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** #81 An arithmetic representation of the inner Tree of
Life**

The (7+7) enfolded Type A polygons of the inner Tree of Life have 524 yods. Four black yods line
the root edge shared by all 14 polygons. Outside it are 260 yods in each set of seven enfolded polygons. This is
the number of yods in **26** tetractyses, showing how YAHWEH, the Godname of Chokmah with number
value **26**, prescribes the yod population of each half of the inner Tree of Life. The seven
polygons in each half have **36** corners and 42 sides, where **36** is the number
value of ELOHA, the Godname of Geburah. The number of yods lining their boundaries = **36** + 2×42
= 120 = 11^{2} − 1

= 3 + 5 + 7 + 9 + 11 + 13 + **15** + 17 + 19 + **21**,

i.e., 120 is the sum of the first 10 odd integers after 1. The number of boundary yods outside
the root edge = 120 − 4 = 116. They are coloured red in the diagram above. Inside their boundaries are
(264−120=144) blue yods, where 144 = 12^{2} and 12 is the number of corners of the dodecagon, the tenth
regular polygon. The Decad (10) determines the boundary and interior of the inner Tree of Life. This 120:144
division is the counterpart to the distinction in the outer Tree of Life between its trunk and its branches. It
manifests in the Polyhedral Tree of Life as the 120 faces of the disdyakis triacontahedron and the 144 faces of
the 144 Polyhedron, which are the polyhedral counterparts of, respectively, the trunk and branches of
the outer Tree of Life.

The pattern of numbers of yods:

524 = 4 + 2×260 = 4 + 2×(116+144)

has an arithmetic counterpart, as now explained. The 11th triangular number is a triangular array of

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66

points. If every point is replaced by the Pythagorean Tetrad (4), the sum of the 66 4's is 264,
which is the number of yods in the seven enfolded Type A polygons. The sum of the **65** 4's below
an apex of the triangular is 260, which is the number of yods outside the root edge of these polygons. The
number **65** is the number value of ADONAI, the Godname of Malkuth. There are 30 4's lining the
boundary of the triangle, that is, 29 4's other than the integer 4 at one corner. Their sum is 116, which is the
number of yods on the sides of the seven enfolded polygons outside their root edge. There are
**36** 4's inside this boundary that add up to 144; this is the number of yods inside the
boundaries of the seven enfolded polygons making up each half of the inner Tre of Life. Two triangular arrays of
66 4's sharing one corner reproduce the boundary and internal yod populations of these halves. They consist
of **131** 4's, where **131** is the number value of *Samael*, the Archangel of
the Sephirah Geburah. The number values of both the Godname and the Archangel of the *same* Sephirah,
namely, Geburah, are present in this pattern. **131** is the **65**th odd integer
after 1. The Tetrad gives this number a unique significance vis-à-vis the inner Tree of Life because the
yod population of the latter = 524 = **131**×4. The **72** internal 4's add up to
288, which is the number of yods inside the sides of the (7+7) enfolded polygons. The number **72**
is the number value of Chesed, the Sephirah preceding Geburah. The number of 4's surrounding the linking one is
130, where

130 = |
1 |

1 + 2 + 3 + 4 |

This pattern of 4's can be regarded as an *arithmetic* representation of the inner Tree
of Life, the two triangular arrays expressing its two halves. The 4's at the two corners of each array can
be thought of as denoting the eight yods that line each square outside the root edge that they share, the square
being, of course, the symbol of the number 4. The three 4's at the corners of the triangular array
therefore express the 12 yods that line the square when — together with the other polygons — it is constructed
from tetractyses.

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