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disdyakis triacontahedron equivalent to inner form of 10 Trees of Life

 

The counterpart in the inner Tree of Life of the 240 corners, 780 sides & 660 triangles surrounding an axis that passes through two opposite A vertices of the disdyakis triacontahedron are the 24 blue yods other than corners outside the root edge of the pentagon, the 78 green yods other than corners in the triangle, square & decagon and the 66 red yods in the hexagon & octagon other than their corners. as discussed in many of the author's articles, these six polygons are a subset of the seven polygons that are themselves a holistic set. The 60 such polygons enfolded in ten overlapping Trees of Life have 240 blue yods, 780 green yods and 660 red yods. They are the counterpart of the 240 corners, 780 sides & 660 triangles that surround this axis of the disdyakis triacontahedron.

The 24:78:66 pattern of yods in the first six polygons enfolded in a single Tree of Life manifests in the simplest Catalan solid — the triakis tetrahedron. When constructed in a way similar to that described above for the most complex Catalan solid, there are 24 corners, 78 sides and 66 triangles in its faces and interior that surround an axis passing through two opposite vertices. It, too, embodies the number value 168 of Cholem Yesodoth, the number 78 of Cholem being the number of sides and the number 90 of Yesodoth being the number of corners & triangles. It is the polyhedral counterpart of the first six polygons enfolded in a single Tree of Life, whereas the disdyakis triacontahedron is their counterpart enfolded in 10 Trees of Life — the complete, expanded representation of the Tree of Life in which each Sephirah is replaced by a Tree.

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