Tree of life superstring theory part 56

Updated: Sep 27, 2020

According to Table 8 here, the number GnN of geometrical elements in the nth-order N-gon is GnN = (3n+1)N + 1,where "1" denotes its centre. Therefore, the number of geometrical elements surrounding the centres of the seven separate types of 1st-order polygons with 48 corners that make up the inner Tree of Life = ∑G1N = (31+1)∑N = 4×48 = 192. Surrounding the centres of the two sets of seven separate 1st-order polygons are (192+192=384) geometrical elements (seehere). According to Table 8, the number of corners surrounding the centre of  an 1st-order N-gon = N, the number of sides = 2N and the number of triangles = N.  The 384 geometrical elements therefore comprise 192 corners & triangles and 192 sides. This 192:192 division is characteristic of the number 384 as the global parameter of holistic systems (see here). It reappears in the combined outer & inner forms of the Tree of Life as their 192 corners & triangles and the 192 sides (see here). According to Table 10 here, it reappears in the 14 enfolded polygons of the inner Tree of Life as the 3840 sides of triangles that are outside the root edge shared by these polygons when they are 4th-order, each set of seven enfolded polygons having 1269 triangles with 1920 sides outside this root edge: 

Including the root edge, the inner Tree of Life with 4th-order polygons contains 2538 triangles with 3841 sides

The representation comprises 91 squares, where 91 = 12 + 22 + 32 + 42 + 52 + 62. The central square 12 corresponds to the root edge. The sum (1920) of the 45 squares of 2-10 in each pentagram is the number of sides of the 1269 triangles in each half of the inner Tree of Life outside the root edge shared by the two sets of seven polygons. This is the arithmetic counterpart of a geometrical object that has a holistic character because it embodies the same patterns and parameters as other sacred geometries.

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