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 Correspondence between disdyakis triacontahedron & 2 Type B dodecagons

#24 Correspondence between the dodecagon and each half of the disdyakis triacontahedron

Just as the first six polygons of the inner Tree of Life constitute a whole, so, too, does the last polygon — the dodecagon. The Type B version has each triangular sector divided further into three sectors that are then turned into tetractyses. It has 181 yods. There are 168 new yods (84 red yods & their 84 mirror-image blue yods reflected across the white central yod) in addition to the 12 black corners.

Although not a dodecagon, the central polygon of the disdyakis triacontahedron perpendicular to an axis passing through two opposite A vertices is a 12-gon with 12 corners & 12 sides (see page 10 in Sacred geometry/Polyhedral Tree of Life). As this polyhedron has 180 edges, there are 168 edges above and below the equator formed by the boundary of the 12-gon. As 120 triangles and 60 vertices surround the axis, there are 60 triangles, 84 edges & 24 vertices surrounding the axis on each side of the equator, i.e, 84 edges and 84 vertices & triangles.

Compare these properties with the two Type B dodecagons. The following correspondences exist:

Type B dodecagon

 

Upper/lower half of disdyakis triacontahedron

1 centre

apex/nadir
84 red yods

84 edges
84 blue yods

84 vertices & triangles
12 corners

12 corners & sides of half of central 12-gon
Total = 181 yods

Total = 181 geometrical elements

 

The 181 yods in each Type B dodecagon symbolize the 181 geometrical elements in each half of the disdyakis triacontahedron. The dodecagon is the single polygonal version of the Tree of Life, as is demonstrated further by the fact that it has 60 hexagonal yods when its sectors are tetractyses — the same number as there are in the Tree of life when its 16 triangles are tetractyses. These hexagonal yods correspond to the 60 vertices needs to be distributed around an axis in order to create the polyhedral version of the outer Tree of Life — the disdyakis triacontahedon.

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