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The 10-fold UPA/superstring as the 10-fold division in the yods on edges of tetractyses in the pair of Type A decagons

The sixth regular polygon in the inner form of the Tree of Life is the decagon. Constructed from tetractyses, it is the polygonal representation of ten overlapping Trees of Life because its 61 yods correspond to the 61 SLs up to Chesed of the tenth Tree. Each sector is the counterpart of a Tree, the six yods per sector being the counterpart of the six SLs per Tree. In the Type A decagon, 120 yods line the 50 sides of its 30 tetractyses and surround its centre. There are 12 boundary yods per sector. The two Type A decagons have (120+120=240) yods surrounding their centres that line the 100 sides of their 60 tetractyses. They comprise (12+12=24) boundary yods per pair of sectors. Therefore, the 240 boundary yods consist of ten sets of 24 yods. Three pairs of sectors (coloured white, grey & dark grey) have (3×24=72) boundary yods and the remaining seven pairs of sectors with the seven colours of a rainbow have (7×24=168) boundary yods. Starting from a point (centre of decagon), 240 yods are needed to delineate the tetractyses that make up two Type A decagons, 24 per pair of sectors. This 72:168 pattern is analogous to what was discussed on the previous page. Instead of ten geometrical elements, each repeated (12+12) times, we now have (12+12) yods that are repeated ten times.

The first six enfolded polygons up to the decagon have 26 corners. One of the corners is an endpoint of the root edge shared not only amongst the six polygons but also with the mirror image set of six polygons. When sets of polygons enfolded in overlapping Trees of Life are considered, the topmost corner of the hexagon coincides with the lowest corner of the hexagon enfolded in the next higher Tree. This means that 25 corners of the set of six enfolded polygons are intrinsic to that set, of which one corner (an endpoint of the root edge) can be associated with that set and one corner can be associated with the mirror image set. Hence, 24 intrinsic corners are associated with the set of of polygons enfolded in each Tree. The 60 polygons of the first six types enfolded in ten overlapping Trees of Life have 240 corners that consist of 24 corners repeated ten times.

The Decad (10) defines both the decagon with ten sides and the tenth polygon — the dodecagon. The pair of either polygon embodies ten sets of 24 geometrical elements or yods the microscopic manifestation of which are the 24 E8 gauge charges carried by each of the ten whorls of the UPA, the subquark state of the E8×E8 heterotic superstring. Here is yet more evidence provided by sacred geometry of the ten-fold nature of the basic unit of matter paranormally described by Annie Besant & C.W. Leadbeater.

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