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6. The yod population of the (4+4) Type A triacontagons matches that of the (7+7) Type B polygons
The yod population of the 8 Type A triacontagons matches that of the (7+7) separate Type B polygons in the inner Tree of Life. |
Surrounding the centre of a Type A triacontagon are 180 yods. The 4 triacontagons in the Coxeter plane projection of a 600-cell (shown as having red, blue, green and violet yods) have (4×180=720) yods surrounding their centres, They correspond to the 720 yods surrounding the centres of the 7 separate Type B polygons in the inner Tree of Life. The 360 yods in the four red polygons and the 360 yods in the three blue polygons correspond to the 360 yods in the two pairs of triacontagons. Similarly, the two subsets of mirror-image polygons correspond to the two pairs of triacontagons in the second 600-cell. This demonstrates that the compound of two 600-cells that is the Coxeter projection in 4-d space of the 421 polytope has Petrie polygons whose yod population when they are Type A is that of the inner form of the Tree of Life when its Type B polygons are separate.
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