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#38 Correspondence between the inner Tree of Life, the heptagon, the Sri Yantra, the 3-torus & the Type C dodecagon

a) The (7+7) enfolded polygons of the inner Tree of Life lie in the plane contained by the side pillars of the outer Tree of Life. Seven black yods lie on each pillar between the top and bottom of each hexagon. The centre of each triangle (indicated by another black yod) lies on the horizontal Path between Chesed and Geburah. Hence, 16 black yods among the 524 yods in the (7+7) enfolded polygons coincide with yods belonging to the outer Tree. (524−16=508) yods are unshared, i.e., there are 504 unshared red & blue yods outside the root edge shared by both sets of polygons.

b) The number of yods in an n-gon whose sectors are 2nd-order tetractyses = 72n + 1, where "1" denotes its centre. A heptagon (n=7) has (7×72=504) yods surrounding its centre.

c) There are two hexagonal yods on each side of the 42 triangles of the Sri Yantra that surround its central one. When each triangle is Type A, there are also six hexagonal yods on internal sides of tetractyses. (42×2×3=252) hexagonal yods line on external sides of tetractyses and 252 hexagonal yods lie on their internal sides. 504 hexagonal yods line the 252 sides of (42×3=126) tetractyses.

d) The 3-torus tiled with 56 triangles is topologically equivalent to six square antiprisms being stuck on the square faces of four triangular prisms. When each hyperbolic triangle is regarded as a deformed Type A triangle, there are two hexagonal yods on each of their 84 sides and two hexagonal yods on each of the three internal sides of the (56×3=168) tetractyses. The number of hexagonal yods lining their (84 + 56×3 = 252) sides = 84×2 + 56×6 = 504.

e) The number of yods in a Type C n-gon = 42n + 1, where "1" denotes its centre. A Type C dodecagon (n=12) has (12×42=504) yods surrounding its centre.

The correspondences exist because these structures are all holistic systems displaying the same pattern of archetypal parameters that are characteristic of such systems of sacred geometry. See Article 43 for a detailed discussion of the correspondence between the heptagon, Sri Yantra, 3-torus & Type C dodecagon.

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