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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** = 2^{0} + 2^{1} + 2^{2} + 2^{3} +
2^{4}

^{ }
=
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(2^{1} + 2^{2} + 2^{3} +
2^{4} + 2^{5}), 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 = 1^{2} + 2^{2} + 3^{2} +… + **26**^{2},

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

**620** = (2^{2} + 3^{2} + ... +
**26**^{2})/(1+2+3+4),

where

**26** = [2^{2} + 3^{2} + ...
+ (24=1×2×3×4)^{2}]/(1^{3} + 2^{3} + 3^{3} +
4^{3}).