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**#40 The geometrical composition of the combined outer &
inner Trees of Life reflects the root composition of E _{8}×E_{8}'**

__Outer Tree of Life__When they are Type A triangles, the 16 triangles making up the
outer Tree of Life have (16×3=

__Inner Tree of Life__

When they are Type A, the (7+7) enfolded polygons making up the inner Tree of Life have (47+47=94) sectors with
**80** corners. Two of these are endpoints of their shared root edge,
**72** corners are unshared with the triangles of the outer Tree and six corners coincide with
Sephirothic corners of triangles in the outer Tree. The 94 sectors have 175 sides, of which one is the root edge
and four sides are sides of triangles in the outer Tree. The inner Tree of Life has 349 geometrical elements, of
which 10 corners & sides are shared, leaving (349−3−10=336) intrinsic geometrical elements outside the root
edge. Each half of the inner Tree of Life comprises **168** geometrical elements that are
unshared with its outer form. *The number value of the Mundane Chakra of Malkuth measures the points, lines
& triangles that are intrinsic to each half of the inner Tree of Life*.

__Combined Trees of Life__When combined, the outer & inner Trees of Life have
(

168roots of E_{8}. This division can be made explicit by suitably dividing the outer Tree of Life into a left-hand half and a right-hand half, each with72geometrical elements (48corners & sides, 24 triangles) and associating each half with the left-hand or right-hand set of seven enfolded polygons, each with168unshared geometrical elements outside their root edge. The metaphysical distinction between the outer & inner Trees finds expression in the special significance of E_{6}, which string theorists have long considered as an intermediate stage in the symmetry breakdown of E_{8}that leads to the symmetries U(1)×SU(2)×SU(3) of the Standard Model. The inner Tree encodes the oscillatoryformof the UPA/subquark state of the E_{8}×E_{8}heterotic superstring, whilst the outer Tree encodes the E_{6}subgroups of each E_{8}. In #37, it was shown that the root and trunk of the outer Tree have three sets of 24 yods, whilst its branches have seven sets of 24 yods. This is the analogue of the three major whorls carrying the72gauge charges of E_{6}, 24 per whorl, and the analogue of the seven minor whorls carrying168gauge charges of E_{8}, 24 per whorl. Whereas the geometrical composition of the outer Tree of Life picks out E_{6}from other subgroups of E_{8}, its yod composition differentiates between the major and minor whorls of the UPA. They correspond, respectively, to the basic distinction between the root and trunk of the Tree of Life with three sets of 24 yods and its branches with seven sets of 24 yods.

This 240:240 division in the geometrical composition of the outer & inner Trees is also discussed in #29.

We find that the combined Trees of Life can be divided into two halves, one the mirror image of
the other. The 240 geometrical elements in each half outside the root edge comprise
**49** corners, 120 sides & 71 triangles, that is, (**49**+71=120) corners
& triangles and 120 sides. The 120:120 division in the number 240 is characteristic of holistic systems
embodying this parameter. It manifests in 4-dimensional sacred geometries as the 120 vertices, edges, faces
& octahedral cells in each half of the 24-cell (see here) and as the 120 vertices of each of the two 600-cells whose
compound is the 4-dimensional projection of the 4_{21} polytope (see discussion under "The
4_{21} polytope" here). See here for its appearance in other sacred geometries.

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