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**#16 Correspondence between the Tetrahedral Lambda, the
first 6 polygons enfolded in 10 overlapping Trees of Life and the 1-tree**

The sum of the 20 integers belonging to the Tetrahedral Lambda is 350. The sum of the integers
at its vertices is 100. The sum of the integers at the centres of its four faces is **50**, which
is the number value of ELOHIM, the Godname of Binah. The sum of the 12 integers on its six edges other than
those at its four vertices is 200.

Compare this with the inner form of 10 overlapping Trees of Life. The first six polygons enfolded in one Tree of
Life have **26** corners, where **26** is the number value of YAHWEH, the
Godname of Chokmah. The highest corner of the hexagon coincides with the lowest corner of the hexagon enfolded in
the next higher Tree. Therefore, 25 corners are intrinsic to each set of six enfolded polygons. The 60 polygons of
the first six types enfolded in 10 overlapping Trees have 250 corners (shown in the diagram as blue & green
yods) that are intrinsic to them, the highest corner of the hexagon enfolded in the tenth Tree being a point shared
with the lowest corner of the hexagon enfolded in the eleventh Tree (it is shown as a bare corner without a blue
yod). The 10 triangles and 10 squares have **50** corners and the 40 other polygons of the first
six types have (250–**50**=200) corners. The former correspond to the sum (**50**) of the
integers at the centres of the faces of the Tetrahedral Lambda and the latter correspond to the sum of the 12
integers on its edges other than those at its vertices. The 10 hexagons and the 10 pentagons also have
**50** corners, and so the selection of the triangles and squares as corresponding to the sum
**50** needs justification. This is provided by the 1-tree, which is discussed next.

The 1-tree has 251 yods when its 19 triangles are Type A triangles. Daath of the 1-tree becomes
Yesod of the second Tree and so the white yod that denotes it in the diagram is the only yod that is not an SL
of the 1-tree but an SL of the next higher Tree. It has to correspond to the topmost corner of the hexagon
enfolded in the tenth Tree, which is shared with the hexagon enfolded in the next higher Tree; in each case the
yod is not intrinsic to the lowest 10 Trees or the 1-tree. The 250 yods that *are* intrinsic to the
1-tree comprise **50** green hexagonal yods on its 25 Paths and 200 blue yods. The (10+1) top
and bottom corners of the hexagons have to correspond to the (10+1) SLs of the 1-tree because Daath corresponds
to the topmost corner of the hexagon in the tenth Tree. As SLs are denoted by blue yods, this means that the
corners of the hexagons have to denoted by blue yods. The sum of the integers at the centres of the faces of the
Tetrahedral Lambda is:

6 + 8 +
12 + 24 = (6 + 24) + (8 + 12) = 30 + 20 =
**50**.

This 30:20 split in the sum **50** is naturally reproduced in the geometry of
the polygons by the 30 corners of the triangles and the 20 remaining corners of the squares. If the sum
corresponded to the **50** corners of the pentagons, this would require the 20 endpoints of
their root edges to correspond to the sum of the integers on the second and third faces, which seems,
intuitively speaking, to be wrong, as these endpoints represent the start and end of the generation of each set
of polygons, whilst these faces are intermediate stages in the generation of the Tetrahedral Lambda. The same
conclusion would apply to the hexagons. Hence, the 'correct' correspondence is with the triangles and
squares.

The squares of the numbers of corners of the first six polygons making up the inner form of the Tree of Life add up
to 250:

This is amazing in itself, given that the 60 polygons of these types enfolded in 10 overlapping Trees of Life have
250 intrinsic corners. What is more remarkable still is that the sum of the first three squares 3^{2},
4^{2} & 5^{2} is **50** and that the sum of the last three squares
6^{2}, 8^{2} & 10^{2} is 200. In other words, the distinction between the
four integers at the centre of the Tetrahedral Lambda and the 12 integers on its edges between its vertices
corresponds to the division of the first six polygons into the first three polygons and the last three polygons.
Such simple correlation and harmony of number and geometry cannot be the result of coincidence. Instead, it is a
clear manifestation of a universal, coherent *design* shared by sacred geometries such as the inner
form of the Tree of Life and the 1-tree.

A Type C triangle has 127 yods. The two triangles in the inner form of the Tree of Life have 250 yods when they are
both Type C. They comprise 30 black yods that are corners of the 54 tetractyses, 20 purple hexagonal yods outside
their shared root edge on the sides of the sectors of each triangle and 200 white hexagonal yods. The two Type C
triangles display the same 30:20:200 pattern as that displayed by the 16 integers in the Tetrahedral Lambda other
than those at its vertices, by the 250 corners of the first six polygons enfolded in 10 Trees of Life and by the
250 yods in the 1-tree!

The reason for this correspondence is that the Type C triangle is the *fourth* stage of the Pythagorean
differentiation of a triangle:

tetractys → Type A triangle → Type B triangle → Type C triangle

and therefore, according to the Tetrad Principle formulated in Article 1, it will embody numbers that are parameters of holistic systems, such as the
three mentioned above (note: not only the same global parameters but also the pattern of their breakdown into
other parameters). Confirmation of this is how the two Type C triangles embody the
**248** roots of E_{8}, the gauge symmetry group describing the unified force between
E_{8}×E_{8} heterotic superstrings of ordinary matter. This is discussed in the section
**Superstrings as sacred geometry/Tree of Life**.
**248** is a parameter of holistic systems, being the number value of *Raziel*, the
Archangel of Chokmah.