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Equivalence of the pair of dodecagons and the Lambda Tetractys

 

 

  (6+48+36) geometrical elements in pair of joined dodecagons

 

6 unpaired red points & lines
48 blue lines & triangles
36 green points & lines

 

Figure 18. The 6:48:36 pattern in the 90 geometrical elements
that surround the centres of the two joined dodecagons.

 

The fact that it requires 138 yods to construct the pair of joined dodecagons — the same number as the sum of the powers of 1, 2, 3 & 4 on the inclined edges of the Tetrahedral Lambda — is evidence of their holistic nature. Their geometrical composition is further evidence because it conforms to the archetypal pattern of the Lambda Tetractys, as now explained. Figure 18 shows the points (corners), lines (sides) & triangles (sectors) in the two joined dodecagons. Each dodecagon divided into its 12 sectors consists of 13 corners and 24 sides of 12 triangles, i.e., 49 geometrical elements, where 49 is the number value of EL ChAI, the Godname of Yesod. As a side consists of a straight line and the point at each end of it, (49–3=46) elements are outside the root edge that it shares with the other dodecagon. 45 such elements surround its centre. Therefore, the two joined dodecagons comprise (3 + 2×46 = 95) geometrical elements. 95 is the number value of Madim, the Mundane Chakra of Geburah (see Table 1). (2×45=90) elements outside the root edge surround their centres. As was pointed out earlier (see Fig. 2), the number 90 is the sum of the 10 integers in the Lambda Tetractys. The two sides diametrically opposite the root edge (shown in red in Fig. 18) are the only sides whose six geometrical elements do not have a diametrically opposite counterpart in the two sets of 45 elements. All the 84 other geometrical elements have such counterparts on the opposite side of the centre of each dodecagon. They comprise 24 blue triangles and 24 blue internal sides, i.e., 48 blue lines & triangles, and 16 green corners and 20 green external sides, i.e., 36 green points & lines. The 90 geometrical elements that surround the centres of the two dodecagons, therefore, display the 6:48:36 pattern of the Lambda Tetractys that is characteristic of holistic systems. Either dodecagon can be regarded as the single, polygonal version of the outer Tree of Life, for 70 yods corresponding to the 70 yods in the 16 tetractyses that make up the latter are associated with each polygon when their 12 sectors are tetractyses (see Fig. 17).

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