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7. A correspondence between the 421 polytope and each half of the inner form of 10 Trees of Life

The two halves of the inner form of 10 Trees of Life represent two E8 groups


The 6720 sides of the 70 Type C polygons in each half of the inner form of 10 Trees of Life correspond to the 6720 edges of a 421 polytope.

The Type C n-gon has 9n triangles with 14n sides. The 7 separate Type C polygons in each half of the inner Tree of Life contain (9×48=432) triangles with (14×48=672) sides. The (70+70) separate Type C polygons in the inner form of 10 overlapping Trees of Life contain (4320+4320=8640) triangles with (6720+6720=13440) sides.The 421 polytope has 6720 edges. This correspondence between sides and edges indicates that each half of the inner form of 10 Trees of Life represents a 421 polytope whose 240 vertices coincide with the 240 roots of E8. It implies that the inner form of 10 Trees represents E8×E8.

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