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In sacred geometry/tree of life, Stephen M. Phillips discussed various methods of transforming examples of sacred geometry in order to decode the scientific and spiritual information that they embody. The next level of decoding sacred geometry after the Pythagorean tetractys is through its next-higher version — the 2nd-order tetractys, in which each of the 10 yods of the tetractys is replaced by another tetractys. This generates 85 yods, which is the sum of the first four integer powers of 4
The yod at the centre of the 2nd-order tetractys denotes Malkuth of the central tetractys, which itself corresponds to this Sephirah. It is surrounded by 84 yods. The 2nd-order tetractys therefore expresses the fact that 84 Sephirothic degrees of freedom in a holistic system exist above Malkuth — its physical form. Of these, (7×7 − 1 = 48*) degrees are pure differentiations of Sephiroth of Construction symbolized by coloured, hexagonal yods in the seven 1st-order tetractyses that are not at the corners of the 2nd-order tetractys. The remaining 36 degrees are denoted by both the 15 white yods at the corners of the 10 tetractyses (these yods formally symbolize the Supernal Triad) and the 21 coloured, hexagonal yods that belong to the tetractyses at the three corners of the 2nd-order tetractys and which, therefore, also refer to the Supernal Triad of Kether, Chokmah & Binah. YAH, the older version of the Godname YAHWEH assigned to Chokmah, has the number value 15 and prescribes the 15 corners of the 10 1st-order tetractyses. ELOHA, the Godname of Geburah with number value 36, prescribes both the 36 yods lining the sides of the 2nd-order tetractys and the 36 yods just discussed. The number 84 is the sum of the squares of the first four odd integers:
where n is any positive integer, n^2 is the sum of the first n odd integers, so that 84 is the sum of (1+3+5+7=16=4^2) odd integers:
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The Tetrad determines the number of yods surrounding the centre of a 2nd-order tetractys. These yods include 15 corners of 1st-order tetractyses, where
15 =(2^0)+(2^1)+(2^2)+(2^3)= 1 + 2 + 4 + 8
(the number value of YAH) is the sum of the first four integer powers of 2. There are (85–15=70) hexagonal yods, where 70 = 10×7 = (1+2+3+4)×fourth odd/prime number. These two properties illustrate again how the Tetrad determines properties of the next higher-order tetractys above the 1st-order tetractys. In mathematics, triangular numbers (1, 3, 6, etc) can be represented by triangular arrays of dots and tetrahedral numbers (1, 4, 10, etc) can be represented as a tetrahedral pile of these arrays. The piles representing tetrahedral numbers can themselves be piled up into 4-dimensional "tetrahedral numbers": 1, 5, 15, 35, 70, etc. The fourth, non-trivial example of these numbers is 70. This is the number of hexagonal yods in the 2nd-order tetractys. Once again, the Tetrad determines both a class of number and a specific member of this class that is a parameter, or measure, of the Pythagorean representation of Wholeness. It is an example of how the Tetrad Principle governs the mathematical nature of holistic patterns and systems (for more details, see Article 1).
