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#29 Correspondence between the disdyakis triacontahedron & the inner form of 10 Trees of Life

The 1680 intrinsic geometrical elements that are outside the root edges of the 70 enfolded polygons making up 10 overlapping Trees of Life consist of 310 corners & 470 triangular sectors, i.e., 780 (=78×10) corners & triangles, and 900 (=90×10) sides of sectors. The factor of 10 arises from the 10 sets of seven enfolded polygons, the number value 78 of Cholem (חלם) being the number of intrinsic corners & triangles in each set of seven polygons and the number value 90 of Yesodoth (יסודות) being the number of intrinsic sides of their sectors.

Compare this with the 1680 geometrical elements that surround an axis of the disdyakis triacontahedron that passes through any two diametrically opposite vertices (see page 1 & page 2 at Superstrings as sacred geometry/Disdyakis triacontahedron). They are composed of 60 vertices & 180 corners of the (3×180=540) sectors of internal triangles (i.e., 240 corners), 180 edges, 60 internal sides terminating at vertices and (3×180=540) sides of these sectors (i.e., 780 sides), as well as 120 triangular faces, i.e., (540+120=660) triangles. (240+660=900) corners & triangles and 780 sides surround the axis. The same pair of numbers (780 & 900) quantifies the geometrical make-up of the disdyakis triacontahedron as it does for the geometrical elements that are intrinsic to the 70 polygons enfolded in 10 overlapping Trees of Life! This amazing fact, of course, is no accident, because the disdyakis triacontahedron is the outer form of the polyhedral Tree of Life and — as proved in several research articles available on this website — its properties are analogous to the inner form of 10 overlapping Trees, which is the full representation of the 10 Sephiroth in a single Tree of Life. Nevertheless, it is remarkable that both the inner form of 10 Trees of Life and its polyhedral counterpart should embody so naturally not only the gematria number of Cholem Yesodoth but also the number values of both Hebrew words in this name. It provides convincing proof that the number value of the Mundane Chakra of Malkuth has, indeed, been computed correctly by taking the value of ם, the final mem, as 40 (the value of מ, mem) instead of as 600. Another example is ELOHIM, whose final mem is counted as 40 but further contracted to 4. In the author's view, it is compelling evidence that the five final letter forms of the Hebrew alphabet and their numbers play no new role in true gematria, which is based solely upon the original 22 letters of this alphabet and their numbers. After all, they are not new letters, only special final forms that appear at the end of a word. So it is fundamentally incorrect to calculate the number value of a Hebrew word containing a final letter as though it were a new letter with a number different from the letter it replaces (as is still done in many works claiming to be authoritative, e.g., "Godwin's Cabalistic Encyclopedia"). God works with 22 letters, not with 27 letters. His mathematics has no extra need for the five final letters and their gematria numbers, for they are, solely, a human invention, done for convenience.

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