# Tree of life superstring theory part 91

Updated: Nov 28, 2020

Shown below are the Petrie polygons of the 24-cell, the 600-cell and the 421 polytope:

Inner Tree of Life pattern of the 24-cell

Each half of the 24-cell has 216 hexagonal yods, where 216 is the number of Geburah. There are 457 yods, of which 24 are vertices, leaving 433 generated by the transformation of the faces into tetractyses. 433 is the 84th prime number, where 84 = 12 + 32 + 52 + 72.216 corners surround the centre when the faces are Type A triangles. 97 of these are internal, where 97 is the number value ofHaniel, the Archangel of Netzach. The five disjoint 24-cells in the 600-cell have (1 + 5×216 = 1081) corners, where 1081 is the number value of Tiphareth ("Beauty"). Including its centre, there are 1081 yods other than vertices in either half of the 24-cell with Type A triangles as its faces.When the faces are Type B triangles, they have 384 corners that are not vertices, 192 in each half. The number 384 and its 192:192 division are characteristic of sacred geometries (see The holistic pattern). There are 385 corners inside the 24-cell, where 385 = 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102. There are 3360 hexagonal yods in the 96 Type B faces. This means that the 600-cell contains (5×3360=16800) hexagonal yods when its five 24-cells have Type B triangles as their 480 faces. The compound of two 600-cells that is the 4-dimensional projection of the 421 polytope defining E8 has 10 24-cells with 33600 hexagonal yods in their 960 faces. This is the amazing way in which the superstring structural parameters 3360 and 16800 are embodied in the 24-cell and 600-cell, themselves holistic entities like the whorl and UPA. Their appearance is so unambiguous that it can leave no doubt that the UPA is, indeed, an E8×E8 heterotic superstring, for its 16800 circularly polarised waves (the circular 1st-order spirillae in its 10 whorls) can be resolved into 33600 plane wave components, each pair of perpendicular plane waves differing in phase by 90°. Each hexagonal yod denotes such a plane wave, confirming our earlier conclusion that the 120 vertices in each 600-cell denote the 120 E8 gauge charges spread along either the outer or the inner half of the UPA. The 1680 turns in each half-revolution of its 10 whorls comprise 3360 plane waves, each denoted by a hexagonal yod in a 24-cell, the five half-revolutions of the outer half of the UPA being generated by the five 24-cells in one 600-cell and the five half-revolutions of its inner half being generated by the five 24-cells in the other concentric 600-cell. In other words, each of the 10 24-cells in the compound of two 600-cells represents a half-revolution of the 10 whorls of the UPA, its 24 vertices signifying the 24 E8 gauge charges that are spread along the length of a half-revolution. Tabulated below is the number of geometrical elements in the faces and interior of the 24-cell:</span>