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The inner Tree of Life basis of the 4_{21} polytope representing the 240 roots of E_{8}.


The counterpart in the inner Tree of Life of the 240 vertices of the 8dimensional Gosset polytope (here is a magnifiable version in PDF format that shows its 6720 edges) are the 240 hexagonal yods in the seven separate, regular, Type A polygons whose 48 sectors are tetractyses. Each hexagonal yod symbolises a vertex of the semiregular 4_{21} polytope whose position vector in 8dimensional space is that of one of the 240 roots of E_{8}, the rank8 exceptional Lie group that appears in E_{8}×E_{8} heterotic superstring theory. 
The Gosset polytope is an 8dimensional polytope with 240 vertices, 6720 edges, etc (see here). A Type C ngon has n Type B triangular sectors, the 9 triangles per sector having 14 sides. The number of sides of the (9×48=432) triangles in the 48 Type B sectors of the 7 separate Type C polygons making up the inner Tree of Life = 48×14 = 672. The inner form of 10 Trees of Life consists of 10 sets of 7 polygons. They are composed of (10×432=4320) triangles with (10×672=6720) sides. They are the counterpart of the 6720 edges of the faces of the 4_{21} polytope. As 10 Trees of Life represent a single Tree in a more differentiated form, its inner form manifests as the Gosset polytope, which is, therefore, a holistic system. 
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