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

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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