passive forces act in space and the resultant of their actions is reflected in form in the surrounding one third remaining volume of the cube.

Thus, the synergetic cube contains within itself the Law of Three in several forms. First, a cube with no tetra enclosed. Second, a cube with one positive tetra, which can be separately stacked. Third, a cube with one negative tetra, which also can be stacked. Fourth, a cube with both positive and negative tetra enclosed within the space of the third force. Thus, a total of four variations in the manifest world.

This has great possibilities as a building block or element in the manifest world the cube can exist independently and be stacked as positively charged, or negatively charged or as a balanced charge of neutral. We see this in the atomic world as independently charged bodies of electrons, protons, and positrons empty cubes as neutrinos and neutrons and atoms. On the sub-atomic scale our own script could be as follows:

Empty Cube--------------- Neutrino--------(0)

Positive Cube------------- Positron--------(+)

Negative Cube------------- Electron-------(-)

Synergetic Cube ----------- Atom (Duo-Tet Cube) (2 interpenetrating triangles)

Stating that the empty space within the synergetic cube represents the third or neutralizing force of the holy ghost is a sort of leap of faith and further explanation is required. This empty space shall be called (after Fuller) the "complementation domain". A cube has a tetra-volume of three and two tetrahedrons have a volume of two. But the remaining complementation domain of the holy ghost is not the remainder of one, because the combined two tetra share a combined common center with the cube center: shared common space which must be less than two volume units. HourGlass , Holy Spirit Plat shows a positive tetra on one-side, a negative tetra on one side and a combined duo-tet in the middle, the internal, trussing of the duo-tet allows their equi-inter-distanced vertexes to define a stable eight cornered cube. The exterior shape of the duo-tet star shaped polyhedron defines the last figure called an hourglass polyhedron. The cube is tetra volume three and within it is l tetra volumes of substance (the hourglass polyhedron) and l volumes of "complementation domain" within the eight vertexes of the cube. The over all cubic domain consists of three tetra volumes: one outside out (l 1/2) and one inside out (l 1/2).

Thus the space or domain of the third force is l tetra volumes and the form of the positive - negative tetra in the hourglass form is also l tetra volumes. This volume of l has an important correspondence in the Law of Twelve where we observed the cuboctahedron volume of twenty (annihilated )reduced to the icosahedron volume of 18, when the nuclear sphere was removed a remainder volume of 1.

As a postscript on the complementation domain of the holy ghost, I recently read the following from the work of Kepler who also recognized the space of the third force:

"Thus for example in the cosmos there are three things at rest, the sun, the fixed stars and the intermedium, and all else is movement; and so in the one God are Father, Son and Holy Spirit. The sphere represents the trinity: the Father is the center, the Son the surface, and the Holy Spirit the uniformity of the distance from center to surface(the radius);...A certain image of the zodiac and of the whole firmament is imprinted by God in the soul of the earth."

Now that the space or complementation domain of the third force (holy ghost) has been established as one and one-half tetra-volumes, what is the action or non-action of the third force within this domain?

We observed in the Law of Seven the symbolic representation of the triangle wholly within the cube as the synthesis of the lower quaternary with the upper triad.

This correspondence can be now brought forward in the concept of the rotation of a triangle in a cube or the holy ghost as wave (spirit) propagation model.

Ours is a universe of radiation in harmonic vibratory motion. Starting with a primary vibrating unit called a photon, the process of emission and movement of these units is called radiation. The space-time ratio of the vibration is the frequency of the radiation and the speed of the outward progression of the speed of radiation is the speed of light. The combination of a vibratory motion and a linear motion perpendicular to the line of vibration results in a path which has the form of a sine curve or wave.

B. Fuller has demonstrated that wave propagation model wave propagation action is cyclically generated by a cube with a triangle rotating in it Synergetics. As shown in Plat No. , the triangle formed by connecting the diagonals of three adjacent faces of the cube is the face of the tetrahedron within the cube. As the triangle rotates in the cube, so that its vertexes move along the edges of the cube, it goes from being congruent with the positive tetrahedron to being congruent with the negative tetrahedron. In one complete cycle, there are six vector wave moves. The half or sine curve is formed when we consider the cube, not as a figure of straight lines, but as an oscillating system in which, as the triangles rotate, their corners describe arcs which convent the cubes 12 edges from straight lines to 12 arcs which produce a pulsating, swollen spherical cube.

Our empty cube is static and forms a rotational base from which the triangles in tetrahedrons can enter and rotate. As the triangles of the tetrahedron rotate within the cube, the static form of the empty cube oscillates to a swollen dynamic condition, from the potential to the radiant. As the triangle rotates, what was once an empty static space, pulsates into a spherical cube as the edges of the cube become the six wave linear (sine curve) diagonals of the tetrahedron.

The electromagnetic sine curve or wave is the six fold path of the photon along the diagonals of the cube faces. The cube face is surface area and the total available energy of a system is related to its surface area, involving the second power of the radius (E=MC). The tetrahedron has the most surface area with the least volume of any symmetrical polyhedra. Positive and negative electromagnetic energy is generated as the rotating triangle passes through the common energy centers of the two tetrahedron and delivers the opposite electromagnetic charge from the base of one tetra to the other tetra. This rapid shuttle of the rotating triangle back and forth between oppositely charged tetra generates electromagnetic energy which is transferred to the faces of the cube.

In conclusion, within the empty space or complementation domain of the third force or Holy Ghost (Spirit), there is an abundance of activity. The rotation of the triangle within the cube with six vector wave moves per cycle, alternately expands from a static cube to a spherical cube and contracts back to a static tetrahedron, which tetra is alternatively positive and negative, propagating electromagnetic waves reflected on the faces of the cube.