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**The first four Platonic solids embody the superstring
structural parameter 168**

The table in **Sacred geometry/Platonic
solids** indicates that, including their centres, the numbers of yods needed to construct
from tetractyses the faces and internal triangles of the first four Platonic solids are:

Tetrahedron: | 71 |

Octahedron: | 135 |

Cube: | 139 |

Icosahedron: | 327 |

Total = | 672 |

The average number of yods needed to construct one of these regular polyhedra = 672/4 =
**168 (**84 yods for each half, the centre being shared by both halves). This shows how they embody
the superstring structural parameter **168**, as well as the dimension **248** of
the exceptional Lie symmetry group E_{8} as the number of corners & sides of the 120 sectors in
their 38 faces. The division: **168** = 84 + 84 is characteristic of holistic systems (see
here). It manifests in the E_{8}×E_{8} heterotic
superstring as the 840 turns in an outer or inner half of each whorl of the UPA, i.e., as the 84
turns in an outer or inner quarter-revolution of a whorl. *When averaged over
the first four Platonic solids, each half of a solid corresponds to a quarter-revolution of an outer or inner
half of a whorl: 336/4 = 84*. The table indicates that there are 124 yods making up what were called
on page 16 the "Type A interiors" of these four Platonic solids. This means that, on average,
**31** yods are needed to construct their interiors and
(**168**−**31**=137) yods are needed to create their faces. It shows how the number
137, which is one of the most important numbers in modern physics because its reciprocal is approximately equal
to the fine-structure constant α = e^{2}/ħc ≈ 1/137, *shapes*
the first four Platonic solids, which were thought by the ancient Greeks to be the forms of the
particles composing the elements Earth, Water, Fire & Air. The fine-structure constant is the
electromagnetic coupling constant that measures the strength of the coupling between the negatively charged
electron and the electromagnetic field. It is also the ratio of the average velocity of an electron in the
hydrogen atom to the velocity of light *in vacuo*. The number 137 is prescribed by EL because
**31** is the number value of this Godname of the Sephirah Chesed. Sixty-eight yods in the 38
faces of the first four Platonic solids are corners of tetractyses, leaving 480 hexagonal yods. This means that
their faces on average are made up of 30 tetractyses with (68/4=17) corners and (480/4=120) hexagonal
yods. The basic distinction in a tetractys between its corners and its hexagonal yods, which
symbolize, respectively, the Supernal Triad and the seven Sephiroth of Construction, generates the
division:

137 = 17 + 120.

This will be referred to in the discussion of how, as the outer form of the Polyhedral Tree of Life, the disdyakis triacontahedron embodies structural and dynamical parameters of superstrings (see here).

The significance of the yod population 672 of the first four Platonic solids vis-à-vis the
4_{21} polytope, whose 240 vertices represent the 240 roots of E_{8}, is
discussed here.

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