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#23 How five sacred geometries embody the (72+168) roots of E8

 

Correspondences between 5 sacred geometries

 

 

 

There are:

1. 240 yods other than Sephiroth in the 1-tree constructed from Type A triangles (see a). They comprise the 72 yods in its trunk & root (see here for their definition) and 168 yods in its branches;
2. 240 yods on the boundaries of the two separate sets of the seven enfolded polygons (see (b)). They comprise 72 black yods at corners and 168 red hexagonal yods (see here for further discussion);
3. 240 hexagonal yods on the faces of the first three Platonic solids whose sectors are tetractyses (see (c)). They comprise 72 black yods in the faces of half the tetrahedron and half the octahedron and 168 red yods in their remaining faces (see here for further discussion);
4. 240 vertices, sides & triangles surrounding the centre of the 2-dimensional Sri Yantra (see (d)). They comprise 69 vertices and the three sides of the central triangle, i.e., 72 geometrical elements, and 168 sides & triangles that surround the central triangle (see here for further discussion);
5. 240 hexagonal yods in the 60 faces in each half of the disdyakis triacontahedron when each face is a tetractys (see (e)). They comprise 72 black hexagonal yods, which are either at centres of tetractyses or on the equator when its plane is perpendicular to an axis passing through two diametrically opposite A vertices, and 168 red hexagonal yods on the 84 edges either above or below the equator (see here for further discussion).

These analogies between the properties of five sacred geometries exist because they are all equivalent representations of the cosmic blueprint that embodies the divine archetypes. This blueprint manifests in the subatomic world as the UPA, the subquark state of the E8×E8 heterotic superstring. Article 53 discusses the correspondences in more detail.

 

 

248 corners of Type B polygons in outer and inner Trees of Life  

 

 

 

 

When regarded as separate from each other, the outer and inner forms of the Tree of Life are composed of 426 triangles with 248 corners (74 in its outer form and 174 in its inner form). Eight corners (denoted by white yods) are either shared between the outer and inner forms or have — as their projections onto the plane of the enfolded polygons — the two endpoints of the root edge of the latter. This leaves 240 corners which are unshared. There are (74−2=72) unshared corners in the outer Tree of Life and (174−6=168) unshared corners in the inner Tree of Life. The 240 unshared corners in the separate outer and inner forms of the Tree of Life denote the 240 roots of E8 and the 72 corners in the outer Tree unshared with those in the inner Tree denote the 72 roots of E6.

In all these sacred geometries, the number 72 plays the more fundamental role in marking out in each case the skeletal foundation, whilst the number 168 "fleshes out", so to speak, the complete form of the geometrical object.

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