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**The five Platonic solids embody the number 137 determining
the fine-structure constant**

The table in **Sacred geometry/Platonic
solids** shows that 1820 yods surround the centres of the five Platonic solids with Type
A triangles as sectors of internal triangles. They include 90 centres of internal triangles and
**50** centres of faces, that is, **140** corners of tetractyses. Hence,
(1820–**140**=1680) yods other than these non-polyhedral corners surround the centres of the five
regular polyhedra. This is remarkable because the UPA, the basic constituent of matter observed with micro-psi
by Besant & Leadbeater, has 1680 turns in each of its ten helical whorls (see page 11 at **Occult
Chemistry**).

The sceptic may argue that, by ignoring the non-polyhedral corners, this number has been merely
obtained by cherry-picking various numbers of yods, so it is not proof that the five Platonic solids embody the
superstring structural parameter 1680. However, it is hardly cherry-picking to point out that these solids have
1680 vertices and hexagonal yods surrounding their centres — a mathematical fact that sceptics must,
implausibly, dismiss as a coincidence. Even so, the remarkable property to be described next refutes their
criticism: their **50** faces have 180 sectors, so that, when these are tetractyses containing
720 hexagonal yods, (720−180=540) such yods line their (90+180=270) sides. The **50** vertices
and the **50** face-centres of the five Platonic solids also line these tetractyses, making a
total of **640** yods that line sides of 180 tetractyses in the faces, where
**640** is the number value of *Shemesh*, the Mundane Chakra of Tiphareth. According to
the table cited above, there are 910 internal hexagonal yods. Of these, (90×3=270) hexagonal yods are at the
centres of the sectors of the 90 internal triangles formed by the 90 edges of the five Platonic solids. This leaves
(910−270=**640**) hexagonal yods lining sides of 270 internal tetractyses. They also have 90 internal
corners, excluding the centres of the solids (**95** when included, where
**95** is the number value of *Madim*, the Mundane Chakra of Geburah), so that
(**640**+90=730=**73**×10) yods other than these points line internal tetractyses, where
**73** is the number value of Chokmah. The number of yods lining the (180+270=450) tetractyses =
**640** + 730 = 1370. But this is the number of yods in the (7+7) enfolded Type B polygons of the
inner Tree of Life (see here)! A number that measures the inner form of the Tree of Life
reappears in the five Platonic solids as a number that quantifies their construction from tetractyses, starting
with the mathematical points at their centres. Given their archetypal status, this cannot be coincidence — especially when it involves the
number 137 regarded by physicists as one of the most important numbers in physics because it
determines the fine-structure constant. Instead, it is remarkable evidence for their constituting the
regular polyhedral counterpart of the inner Tree of Life. Just as the superstring structural parameter 1680 is
embodied in the latter, as demonstrated in many pages and articles on this website, so, too, it can be found in
the collective yod composition of its regular polyhedral counterparts. It is *neither* by mere
chance nor by contrivance that this happens. Instead, these numbers reappear in different sacred geometrical
contexts because these geometries are analogous holistic systems and, therefore, they *must* possess
the *same* parameters and patterns of division. This will be demonstrated on the next page in the
case of the first four Platonic solids.

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