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 The inner Tree of Life basis of the 421 polytope representing the 240 roots of E8.


Counterpart of Gosset polytope 421 in inner Tree of Life

Correspondence between Gosset polytope and inner form of 10 Trees of Life

The counterpart in the inner Tree of Life of the 240 vertices of the 8-dimensional 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 semi-regular 421 polytope whose position vector in 8-dimensional space is that of one of the 240 roots of E8, the rank-8 exceptional Lie group that appears in E8×E8 heterotic superstring theory.

The Gosset polytope is an 8-dimensional polytope with 240 vertices, 6720 edges, etc (see here). A Type C n-gon 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 421 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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