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The table lists the numbers of vertices (V), edges (E), faces (F) & yods (I) inside each face of the Platonic
solids. Also listed are the numbers of yods (including hexagonal yods) in their surfaces and the number of yods
(including hexagonal yods) in their interiors. As an internal triangle can be regarded as either a tetractys (let
us call such an interior "Type A") or as having three sectors that are tetractyses (let us call it "Type B"), there
are two cases to consider. The first four Platonic solids have 548 yods in their 38 faces. The average number of
yods needed to construct their faces = 548/4 = 137. This is the number that is well-known in physics because
it determines the fine-structure constant α. The total number of yods in the first four Platonic solids is 672.
The average number of yods needed to build their faces and interiors = 672/4 = **168**. This is
remarkable because **168** is the Mundane Chakra of Malkuth and the average number of turns in
a half-revolution of a whorl of the superstring making up the quarks in protons and neutrons inside atomic
nuclei, as remote-viewed by Annie Besant & C.W. Leadbeater (see **Occult Chemistry**).
**Hence, the surface and volume of the first four Platonic solids associated with the Elements Fire, Air,
Water & Earth embody the numbers determining the fine-structure constant and the winding number of the
E _{8}×E_{8} heterotic superstring!** The latter is discussed in detail here. As explained in

According to the table, the faces of the five Platonic solids with tetractyses as their sectors
have 820 yods. This is the sum of the squares of the integers 1, 3, 9 & 27, the first four members of a
geometric series that mark out one side of Plato's Lambda, the strip of the material of the World Soul from
which, according to Plato's *Timaeus*, God fashioned the celestial sphere (see here):

1^{2} + 3^{2} + 9^{2} + 27^{2} = 820.

The average number of yods needed to construct their faces = 820/5 = 164 = 3^{2} +
5^{2} + 7^{2} + 9^{2}. This illustrates the Tetrad Principle formulated in Article 1, whereby properties of holistic systems are quantified by either the
*fourth* of a class of mathematical object or the sum of the first *four* members of such a class.
In this case, 164 is the squares of the first *four* odd integers after 1. The number of corners of their
180 tetractyses = 100 = 1^{3} + 2^{3} + 3^{3} + 4^{3}. The average number of
corners = 100/5 = 20 = 2 + 4 + 6 + 8. The number of hexagonal yods = 720 = 30×24 = 1×2×3×4(1^{2} +
2^{2} + 3^{2} + 4^{2}). The average number of hexagonal yods = 720/5 = 144 = 9×16 =
9×4^{2} = 9(1 + 3 + 5 + 7) = 9 + 27 + 45 + 63

1

^{0}2^{0}3^{0}4^{0}1

^{1}2^{1}3^{1}4^{1}=

1^{2}2^{2}3^{2}4^{2}1

^{3 }2^{3}3^{3}4^{3}.

The dodecahedron with Type B interior triangles has 550 hexagonal yods. This number is
defined by the Decad (10) because 550 = 55×10, where 55 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10. It is a basic
parameter of all holistic systems. **Maps of reality** discusses how
the number 550 is found in other sacred geometries to be a measure of the spiritual cosmos.

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