The Polyhex Key
To the Tree of Life

Now Available!... The Polyhex Tree of Life (full colour wall-chart)

The manifestation of the kabbalistic Tree of Life involves the coming together of two primary principles called Spirit and Matter (or Form). The merging of these two principles produces a third middle principle called Consciousness (or Soul). The merging process can be illustrated very simply using two overlapping circles. (See the figure below.)

Before the beginning of Time and Space the two circles are separated, but eventually they approach each other, intersect, and partly merge together. The area of their overlap forms the Soul/Consciousness principle.


To build the complex form that is the Tree of Life diagram we must replace the Spirit and Form circles with polyhexagons.

The special polyhexagonal form upon which the Tree of Life is based is a structure that consists of nineteen individual hexagons arranged in a composite hexagonal shape. This special polyhexagon is characterized by two sub-groups of component hexagons. Firstly, a group of seven hexagons, six of which are located around the perimeter of the polyhex, and a seventh located precisely at its centre. The second sub-group consists of twelve individual hexagons that fill the main body of the polyhex construct.


You may recognize the significance of the figures seven and twelve as coinciding with the number of Hebrew Double and Simple letters respectively. This is a very important correspondence that we will examine more closely below.

The Tree of Life polyhexagon is a special modification of another 19-Hex polyhex that I call the Genesis polyhexagon. In my understanding, the Genesis polyhex is the natural organic form upon which the Tree of Life polyhexagon is based. The Tree of Life polyhexagon rearranges the nineteen hexes of the Genesis polyhex so that the inner dynamics of the Genesis polyhexagon are more easily perceived. The Tree of Life polyhex reveals the structure of the pathways of interconnection that exists between the various hexes of the Genesis polyhexagon.

The Genesis polyhexagon resembles an organic cell. It has a nucleus and an outer membrane. Cosmically, we can understand the nucleus as composed of the seven astrological planets (or planetary gods/logoi) while the outer membrane consists of the twelve zodiacal signs (or major angelic/devic forces). The interaction between these two groups of divine Beings produces All-That-Is. The Tree of Life polyhexagon reveals more clearly how the two groups energetically interact with each other.


There are two types of Genesis polyhexagons—a Spirit polyhex, and a Form polyhex. They both have a seven-fold nucleus surrounded by a twelve-fold membrane. Correspondingly, there are also two Tree of Life polyhexagons and it is these latter two polyhexes that we are considering in this chapter.

The merging of the two Tree of Life polyhexagons produces interesting results. The Tree of Life diagram is now clearly revealed in the composite hexagonal design (below right). The three white hexagons at the top of the yellow polyhexagon represent the three highest sefirot of the Tree of Life—Keter, Hockmah, and Binah. They remain wholly detached from the Form principle polyhexagon (shaded blue).

Only seven yellow hexagons remain visible in the main body of the Spirit polyhexagon. These represent the seven Hebrew Double letter pathways of the Tree (as I have delineated them in my book Formation of the Tree of Life). The correspondence to my original pathway findings is precise as I will demonstrate shortly.


In numbering the component hexagons (below) I have placed all of the even numbers on the right side of the polyhexagon and the odd numbers on the left. I have chosen to use this convention merely to identify the right side as 'male' (even) and the left side as 'female' (odd). But it is also interesting to note that this convention shows the natural sequence of the lower sefirotic hexagons (shaded grey) progressing from Tifaret (4) to Hod (5) which is contrary to the traditional numbering system which has Netzah (6) following numerically after Tifaret (4). Thus, this odd/even rule results in a more accurate presentation of the 'hierarchy of the planes'[1] because Hod (as Mercury) represents the lower mental plane and therefore it should come before Netzah who as Venus symbolizes the astral plane.


The three highest sefirot represent the sacred trinity of divine Powers. The seven Double letter pathways symbolize the seven Heavens/Palaces[2], the seven planetary Spirits (or Logoi), the seven angels who attend the Throne of God, etc. They represent supernal powers guiding and administrating the lower worlds. Each of these seven Double letter pathways is the ensouling spiritual source of one of the seven lower sefirot (or 'planetary spheres').

The Form principle polyhexagon includes the seven lower sefirot (i.e. corresponding to the seven grey shaded hexagons) and the twelve Simple letter pathways (corresponding to the twelve blue shaded hexagons above).


An important consequence of the polyhexagon merging and overlapping process is that five of the Spirit principle pathways become concealed beneath the upper portion of the Form principle polyhexagon—that is, they become hidden below the surface of the newly formed Soul principle. My thinking is that these five concealed pathways correspond to the five Final Hebrew letters—Kaf final (ך), Maym final (ם), Nun final (ן), Peh final (ף), and Tzaddie final (ץ). The implication of this geometric symbolism is fascinating.


The Soul principle is formed as a result of the intersection, overlapping, and interaction of the Spirit and Form principles. This area of overlap is indicated in the diagram above by the five green hexagons and their four bounding grey hexagons (i.e. numbered with white numerals). The soul is thus seen to be an admixture of Spirit and Form.

In terms of the Tree of Life diagram the Soul (or Consciousness) principle is divided into two interconnected triads—a soul triad and a monadic triad. The monadic triad is composed of the sefirot Da'at (♄), Hesed (♃), and Geburah (♂). The soul triad is composed of the sefirot Hesed (♃), Geburah (♂), and Tifaret (☉). The human monad (proper) exists within the Spirit polyhexagon—that is, beneath the sefirot and pathways that compose the two triads of the Soul principle. The monadic triad represents the closest region of contact to the human monad that is possible for 'human consciousness'—that is, without relinquishing the Consciousness principle and entering the pure realm of the Spirit polyhexagon.

The Soul principle is seen to be a relatively impermanent principle (or state of being). It manifests only when the Spirit principle merges with the Form principle. The significant implication of this is that when it comes time for the Spirit and Form principles to once again separate themselves the Soul principle dissolves (or disassembles). In terms of our geometric symbolism, the area of intersection between the Spirit and Form polyhexagons disappears. This process of separation occurs during what Theosophists call a period of 'pralaya'[3].

Your first feelings on hearing this proposition may include some disappointment. You may feel that the dissolution of your soul will lead to the loss of your identity (or your existence as an individual). This is not truly the case however. The soul is merely a temporary vehicle that allows the Spirit to involve itself in the substance of matter.[4] Your spirit (i.e. your monad—the essence of your being) remains in existence during the period of Pralaya.

Before the soul's dissolution during Pralaya, its essence is absorbed into and stored in the monad. I believe this process is made possible by the existence of an occult mechanism involving the five Hebrew Final letter pathways.


The five Final letter pathways are concealed beneath the five visible Simple letter pathways of the Soul principle. The five Finals belong to the Spirit principle polyhexagon, but they are covered and concealed by the Simple letter 'soul pathways' of the overlapping Form principle. My theory is that the esoteric function of the five Final letter pathways is to gather in and absorb the Knowledge that has been gained during the term of the soul's existence. By 'Knowledge' is meant the combined Wisdom and Understanding (or 'love-wisdom') that the soul has acquired during its term of existence. These qualities are collected and stored within the monad during each period of Pralaya.

Thus, when the Spirit polyhexagon detaches itself from the Form polyhexagon it carries with it the five concealed Final letter pathways because they are part of its fundamental structure. So, nothing of value is lost during a Pralaya.

The Hebrew letters are arranged on the Spirit and Form polyhexagons as per the diagram above.[5]

The seven Double letter pathways are shaded yellow. The twelve Simple letter pathways are shaded blue. The five Final letters (coloured blue) are positioned on five yellow hexagons near the base of the Spirit polyhexagon (above left). They are bounded by four hexagons containing the letters of the Tetragrammaton—YHVH (orange lettering). This small subset of hexagons bounded by YHVH (יהוה) basically represents the human monad. The overlapping hexagons of the Soul principle are merely a garment the monad wears when it descends into the realm of 'physical existence'.

The YHVH group of hexagons establishes the basic structure of the human monad. It's an extension of the mother letter hexagon group located at the top of the Spirit polyhexagon. The Yud (י) hexagon is an extension of Maym (מ). The two Heh (ה) hexagons are extensions of Shin (ש). The Vav (ו) hexagon is an extension of Alef (א). These Hebrew letter correspondences are based on information provided in the Sefer Yetzirah.

1:13. He chose three letters from among the Simples
[in the mystery of the three Mothers: Alef, Mem, Shin]
And He set them in His great Name...

Of course, 'His great Name' is YHVH, and the three Simple letters 'set in it' are Yud, Heh, and Vav. Together these three Hebrew letters form the signature of the divine Creator. And every human monad is therefore seen to be a unique expression of the creative essence of the supreme Creator YHVH.


The twelve Simple letters are expressions of the Form principle, or Great Mother 'Shekinah' principle.

The seven Double letters have two variant forms—a 'soft' pathway form representing supernal spiritual forces, and a 'hard' sefirotic form (i.e. identified by a dagesh, or dot) representing lower, more material projections of the supernal pathways.

The five Finals are differentiated as follows:

Thus, all the three major Hebrew letter groups—Mothers, Doubles, and Simples, are represented in the five Finals.

My current hypothesis is that Maym Final collects the essence of the two Mother letter pathways (i.e. the vertical pathways of Maym and Shin) that infuse the Form principle polyhexagon. Similarly, Kaf Final and Peh Final gather the essence of the seven Double letter sefirot of the Form principle polyhexagon. Lastly, Nun Final and Tzaddie Final collect the essence of the twelve Simple letter pathways of the Form principle polyhexagon. So when the Spirit principle polyhexagon detaches and separates from the Form principle the threefold essence of its experience within the substance of matter (i.e. as recorded by the soul) is taken with it via the five Hebrew Final letter pathways.


You may notice that there are only nineteen pathway hexagons included in the natural structure of the polyhex Tree of Life design. (See the diagram above.) Three of the twenty-two pathways of the Tree of Life appear to be missing. I have also omitted them from the traditional drawing of the Tree of Life (above left). The missing three are the three Mother letter pathways—Alef, Maym, and Shin.

Most kabbalistic commentators assign the three Mother letters to the three horizontal pathways of the Tree diagram[6], but my findings indicate that their more metaphysically meaningful placements are with the three vertical pathways of the Middle Pillar of the Tree of Life.

In my view the Double letter Bayt (ב) is assigned to the highest horizontal pathway (i.e. joining Hockmah with Binah) because it is responsible for formulating the first of the seven lower sefirot—Da'at. The sefirah Da'at arises as a result of the interaction between Hockmah and Binah—an interaction facilitated by the horizontal Bayt pathway. The hard form of the letter Bayt consequently emerges as the distinguishing archetype of the sefirah Da'at.

The Tree of Life formation formula (as described in my book) posits the location of the Hebrew letters on the sefirot and pathways of the Tree diagram in a descending hierarchy that follows the sequence 3:7:12—that is, Mothers-Doubles-Simples. For this reason, the formula cannot be reconciled with the traditional numeric method of assigning the letters to the horizontal, vertical, and diagonal pathways. The old method places the three Mother letters on the three horizontal pathways, the seven Double letters on the seven vertical pathways, and the twelve Simple letters on the twelve diagonal pathways of the Tree diagram.

The traditional methodology appears, at first glance, to be most agreeable, but I believe it is an erroneous correspondence. The geometric framework of the Tree diagram is built according to the fundamental esoteric ratio 3:7:12 because it represents a blueprint of the divine Creation. The Hebrew alphabet is also constructed according to the 3:7:12 ratio because it represents the twenty-two divine archetypes. It does not necessarily follow however, that the two are meant to be combined together purely on the numerical basis of this 3:7:12 ratio. In fact, the Sefer Yetzirah states:

One on three,
three on seven,
seven on twelve,
And all are bound, one to another.
These are the twenty-two letters...[7]

Obviously, a 3:7:12 hierarchical arrangement of the Hebrew letters is indicated by this statement. Clearly, it is a contradiction of the principles of the Sefer Yetzirah to widely intermingle the three classes of Hebrew letters on the Tree diagram (i.e. as does the orthodox numerical letter-pathway arrangement).

To put it simply, the Sefer Yetzirah is saying...

One (All-encompassing Ain Sof) on three (supernal sefirot)
Three (supernal sefirot) on seven (supernal pathways)
Seven (lower sefirot) on twelve (lower pathways)
And they are all interconnected

(See the figure below.)

The Zohar is similarly supportive of the hierarchical approach. In its anthropomorphosis of the Tree of Life the Zohar associates the three highest sefirot with the head of Adam, and the lower sefirot with his body. These correspondences combine well with the Sefer Yetzirah's assignment of the seven Double letters to the eyes, ears, nostrils, and mouth.


Logically, the seven Double letter pathways (symbolizing seven physical attributes of the human head) need to be arranged upon the head of Adam at the top of the Tree of Life diagram.

The Sefer Yetzirah assigns the twelve Simple letter pathways to the torso, limbs, and internal organs of the human body, and therefore logically these should be located within the lower portion of the anthropomorphic Tree diagram—that is, below the head.

One of the key arguments for the old numerically-based arrangement is that the Sefer Yetzirah describes the twelve Simple letter pathways as 'diagonal boundaries' [8] (גבולי אלכסון). It is true that twelve of the Tree of Life pathways are diagonal (or sloping), but the diagonal pathways do not resemble 'boundaries' on the Tree diagram. In the hierarchical pathway arrangement however, the twelve Simple letter pathways do resemble diagonal boundaries (or 'sloping sides') because they form the twelve bounding sides of six adjacent triangles that surround Tifaret in the lower portion of the Tree diagram. (See the diagram above left. The twelve Simple letter pathways are coloured blue.)

The three vertical Mother letter pathways unite the four sefirot of the Middle Pillar of the Tree of Life, but they are not included in the polyhexagonal structure of the Tree. This reflects the mysterious nature of these three pathways. They represent the fluid essence of Being. Their movement, interaction, and intermingling produces the flowing stream of awareness that we call consciousness, and necessarily also the illusion of time and space. Because of this, they move within and beneath the surface of consciousness and are not directly perceived by it. Only their effects are perceptible. What is inferred is that consciousness is not a fixed enduring principle, but rather, is a fluid process.

Interestingly, in the polyhexagon Tree diagram, the Shin (Fire) pathway is invisibly located beneath the Tet (Leo) hexagon. The Fire of Shin is associated with Nachash—the 'Kundalini Serpent'. Tet also means serpent, and Leo (ruled by the Sun) is a fire sign that epitomizes the fiery principle of consciousness.

The Maym (Water) pathway is invisibly located beneath the Tzaddie (Aquarius) hexagon. Of course, Aquarius is known as the 'Water Carrier'[9], and is also strongly associated with the consciousness principle. These two signs, Leo and Aquarius, form the vertical axis of the Fixed zodiacal cross.

The Alef (Air) pathway is invisibly located beneath the Bayt (Saturn) pathway hexagon. This is appropriate because Bayt is chief of the seven Double letters, and Alef is chief of the three Mother letters. Also, Alef is thought to stand invisibly behind Bayt during the process of Creation (which is why Berashit[10] begins with a Bayt and not an Alef).


You may have noticed in the diagrams that the two Simple letter pathways Qof (Pisces) and Sameck (Sagittarius) are placed differently in this polyhex arrangement—i.e. compared to the arrangement I described in the early chapters of my book Formation of the Tree of Life. The reason for this slight deviation is that although normally these two pathways extend from Hesed and Geburah to Yesod, they are also capable of extending to Da'at (i.e. from Hesed and Geburah). This only occurs during the process of 'divine inspiration' (i.e. conscious contact with the monad)—an experience that rarely happens in an average person's lifetime. In the polyhexagon Tree diagram these two pathways are placed in their elevated positions adjacent to Da'at. Thus, this particular pathway configuration reflects the conscious alignment strived for by Disciples (or Tzadikim) on the Path. The state of consciousness that this configuration represents grows stronger and more stable as a disciple continues on his/her path of inner development.


For disciples and initiates, the Fire (Shin, ש) of creative inspiration flows from Da'at to Geburah (i.e. representing the Abstract Mind) along the Sameck (Sagittarius) pathway. The Water (Maym, מ) of spiritual intuition flows from Da'at to Hesed (i.e. representing the Intuitive Mind) along the Qof (Pisces) pathway.

While the Sameck and Qof pathways remain exclusively attached to the sefirah Yesod they symbolize the presence in a person's mind of worldly illusions (Sagittarius) and glamours (Pisces). These illusions are fostered within, and perpetuated by the collective mindset of mundane human society. They effectively fill the pathways of Sameck and Qof with a darkness that blocks access to the higher sefirot Geburah and Hesed. But as a person frees themselves from the glamours and illusions of society they simultaneously become consciously open to the higher sefirot and thus to divine impressions entering into and through the human soul (i.e. flowing from Da'at to Hesed and Geburah).

The divine inspiration that is received through the pathways of Sameck and Qof is expressed and applied (in the mundane world) via the lower and complementary pathways of Zayn (Gemini) and Yud (Virgo). Together these four pathways constitute the Mutable Cross of the Heavens (i.e. the cross of mutable zodiacal signs). On the Tree of Life, the primary creative-evolutionary purpose of the Mutable Cross is to positively transform the human expression of the psychic influence of the astrological Moon (i.e. as it is felt within the sefirah Yesod).


The main evolutionary function of the four signs (and pathways) of the Cardinal Cross is to stabilize the expression of the astrological Sun upon the Path of Righteousness. Thus, on the Tree of Life diagram we see the four cardinal sign pathways anchoring and holding the sefirah Tifaret (i.e. the Sun) upon the Middle Pillar of the Tree. Their role is to hold Tifaret steady so that it doesn't drift too far towards the left-hand Pillar of Severity, or conversely, too far towards the right-hand Pillar of Mercy. As long as Tifaret's central position upon the Middle Pillar is maintained then it retains direct access to 'HaShem'[11]—that is, to the forces of Shin (ש) and Maym (מ) flowing through the 'invisible' Middle Pillar pathways. When this condition is fulfilled, a human-being becomes a Tzadik—i.e. one who is faithfully aligned upon his/her 'path of righteousness'.

The four signs (and pathways) of the Fixed, or Cherubic Cross are responsible for refining the four main faculties[12] of human consciousness as represented by the four 'directional' sefirot—Hesed, Geburah, Hod, and Netzah. These faculties are associated with the four elements and the four magical implements—the Cup, the Wand, the Sword, and the Disk (or Pentacle). The four cherubic 'animals' represent active intelligent expressions of the four esoteric elements. They signify powerful forces that are responsible for the diversity of life and life experience on our planet. On the Tree diagram their four pathways form a square enclosure whose four walls intersect at the four 'corner' sefirot—Hesed, Geburah, Netzah, and Hod.


The following diagram substitutes the Hebrew letters (as per the figure above) with their astrological correspondences.


An Alternative Arrangement
Of the Twelve Simple Letters

As explained in my book Formation of the Tree of Life, the Sefer Yetzirah uses a system that attaches the cardinal signs of the zodiac to the sefirah Tifaret; the mutable signs to Yesod/Da'at, and the fixed signs to the four directional sefirot Hesed, Geburah, Hod, and Netzah. (See the diagram above.) This does not mean, however, that the twelve simple letters are necessarily restricted to those placements.

I mentioned in my book that I consider the association of the twelve Hebrew 'simple' letters to the pathways of the Tree of Life as somewhat flexible. The only limitation I put on them is that they remain associated with the twelve lower pathways of the Tree diagram—i.e. those contained within the body of the Form principle polyhexagon (coloured blue in the diagrams below). The reason for this flexibility is that I believe that the twelve zodiacal pathways are meant to move around (i.e. cycle between) the seven sefirot of the Form principle polyhex.

During my meditations upon the polyhex Tree of Life I noticed that one particular arrangement of the twelve simple letters produced a design that resonated with my understanding of the Tree from a Theosophical perspective. This arrangement is presented in the diagrams below.


The above arrangement is based on the odd/even left/right distribution of the numbers from one to twelve. The simple letter sequence begins from the base of the Tree and proceeds to the number twelve (i.e. positioned top-right of the blue Form principle polyhex).

The overlap region of the Soul principle is outlined in red, and the five zodiacal signs that are included in the soul principle are also highlighted red. These consist of the final five signs of the zodiac. Significantly, these five signs are associated with the major initiations that release each human-being from the 'chains of matter' (i.e. from identification with the Form principle).

Therefore, it is most appropriate for these five final zodiacal signs to be connected with the human soul/monad principle, and for them to overlay (in the polyhex Tree diagram) the five final Hebrew letters of the human monad.[13] As explained above, the essence of these five Soul principle hexagons/signs is 'harvested' and absorbed into the hexagons of the underlying Spirit polyhex where it is safely stored during periods of Pralaya.

Here follows a standardized Tree of Life diagram of the polyhex version figured above.


You can see in the diagram above that the final three zodiacal signs—Capricorn (♑), Aquarius (♒), and Pisces (♓) are wholly contained by the monadic triad (i.e. as it is delineated by the three planets Saturn (♄), Jupiter (♃), and Mars (♂)). In other words, these three signs do not extend below the confines of the monadic triad.

The preceding two zodiacal signs are Scorpio (♏) and Sagittarius (♐). These two signs extend below the monadic triad and attach it to the causal body—i.e. as represented by the Sun (☉).

The positioning of Scorpio and Sagittarius below the monadic triad reflects the role that these two signs play in the early initiations—i.e. the first and second initiations. The third to fifth initiations involve more directly the monadic triad (and thus also, the final three zodiacal signs that circumscribe it).

Author: Patrick Mulcahy
(An expanded & revised excerpt from the book:
Formation of the Tree of Life - 2010 Edition)
(March, 2011)


[1] That is, as described in the teachings of Theosophy.

[2] Hebrew: Shamayim (שמים), and Hekhalot (היכלות).

[3] Pralaya (Sanskrit) [from pra away + the verbal root li to dissolve] Dissolving away, death, dissolution, as when one pours water upon a cube of salt or sugar: the cube of salt or sugar vanishes in the water, dissolves, and changes its form. So during a pralaya, matter crumbles or vanishes away into something else which is yet in it, surrounds it, and interpenetrates it. Pralaya is often defined as the state of latency or rest between two manvantaras or great life cycles. [From: The Rakefet Theosophical Dictionary.]

[4] In fact, human-beings are destined to evolve beyond soul-based consciousness. The soul becomes obsolete as a vehicle of consciousness at the 4th Initiation (called the Great Renunciation). It is then transcended and replaced with 'monadic' consciousness.

[5] But note that the arrangement of the twelve Simple letters is somewhat flexible.

[6] Without much explanation besides the obvious numerically based correspondence.

[7] Sefer Yetzirah, 6:5-6.

[8] Sefer Yetzirah, 6:1. Note that it does not, however, describe the three Mother letter pathways as 'horizontal', or the seven Double letter pathways as 'vertical'.

[9] The Tzaddie pathway carries the Water of Maym from the sefirah Hesed to the sefirah Geburah.

[10] That is, the Book of Genesis.

[11] Hebrew – The 'Name', spelled Shin-Maym, referring to the divine Name of God.

[12] That is, the intuitive mind, the abstract mind, the rational mind, and the astral body (or desire mind).

[13] It should be noted that in terms of the Tree of Life diagram the Soul (or Consciousness) principle is divided into two interconnected triads—a soul triad and a monadic triad. The monadic triad is composed of the sefirot Da'at (♄), Hesed (♃), and Geburah (♂). The soul triad is composed of the sefirot Hesed (♃), Geburah (♂), and Tifaret (☉). The human monad (proper) exists within the Spirit polyhexagon—that is, beneath the sefirot and pathways that compose the two triads of the Soul principle. The monadic triad represents the closest region of contact to the human monad that is possible for 'human consciousness'—that is, without relinquishing the Consciousness principle and entering the pure realm of the Spirit polyhexagon.