#36 Correspondence between the 7-tree, the Sri Yantra, the
(7+7) polygons, the 64 hexagrams, the first (6+6) enfolded polygons & the 3-torus

The 7-tree This maps the physical plane (physical universe). When its 91 triangles are turned
into tetractyses, it contains 380 yods. Up to the top of the 7-tree, there are two yods on either side of the
central Pillar of Equilibrium that belong to the eighth Tree of Life. Hence, there are 384 yods up to this point.
192 red yods are below Chesed of the fourth Tree and 192 blue yods extend down to the Path between this SL and
Geburah opposite it.

The (7+7) separate polygons Four geometrical elements per sector
surround the centre of a polygon: a corner, an outer side, an inner side & a triangle. The seven separate
polygons of the inner Tree of Life have 48 sectors. Hence, (4×48=192)
geometrical elements surround their centres. Both sets of seven polygons have (2×192=384) geometrical elements
surrounding their 14 centres.

The first (6+6) enfolded polygons When their 47 sectors are tetractyses, the
seven enfolded polygons have 264 yods. The seventh polygon — the dodecagon — has 73 yods (69
outside their root edge). The first six enfolded polygons have (264−69=195) yods. The topmost corner of the hexagon
coincides with the lowest corner of the hexagon enfolded in the next higher Tree. This means that
194 yods are intrinsic to the first six polygons enfolded in any Tree because
they are unshared with the polygons enfolded in the next higher Tree. 194 is the number value
of Tzadekh, the Mundane Chakra of Chesed. Two yods on the root edge shared by the polygons are associated
with each set of polygons, so that 192 yods are associated with each set of the first six enfolded polygons. Both
sets have 384 intrinsic yods.

The 3-d Sri Yantra When the 43 triangles in the 3-dimensional Sri Yantra are
regarded as tetractyses, there are nine yods per triangle linked together in each layer, so that the 42 tetractyses
surrounding the central one have (9×42=378) yods. 189 red yods belong to the 21 triangles in
one half of the Sri Yantra and 189 blue yods belong to the 21 triangles in its other half.
The three corners of the central triangle symbolize the triple Godhead (Shiva, Brahma & Vishnu in Hinduism) and
its centre symbolizes the Absolute. Including its six hexagonal yods (three red yods and three blue yods at the
corners of two intersecting triangles), there are (189+3=192) red yods and 192 blue yods surrounding the centre of
the 3-dimensional Sri Yantra, or central axis, if we include the bindu point. 384 yods are needed to construct the
43 triangles of the Sri Yantra other than the corners of its central triangle symbolizing the triple Godhead that
stands outside all planes of existence.

The I Ching table of 64 hexagrams As each of the
64 hexagrams is composed of six lines & broken lines, 384 lines & broken lines are in
the table. There are 192 lines and 192 broken lines. Each diagonal half of the 8×8 array contains 192 lines &
broken lines.

The {3,7} tiling of the 3-torus The 168 automorphisms
of the Klein quartic are elements of PSL(2,7) that can be represented by the {3,7} tiling of the 3-torus with 56
triangles having 168 vertices and 84 sides. Although the tetractys has no obvious bearing on
the mathematics of the Klein quartic, the fact is that, when these triangles are tetractyses and the 3-torus is
assembled from four triangular prisms and six square antiprisms, there are 192 yods lining their sides and 192 yods
lining the sides of its version when it is turned inside-out (see the table here). This 192:192 division is characteristic of holistic systems
(see The holistic pattern). The two 3-tori correspond to the lower and upper
halves of the 7-tree and to the two mirror-image halves of the other sacred geometries. The inside-out 3-torus
maps the 168 anti-automorphisms of the Klein quartic, so that a complete, mathematical
description of its symmetries requires both tori. Moreover, the pattern of the 24 vertices of the assembled
prisms and antiprisms and the 168 hexagonal yods that line their 84 sides conforms to the
24:168 divisions displayed by the other sacred geometries and by each diagonal half of the
8×8 array of hexagrams. They are analyzed in Article 43.

Such amazing consistency in both the number of degrees of freedom making up these sacred
geometries and their division into various analogous subsets constitutes powerful evidence for their being
equivalent representations of a unique, mathematical pattern that characterizes holistic systems. See also a
discussion of the number 384 in #19.