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**#33 How sacred geometries embody the superstring
structural parameter 1680**

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a) ADONAI, the Godname of Malkuth, prescribes the lowest 10 Trees mapping the 10 spatial
dimensions of 11-dimensional space-time predicted by M-theory because its number value **65** is
the number of SLs in the 10-tree. Below the **65**th SL are __1680 yods__ when all the
triangles are Type A. They symbolize the 1680 circular turns of each helical whorl of the UPA, the subquark state
of the E_{8}×E_{8} heterotic superstring remote-viewed by Annie Besant & C.W. Leadbeater
(see **Occult Chemistry**). This Tree of
Life representation of each whorl is discussed further in #2.

b) The two sets of the first six enfolded polygons of the inner Tree of Life constitute a
holistic system, containing 384 yods unshared with polygons enfolded in the next higher Tree when their 70 sectors
are tetractyses. They comprise **48** corners of the 12 polygons and 336 yods.
**168** yods other than these corners are associated with each set of six polygons. Associated
with each set of 60 polygons enfolded in the 10-tree are 240 corners and __1680 yods__. Each yod denotes a turn
of a helical whorl of the subquark superstring. This is discussed in #3.

c) The 12 sectors of a Type B dodecagon have 13 corners and **168** other
yods. The two joined Type B dodecagons have 24 corners of sectors and 336 yods, **168** yods
being associated with each one. Hence, __1680 yods__ other than such corners are associated with each set
of Type B dodecagons enfolded in 10 Trees of Life. See #3 for further discussion.

d) The seven enfolded polygons of the inner Tree of Life comprise 176 corners (points), sides
(lines) & triangles. Outside the root edge with two endpoints and a line there are three corners & two
lines that coincide with either side pillar of the outer Tree of Life. Therefore,
(176−2−1−3−2=**168**) geometrical elements in each set of seven enfolded polygons outside the root
edge are intrinsic to the inner Tree of Life because they are unshared with the outer Tree. Outside the root edges
of each set of 70 polygons enfolded in the 10-tree are __1680 intrinsic geometrical elements__. This is
discussed in #18.

e) The 94 sectors of the (7+7) enfolded polygons have **80** corners. When the
polygons are Type B, 94 corners (centres of sectors) are added. Of the 174 corners of the
**282** triangles in the (7+7) Type B polygons, six corners coincide with corners of triangles
belonging to the outer Tree of Life. This leaves **168** unshared corners that are
*intrinsic* to the inner Tree of Life. The 2820 triangles in the 940 sectors of the (70+70) polygons
enfolded in the 10-tree have __1680 intrinsic corners__. See also #26.

f) Surrounding an axis of the disdyakis triacontahedron with its edges as sides of internal Type
A triangles are __1680 geometrical elements__. They comprise 240 corners, 780 sides & 660 triangles. Compare
this with the fact that associated with each set of the first six polygons enfolded in the 10-tree are 1680 yods
other than their corners that comprise 240 yods in the pentagons, 780 yods in the triangles, squares & decagons
and 660 yods in the hexagons & octagons. This is also discussed in #4.

g) **21** Platonic solids that are either tetrahedra, octahedra, cubes or
icosahedra can be fitted in the vertices of the disdyakis triacontahedron. They have __1680 hexagonal
yods__ in their faces when the latter are constructed from tetractyses. See further discussion in
#5.

h) When their vertices and centres of faces are joined to their centres, the tetrahedron,
octahedron, cube & icosahedron have __1680 geometrical elements__ surrounding axes passing through
their centres and two opposite vertices (its centre and any two vertices in the case of the tetrahedron). Like the
disdyakis triacontahedron, they, too, comprise 240 corners, 780 sides & 660 triangles. This is analyzed further
in #20 & #31.

i) The 2-dimensional Sri Yantra is the result of the overlap of nine primary triangles (see
here). **26** of their 27 corners belong to the 42 resulting
triangles that surround the central one. When these triangles are Type B, they contain __1680
yods__ other than these **26** original corners (denoted in the diagram by white yods)
and the **168** internal corners (also coloured white) of the 378 tetractyses in these
triangles. See #6 discussed at **Superstrings as sacred
geometry/Sri Yantra**.

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