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#71 The 120:144 division in four sacred geometries

a) Disdyakis triacontahedron
Suppose that the centres of the 120 triangular faces of the disdyakis triacontahedron are joined to its centre. The (120×3=360) sides of their (120×3=360) sectors inside their Type A triangular faces are sides of 360 internal triangles. When the latter are Type A triangles, this construction generates 360 internal corners and (360×3=1080) sides of their (360×3=1080) sectors, that is, 1440 corners & triangles. Also generated are 120 internal sides of these 360 internal triangles. Hence, (120+1080=1200=120×10) sides are generated, as well as 1440 (=144×10) corners & triangles. Sides of sectors of the faces create (1200+1440=2640=264×10) geometrical elements inside the polyhedron.

b) Two Type B dodecagons
Transforming a dodecagon with 12 corners into a Type B dodecagon requires 181 yods, i.e., (181−12=169) extra yods, including its centre. These new yods comprise 36 hexagonal yods (not shown in the diagram opposite, for the sake of clarity) at the centres of its 36 tetractyses, 61 red yods either on its sides, on its internal sides of sectors or at the centres of its 12 sectors and 72 blue hexagonal yods on sides of tetractyses inside each sector. The two joined, Type B dodecagons contain 358 yods. (358−3636=286) yods line the 119 sides of their 72 tetractyses. Of these, 22 yods are corners of the two joined dodecagons, leaving (286−22=264) boundary yods that are not their corners. In other words, 264 new yods on sides of tetractyses are needed to construct the joined pair of Type B dodecagons from these tetractyses. They comprise 120 red yods and 144 blue yods. The former belong entirely to the 24 sectors of the two Type A dodecagons when turned into tetractyses, whilst the latter yods further transform them into Type B dodecagons. The 120:144 division flags the presence of two levels of encoding of the morphology of the inner Tree of Life.

c) Inner Tree of Life
When the 47 sectors of the seven enfolded polygons of the inner Tree of Life are tetractyses, they contain 264 yods. 120 red yods line the sides of the polygons, shaping them, and 144 blue yods are inside their boundaries.

d) Polyhedral Tree of Life
The division: 264 = 120 + 144 is characteristic of holistic systems, such as the disdyakis triacontahedron, the seven enfolded, Type A polygons of the inner Tree of Life and the two joined, Type B dodecagons. It manifests in the Polyhedral Tree of Life (see here) as the 144 triangular faces of the 144 Polyhedron and the 120 triangular faces of the disdyakis triacontahedron. The 144 yods inside the boundaries of the seven enfolded polygons denote the former and the 120 yods on their boundaries denote the latter. The two types of yods — one shaping the polygons as their boundaries, the other constituting their interiors — reflect the Yang/Yin-type polarity or duality of functions that is embodied in the 144 Polyhedron and the disdyakis triacontahedron. These functions are represented in the masculine Pillar of Mercy and the feminine Pillar of Judgement of the outer Tree of Life (remember that the words "masculine" and "feminine" are used here in a metaphysical, not psycho-sexual, sense).

The Tetrad expresses both the holistic parameters 120 & 144 as 4×4 square arrays of the integers 1, 2, 3 & 4 raised, respectively, to the power of 2 and to the first four powers, namely, 0, 1, 2 & 3 (see diagram). Including the centres of their tetractyses, the two joined, Type B dodecagons contain 354 yods outside their shared side, where 354 = 14 + 24 + 34 + 44. Such mathematical beauty reflects the status of this regular polygon as the polygonal representation of the Tree of Life (see here). As

121 = 112 = 1 + 3 +... + 21,

120 = 3 + 5 + ... + 21,

i.e., 120 is the sum of the first ten odd integers after 1, whilst 144 = 122, where 12 is the number of corners of the tenth polygon, counting from a triangle with three corners. This shows how the Decad determines the holistic parameters 120 & 144. It also determines the 524 yods in the (7+7) enfolded polygons of the inner Tree of Life because this number is the sum of the cubes of the integers 1, 2, 3 & 4 assigned to the 61 yods of a decagon, which symbolizes the number 10 because it has 10 corners:

 524 = =

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