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**#22 The outer Tree of Life with Type B triangles & the
combined Trees of Life with Type A polygons embody the number 620 of Kether**

**a) Outer Tree of Life**The Type B triangle has 46 yods (see here). Nine yods line its perimeter, which encloses 37 yods. Therefore,

**b) Combined Trees of Life**The Type A triangle has 19 yods (see here). Inside it are ten yods. Inside the 16 Type A triangles of the outer Tree of Life
are (16×10 = 160) yods that comprise 16 corners of tetractyses and (160−16=144) hexagonal yods. 44 hexagonal
yods are on their 22 sides. The number of hexagonal yods in the outer Tree of Life = 144 + 44 = 188. They
comprise

The inner Tree of Life has 444 hexagonal yods when the 94 sectors of its (7+7) enfolded polygons
are turned into tetractyses (see here). When they are superposed onto the outer Tree, the centres of the
two enfolded triangles, which are corners of tetractyses, coincide with the two hexagonal yods on the Path
connecting Chesed and Geburah, thereby removing them from the count of the *total* number of
hexagonal yods in the combined outer & inner Trees, although they remain, of course, hexagonal yods as far
as the former is concerned. Four white hexagonal yods on each side pillar coincide with hexagonal yods on the
vertical, internal sides of the sectors of the two hexagons. The total number of hexagonal yods in the combined
outer & inner Trees of Life = 188 − 2 + 444 − 4 − 4 = 622. There are **620** hexagonal
yods other than the two hexagonal yods on the root edge of the (7+7) enfolded polygons.

**c) Decagon**

Suppose that each sector of the decagon is turned into a 2nd-order tetractys. 720 yods surround its centre, of
which (100 = 1^{3} + 2^{3} + 3^{3} + 4^{3}) yods are corners of 10
tetractyses and **620** yods are hexagonal yods (see #5). The factor of 10 in this polygonal representation of the number of
Kether arises from the 10 sides of the decagon, there being **72** yods and
**62** hexagonal yods per sector, where **72** is the number of Chesed and
**62** is the number value of *Tzadkiel*, the Archangel of this Sephirah. That this
factor should aptly appear also in the 10-fold outer Tree of Life, as well as in its combination with its inner
form, is non-trivial. These numbers illustrate the geometrical basis of the Kabbalistic system of Sephiroth,
their Divine Names, etc and their gematria number values.

**General comments**

The outer Tree of Life has 214 yods. 16 yods (seven yods on each side pillar and the two
hexagonal yods on the Path connecting Chesed and Geburah) are shared with the (7+7) enfolded polygons, which
have 524 yods. The combined outer & inner Trees of Life contain (214−16+524=722) yods. Ten of these are
Sephiroth and another 12 yods are centres of polygons. Therefore, there are (722−10−12=700) yods other than
Sephiroth or centres. The significance of this is that 700 = 70×10, where *70 is the number of yods in the
outer Tree of Life with its triangles turned into tetractyses*. The combined Trees are composed of
(**48**+94=142) tetractyses, each with a hexagonal yod at its centre. The number of yods lining
their 241 sides = 722 − 142 = 580. Outside the root edge are 576 yods on 240 sides of 142 tetractyses, where 576
= 24^{2} = 1^{2}×2^{2}×3^{2}×4^{2}. This illustrates once again how
the Tetrad expresses properties of sacred geometries. The number of yods in the combined Trees that are unshared
with each other = 722 − 16 = 706. There are 702 unshared yods outside the root edge, where

702 = 2×**351** = 2(1 + 2 + 3 + ... + **26**) = 2 + 4 + 6 + ... +
52

is the sum of the first **26** even integers, **351** is the
number of *Ashim*, the Order of Angels assigned to Malkuth, and **26** is the number of
YAHWEH. This shows how this Godname prescribes the number of unshared yods outside the root edge. As

700 = 702 − 2 = 4 + 6 + 8 + ... + 52,

we see that the sum of all the even integers, starting with the Tetrad, up to 52 (the
**26**th even integer) is the number of yods in the combined Trees of Life other than Sephiroth and
centres of the 14 polygons of the inner Tree. In the discussion of the Tetrahedral Lambda (see Figure 5 here), it was pointed out that the sum of the 20 integers in the tetrahedral
array is 350, whilst the sum of the integers in its four separate faces is 700. This sum is, therefore, the
number of yods in the combined Trees other than Sephiroth and centres of polygons.

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