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**#56 How the hexagram determines the superstring structural parameter
336**

336 = |

The 22nd triangular number is

1 + 2 + 3 +... + 22 = 11×23 = 253.

It is represented by an equilateral triangular
array of 253 dots, with 22 dots along each side of the array. 252 dots surround its centre, where 252 is the sum of
the first **21** integers after 1:

252 = 2 + 3 + 4 +... + 22.

The hexagram (or Star of David) that is formed
by the intersection of two such arrays has six triangular points with eight dots arranged along each side. A
point of the star has (1+2+3+4+5+6+7+8=**36**) dots. The complete star is composed of six
parallelograms, with eight dots along each side. A separate parallelogram comprises
(8^{2}=**64**) dots. When part of the star, it shares eight dots with its neighbour on one
side and eight dots with its neighbour on the other side. It contributes (**64**-8=56) dots to the
total population of dots surrounding the centre of the star, which is (56×6=336) dots. Each triangular array
contributes (336/2=**168**) dots, so that the pair of intersecting triangles forming the hexagram
expresses the split into two equal numbers:

336 = **168** + **168**

that is characteristic of holistic systems
embodying this parameter. In particular, each complete revolution about its axis of spin of a helical whorl of the
UPA/E_{8}×E_{8} heterotic superstring comprises 336 circular turns, of which **168**
turns make up an outer half-revolution of the whorl and **168** turns comprise an inner
half-revolution. This is the superstring manifestation of the pair of intersecting triangles in the hexagram, whose
traditional meaning is one of symbolising the union of Divine Spirit and matter.

The superstring structural parameter 336 is
the arithmetic mean of the squares of the first **31** integers:

336 = (1^{2} + 2^{2} +
3^{2} +... + **31**^{2})/**31**,

where **31** is the number value
of EL ("God"), which is the Godname assigned to Chesed, the first Sephirah of Construction.

When constructed from 1st-order tetractyses,
the hexagram has **73** yods, where **73** is the number value of Chokmah:

73 = |

The Archangel assigned to this Sephirah is
*Raziel*, whose number value is **248**. This number is the dimension of the rank-8, exceptional
Lie group E_{8}, whose symmetries belong to the unified force between E_{8}×E_{8} heterotic
superstrings. The UPA described by Besant & Leadbeater is their subquark state. The hexagram therefore provides
a connection between the structural and dynamical parameters of this state of the E_{8}×E_{8}
heterotic superstring.

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