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#36 The sacred-geometrical nature of the Vesica Piscis

What is the real reason why the Vesica Piscis possesses sacred geometry? It is not because it is an ancient Christian icon due to its resemblance to the ichthys (actually, the use of this shape predates the early Christian era when Christians took it over in the late second century as a token of their religion). Any object that is merely a symbol of a religion cannot for that reason alone be given the status of sacred geometry. Rather, the Vesica Piscis is sacred because of its potential to generate both the outer and the inner forms of the Tree of Life (see third image below). It may seem ironic that a Christian icon is so deeply connected to the geometrical object that is central to the Jewish mystical tradition — the Etz ha-Chayim ( עץ החיים). But true, religious esotericism, freed from historical chance and misinterpretation, knows no man-made, theological boundaries. There is but one truth, however differently religions may package it. (See also #12 in Sacred geometry/Tree of Life).

da Vinci's Jesus Christ

Mandoria of  Generation of inner Tree of Life from 5 Vesica Piscis

"Salvator Mundi," Leonardo da Vinci's recently restored portrait of Jesus Christ, c. 1490-1519.


A mandoria of “Christ in Majesty.” (From a Romanesque illuminated manuscript Gospel Book, c. 1220). Christ in his cosmic aspect was sometimes depicted as surrounded by a spiritual radiance, or aureola, with the shape of the Vesica Piscis, although the ichthys (from the Greek word for "fish") was its more likely artistic inspiration. The four creatures within circles are the Chaioth ha Qadesh (Holy Living Creatures), the Order of Angels assigned to Kether at the apex of the Kabbalistic Tree of Life.

The generation by five Vesica Piscis of the inner form of the Kabbalistic Tree of Life representing Adam Kadmon, or "Heavenly Man." Pairs of coloured, dashed, straight lines that pass through 18 white dots on the boundaries of these Vesica Piscis at the ends of horizontal and vertical diameters intersect at the 70 corners of (7+7) enfolded, regular polygons. In the order of their generation: violet = triangle, indigo = square, blue = pentagon, green = hexagon, yellow = octagon, orange = decagon, and red = dodecagon. The two dashed lines passing through every two pairs of white dots are mirror images of each other because corresponding white dots on either side of the central root edge shared by the two sets of seven enfolded polygons are mirror images of each other. Notice the analogy between the shaded Vesica Piscis surrounded by four circles and the mandoria of Christ depicted in the diagram on the left.

The stacking of similar Vesica Piscis generates the uppermost nine Sephiroth in the Tree of Life as the endpoints of their horizontal and vertical diameters. The Ennead of nine deities, or neteru, in the ancient Egyptian pantheon are their counterparts:

9 Sephiroth in 3 Vesica Piscis correspond to Ennead

The gematria numbers of Kether (620), Chokmah (73), Binah (67) & Daath (474) located at the four endpoints of the horizontal and vertical diameters of the topmost Vesica Piscis (coloured grey in the diagram below) add up to 1234:

Numbers of Kether, Chokmah, Binah & Daath add up to 1234

1, 2, 3 & 4 are the Pythagorean integers symbolised by the 1, 2, 3 & 4 dots that form the four rows of a tetractys; they add up to 10. The number 1234 can be represented as a tetractys made up of 10 raised to the first four powers of 10, starting with 0.

The next lower Vesica Piscis has Daath with number value 474 and Tiphareth, whose Godname is YAHWEH ELOHIM (76), located at the ends of its vertical diameter. At the ends of its horizontal diameter are Chesed, whose Godname EL has the number value 31, and Geburah, whose Godname ELOHA has number value 36. As shown in #7 of Maps of reality/Cosmic Tree of Life, the (7+5) regular polygons map CTOL because, separately (together with the root edge), they contain 550 yods symbolising its 550 SLs, of which 91 are corners symbolising its 91 Trees of Life (actually, their Tiphareths, that is, their centres). As shown in #9 of Maps of reality/Cosmic Tree of Life, these 12 polygons have 67 corners when enfolded, the set of seven enfolded polygons having 36 corners and the remaining five enfolded polygons having 31 corners. As 550 = 474 + 76, and 67 = 36 + 31, we see that the second Vesica Piscis, whose vertical diameter is the shared root edge of the polygons, determines the number of SLs in CTOL:

12 polygons and root edge contain 550 yods

550 and 67 as sums of gematria numbers

The phrase "knowledge* of God the Creator**" has the very number of SLS in CTOL as the sum of the gematria number values of its constituent words Daath and YAHWEH ELOHIM. All knowledge of God's Creation springs from the root edge as the information embodied in the inner form of the Tree of Life, its endpoints being located at Daath and Tiphareth (or, rather, their projections onto the plane containing the (7+7) enfolded polygons).

(36+31) corners of (7+5) polygons

26 & 50 corners of sectors of (7+5) enfolded polygons 

The number value 31 of EL, the Godname of Chesed, is the number of blue corners of the five largest polygons in the left half of the inner Tree of Life; the number value 36 of ELOHA, the Godname of Geburah, is the number of corners of the seven enfolded polygons in its right half.

The (7+5) enfolded polygons, when separate, contain 550 yods symbolising the 550 SLs of CTOL. They have 87 sectors with 76 corners, where 87 is the number value of Levanah, the Mundane Chakra of Yesod, and 76 is the number value of YAHWEH ELOHIM, the Godname of Tiphareth. The number value 26 of YAHWEH is the number of white corners outside the root edge of the 30 sectors of the three largest polygons, apart from the centre of the decagon, which, unlike the white corners, is not intrinsic to them because it coincides with a black corner of the pentagon. The number value 50 of ELOHIM is the number of black corners of the 57 sectors of the nine other polygons.

The vertical axis of the third Vesica Piscis has Tiphareth with Godname number 76 at its top and Yesod at its bottom whose complete Godname SHADDAI EL CHAI ("Almighty Living God") has the number value 363. The Sephirah Netzach with Godname number 129 and the Sephirah Hod with Godname number 153 are located at, respectively, the right-hand and left-hand ends of its horizontal diameter. The sum of these four Godname numbers = 76 + 129 + 153 + 363 = 721. This is the number of yods (including its centre) in a decagon whose sectors are 2nd-order tetractyses:

721 =

721 yods in a decagon with 2nd-order tetractyses as sectors

The third Vesica Piscis therefore spans four Sephiroth whose Godname numbers add up to the yod population of the decagon constructed from 2nd-order tetractyses. Having 10 corners, this polygon is the symbol of the Decad, as expressed by the 1st-order tetractys. The number 721 can therefore be said to have a very Pythagorean character! The sum of the number values of the Hebrew names of these four Sephiroth = 1081 + 148 + 15 + 80 = 1324. Once again, the Pythagorean integers 1, 2, 3 & 4 appear in the sum of the number values of four Sephiroth at the extremities of a Vesica Piscis.

The sum of the gematria number values of the Hebrew names of the last five Sephiroth of Construction = 1081 + 148 + 15 + 80 + 496 = 1820. This is the number of yods, starting each time from their centres, that are needed to construct the faces and interiors of the five Platonic solids from Type A triangles (see here and here). Just as the ancient Greeks (following Plato and Aristotle) regarded the five regular polyhedra as the shapes of the basic particles of the five Elements Earth, Water, Air, Fire & Aether, so many Kabbalists associated the latter with the last five Sephiroth of Construction: Malkuth, Yesod, Hod, Netzach & Tiphareth, respectively. The arithmetic connection between these Sephiroth and the five Platonic solids is evidence that the association cannot be regarded as invented. To dismiss it as coincidence does not seem plausible even though it is a logical possibility. The tetractys is what reveals the mathematical harmony between the gematria number values of the Sephiroth and the properties of sacred geometries such as the five Platonic solids.

* The word 'Daath' means knowledge.
** The translation of the Godname YAHWEH ELOHIM is "God the Creator." In his "Cabalistic Encyclopedia," David Godwin associates this Divine Name with Binah, whilst not assigning ELOHIM to any (!) Sephirah, even though he calls it a "name of God"! This is wrong — or, rather, it is the original interpretation of this Godname by the Order of the Golden Dawn, to which Godwin frequently pays lip service, that is incorrect. In the traditional Jewish view, ELOHIM is the Name of God as the Creator and Judge of the universe (Gen 1:1-2:4a). As the very first reference to God in the opening chapter of Genesis, it can hardly be regarded as just one of the many names of God, as Godwin seems to believe! Here is scriptural confirmation:

"The Holy One, Blessed be He, said to those, You want to know my name? I am called according to my actions. When I judge the creatures I am Elohim, and when I have mercy with My world, I am named YHVH" (Ex R. 3:6).

This is consistent with the Pillar of Mercy in the Tree of Life being headed by Chokmah, whose Godname is YAHWEH, and with the Pillar of Judgement being headed by Binah, whose Godname is ELOHIM. In terms of Jewish Kabbalah, it is clear that the attribution by the Order of the Golden Dawn of YAHWEH ELOHIM to Binah is wrong. This Godname is that of Tiphareth, not Binah. It is the assignment that Z'ev ben Shimon Halevi (1933–2020), the well-known Jewish teacher on Kabbalah, correctly gives in his book A Kabbalistic Universe (Samuel Weiser, 1977; Gateway, 1988).

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