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**19. The Godname EL CHAI prescribes the number of edges of
the 4 _{21} polytope**

Each half of the 4 |
The number value 49 of EL CHAI, the Godname of
Yesod, is the number of yods in an octagon with tetractyses as sectors. 336 yods surround the
centre of a Type C octagon. Weighted with the Decad, the 672 yods surrounding the centres of the
two Type C octagons generate the number (6720) of edges of the 4_{21}
polytope. |

An octagon whose sectors are tetractyses contains **49** yods. This is the
number value of EL CHAI ("God Almighty"), the Godname of Yesod. The centre of the Type C octagon is surrounded by
336 yods.* Weighted with the number 10 (Decad), the 672 yods surrounding the centres of the two Type C octagons
that are part of the inner Tree of Life generate the number 6720. *This is the number of
edges of the 4 _{21} polytope*. When they are Type B, the two octagons have 240 yods
surrounding their centres.**

The physical significance of the Decad in this context is that it refers to the 10 whorls of the UPA. The 336 yods surrounding each Type C octagon denote the two sets of 336 plane wave components of the 336 circularly polarised waves in each revolution of a whorl, the weight 10 assigned to them indicating that this oscillatory pattern is repeated in all 10 whorls.

As

**15**^{2} − 1 = 224,

**15**×(**15**^{2} − 1) = 5×3×224 = 5×672 = 3360 =
**15**^{3} − **15**.

This shows how the Godname YAH with number value **15** prescribes the 3360
edges in each half of the 4_{21} polytope. As

3360 = **15**×(**15**^{2} − 1) =
**15**×(3+5+7+...+29),

6720 = 2×3360 = 30×(3+5+7+....+29) =
10×(9+**15**+**21**+...+**87**).

This shows how the number of edges in the 4_{21} polytope is determined not only by
the Godname of Yesod but also by the number value **87** of its Mundane Chakra, *Levanah*.
As 6720 = 84×**80**, this number is generated by assigning the number **80** of
Yesod to the 84 yods surrounding the centre of a 2nd-order tetractys:

The
number |

The Tetrad is symbolised by the four corners of a square. When the 25 yods of a Type A square are weighted with the number 672, they generate the number 16800:

The Tetrad symbolised by the square
generates the number of turns in the 10 helical whorls of
the UPA/superstring through the number 672 embodied in sacred geometries and in the
4_{21} polytope. |

This is evidence showing the mathematical connection between the superstring structural
parameter 16800 paranormally discovered over a century ago, the geometrical symbol of the four Elements of Earth,
Water, Air & Fire and the holistic parameter 672 found in sacred geometries and in the
4_{21} polytope.

For more details on how sacred geometries embody properties that are analogous to the vertices
& edges of the 4_{21} polytope, see Article 63 (Web, PDF).

* Proof: A Type C polygon with n sides has (42n+1) yods. A Type C octagon (n=8) has 337 yods. 336 yods surround its centre.

** Proof: A Type B polygon with n sides has (**15**n+1) yods. A Type B octagon has
121 yods. 120 yods surround its centre. (120+120=240) yods surround the centres of two Type B octagons.

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