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#67 The (192+192) permutations of the 2nd, 3rd & 4th rows of tetractyses in two hexagons conform to the pattern of holistic systems

The two objects in the second row of a tetractys have (2!=2) permutations, the three objects in the third row has (3!=6) permutations and the four objects in the fourth row have (4!=24) permutations. The nine objects in the lowest three rows form 32 permutations. An n-gon with tetractyses as its sectors contains 6n yods surrounding its centre. There are 32 permutations of these yods per sector, so that the 6n yods form 32n permutations. Surrounding the centre of a hexagon (n=6) are 36 yods with (6×32=192) permutations. ELOHA, the Godname of Geburah with number value 36, prescribes the 192 permutations of the 18 rows of yods in the hexagon. The four yods lining any side, in particular the left-hand side that becomes the root edge when it is part of the inner Tree of Life, have 24 permutations. The 192 permutations consist of these 24 permutations and the 168 permutations of the 32 yods in the remaining 17 rows. Similarly, the other hexagon in the inner Tree of Life has 36 yods surrounding its centre with 192 permutations that comprise the 24 permutations of the four yods in its right-hand side and the 168 permutations of the 32 yods in the remaining 17 rows. This 24:168 division is characteristic of holistic systems embodying their defining parameter 192 (see The holistic pattern). For example, the 64 trigrams making up each diagonal half of the 8×8 array of 64 hexagrams have 192 lines & broken lines. They consist of the 24 lines & broken lines in the eight diagonal trigrams and the 168 lines & broken lines in the 56 off-diagonal trigrams. The division manifests uniquely in this polygon because the hexagon is the fourth regular polygon and the Tetrad Principle formulated in Article 1 states that the fourth member of any class of mathematical objects embodies parameters of holistic systems. The two hexagons have (36+36=72) yods surrounding their centres with (192+192=384) permutations. This is the number of permutations of the 36 rows of yods in a dodecagon for the simple reason that this polygon has twice the number of sectors as a hexagon. The number 384 is another parameter of holistic systems (see #58 & #59; for its musical counterpart, see #60). It is prescribed by the Decad (10) because the dodecagon is the tenth regular polygon.

The hexagon is unique amongst polygons in having permutational properties of its yods that match the archetypal pattern characterizing holistic systems — or rather, that in each half of such a system. Only the dodecagon possesses permutational properties that match the whole system. This confirms its holistic character, as discussed in Power of the polygons (see here).

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