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#5 The decagon with 2nd-order tetractyses as sectors embodies the number 620 of Kether

Kether is the seed from which the nine other Sephiroth of the Tree of Life grow. An n-sided regular polygon with its sectors turned into tetractyses is a representation of n overlapping Trees of Life up to the first Sephirah of Construction of the nth tree. This is because it has (6n+1) yods, whilst there are (6n+1) SLs up to Chesed of the nth Tree. Dividing a decagon into ten tetractyses generates 61 yods, the number of AIN, the Absolute. The interpretation of this is that ten Sephiroth emanate from the Unmanifest of AIN, each with its own Tree of Life structure corresponding to one of the ten tetractys sectors of the decagon. Each yod denotes a Sephirothic level of the tree representing one of the Sephiroth, which in turn has its own Tree of Life/tetractys representation. A decagon with 2nd-order tetractyses as sectors has 721 yods, of which 101 are corners of tetractyses and 620 are hexagonal yods symbolizing the seven Sephiroth of Construction, where 620 is the number value of Kether. Just as an acorn can be said to contain a potential oak tree, Kether ‘contains' the other Sephiroth. Kether has the number 620 because the ten-fold differentiation of each of the ten Sephiroth generates 620 hexagonal yods signifying Sephiroth of Construction. This number therefore signifies the potential number of ‘degrees of freedom' required to express the ten-fold Adam Kadmon, the divine prototype.

As

31 = 20 + 21 + 22 + 23 + 24

= 1 + 2 + 4 + 8 + 16,

then

 620 = 20×31 = 20(1 + 2 + 4 + 8 + 16) = 20×1 + 20(4 + 16) + 20(2 + 8) = 20×1 + 20×20 + 20×10 = 20 + 400 + 200,

which reproduces the respective number values of the three Hebrew letters kaph, tav & resh of Kether: KTR (see here).This powerfully demonstrates how the Pythagorean tetractys and its higher order versions reveal the geometrical basis of the Kabbalistic system of the names of the Sephiroth, their Godnames, etc.

As 620 = 10×62 = 10×2×31 = 10(21 + 22 + 23 + 24 + 25), the number of Kether is the sum of (10×5=50) powers of 2, where 50 is the number of ELOHIM, the Godname of Binah.

Another representation of 620 in terms of 1, 2, 3 & 4 can be derived from the identity:

6201 = 12 + 22 + 32 +… + 262,

where 26 is the number of YAHWEH, the Godname of Chokmah. This gives:

620 = (22 + 32 + ... + 262)/(1+2+3+4),

where

26 = [22 + 32 + ... +  (24=1×2×3×4)2]/(13 + 23 + 33 + 43).

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