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 #32 Correspondence between the Type B dodecagon, the five Platonic solids & the disdyakis triacontahedron


  Correspondence between Type B dodecagon, 5 Platonic solids & disdyakis triacontahedron 

A Type B dodecagon has 180 yods surrounding its centre. They consist of 12 corners (black yods) and 168 yods made up of 24 red hexagonal yods on its boundary, 24 yellow hexagonal yods on radial sides of sectors, 60 green yods & 60 blue yods. Hence, there are 60 black, red & yellow yods that belong to the Type A dodecagon, 60 green yods & 60 blue yods. The 168 yods comprise 84 red & green yods and 84 yellow & blue yods.

Compare this composition of yods with the 180 sectors of the 50 faces of the five Platonic solids. The four triangular faces of the tetrahedron have 12 sectors, the eight triangular faces of the octahedron have 24 sectors, the six square faces of the cube have 24 sectors, the 20 triangular faces of the icosahedron has 60 sectors and the 12 pentagonal faces of the dodecahedron have 60 sectors. The 180 sectors therefore group into the 60 sectors of the tetrahedron, octahedron & cube, 60 sectors of the icosahedron and 60 sectors of the dodecahedron. The octahedron, cube, icosahedron & dodecahedron have 168 sectors (84 in the octahedron & icosahedron, 84 in the cube & dodecahedron).

Compare it also with the 180 edges of the disdyakis triacontahedron. They comprise 60 AB edges, 60 BC edges & 60 AC edges. They consist of the 12 edges that are sides of the central 12-gon perpendicular to an axis passing through two diametrically opposite A vertices and the 84 edges in each half of the polyhedron above and below the 12-gon.

Not only do the three sacred geometries have properties quantified by the parameter 180 but the latter displays in all cases the patterns of division:

180 = 12 + 168,
180 = 60 + 60 + 60,
168 = 84 + 84.

The number 12 refers to the basic shape that builds the sacred geometry in each case, namely, the 12 corners of the dodecagon, the 12 sectors of the faces of the simplest Platonic solid & the 12 vertices in the central plane of the disdyakis triacontahedron when its axis passes through two opposite A vertices. The number 168 is the number that builds up the form of the sacred geometry in each case. This is consistent with its being the gematria number value of Cholem Yesodoth, the Mundane Chakra of Malkuth, which is the outer, physical form of any realization of the Tree of Life blueprint. Moreover, its division: 168 = 84 + 84 expresses the inversion or mirror symmetry of each geometry wherein each yod, sector or edge has its counterpart mirror image. Such correspondences confirm how these geometries are equivalent representations of the universal, mathematical paradigm governing holistic systems.








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