An arithmetic connection between the outer form of the 1-tree and its inner form.
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#77 The corners of the first 6 polygons in the inner Tree of Life arithmetically determine the yod population of the 1-tree
When the 19 triangles making up the 1-tree are Type A triangles, they contain 251 yods. 11 of these are their corners, (4×19=76) are either their centres or hexagonal yods at the centres of their (3×19=57) tetractyses, (25×2=50) are hexagonal yods lining their sides and (6×19=114) are hexagonal yods lining the 57 sides of tetractyses inside the 19 triangles. Hence, (11+76=87) yods are either corners or centres of tetractyses and (50+114=164) hexagonal yods line their 82 sides.
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87 is the number value of Levanah, the Mundane Chakra of Yesod, where 87 = 12 + 32 + 42 + 52 + 62, whilst 164 = 82 + 102. Therefore, the yod population of the 1-tree is
251 = 12 + 32 + 42 + 52 + 62 + 82 + 102.
The integers 3, 4, 5, 6, 8 & 10 are the numbers of corners of the first six regular polygons making up the inner form of the Tree of Life. 247 yods line the 48 tetractys sectors of all seven separate polygons. Including with this set of polygons the root edge lined by four yods, there are (247+4=251) yods. This is the number of yods in the 1-tree! The number 1 can be associated with one endpoint of the root edge. The squares of the numbers 1, 3, 4, 5 & 6 add up to the number of yods that are either corners or centres of the 57 tetractyses in the 1-tree. The squares of the integers 8 & 10 denoting the numbers of corners of the octagon and decagon add up to the number of hexagonal yods lining the sides of these tetractyses.
More evidence for the holistic nature of the number 251 as both the yod population of the 1-tree and the number of yods creating the root edge and the 48 sectors of the seven polygons is the following: the three regular polygons absent from this set of polygons are the heptagon with seven corners, the nonagon with nine corners and the undecagon with eleven corners. There are 10 polygons up to the dodecagon. The first six polygons bear a correspondence to the six Sephiroth of Construction above Malkuth, which corresponds to the last polygon, the dodecagon, whilst the three absent polygons correspond to the three members of the Supernal Triad, representing the hidden triple Godhead. Assigning the squares of 7, 9 & 11 to the corners of a tetractys, which symbolise the Supernal Triad, and the squares of 3, 4, 5, 6, 8, 10 & 12 to the seven hexagonal yods in this tetractys, which symbolise the seven Sephiroth of Construction (with 122 assigned to the central hexagonal yod symbolising Malkuth), their sum is 645:
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72 |
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32 |
42 |
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645 = |
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102 |
122 |
52 |
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92 |
82 |
62 |
112 . |
It is truly remarkable that the sum of the squares of the numbers of corners of the three absent polygons is also 251:
251 = 72 + 92 + 112.
Its holistic nature is discussed here. How it is embodied in the seven enfolded polygons is discussed here.
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