Updated: Sep 27, 2020
When their 35 sectors are turned into tetractyses, there are 168 yods associated with each set of the first six enfolded polygons other than their 26 black corners. The pentagon has 24 blue yods, the triangle, square & decagon have 78 green yods and the hexagon & octagon have 66 red yods. The 168 yods divide naturally into 78 yods of one subset of polygons and 90 yods of a second subset — a circumstance that is highly unlikely to occur by chance, given that: 1. 168 is the number value of Cholem Yesodeth, the Mundane Chakra of Malkuth, 2. 78 is the number of Cholem, and 3. 90 is the number of Yesodeth, allowing for contraction of the gematria number 400 of its letter tav to 4.
The first six polygons embody the number of Cholem Yesodeth because this subset of the seven polygons forming the inner Tree of Life constitute a holistic system in itself, so that their properties are quantified by the same table of number values of Sephiroth, Godnames, etc that quantify all seven polygons. For example, see page 4 of Article 4 for how the Godnames prescribe each set and both sets of the first six polygons.
For the 60 polygons of the first six types enfolded in 10 Trees of Life, the numbers 24, 78 & 66 merely increase by a factor of 10, so that the 1680 yods associated with each set of 60 polygons other than their corners comprise 240 blue yods in pentagons, 780 green yods in triangles, squares & decagons and 660 red yods in hexagons & octagons. Compare these numbers with the geometry of the disdyakis triacontahedron. When its internal triangles are divided into sectors, 240 corners and 780 sides of 660 triangles surround an axis passing through two opposite vertices, i.e., 780 sides & 900 corners & triangles. The gematria number values of Cholem and Yesodeth are reproduced in the very geometry of the disdyakis triacontahedron because it is the polyhedral counterpart of the outer Tree of Life.
This is a remarkable illustration of how bits of information about the polyhedral version of the inner form of the Tree of Life are encoded in its polygonal representation. 1680 geometrical elements in the disdyakis triacontahedron surround the axis, illustrating the formative character of this number. It is the polyhedral counterpart of the 1680 turns in each helical whorl of the UPA/superstring.
The superstring structural parameter 1680 is also embodied in the geometry of all seven regular polygons enfolded in each of the 10 Trees of Life. For details, see #18.