1
Figure 1
The quartic equation:
x^{3}y + y^{3}z + z^{3}x = 0
was studied by the mathematician Felix Klein. He showed that its Riemann
surface is mapped onto itself (hence “automorphisms”) by 168 analytic transformations. These
symmetries are mapped onto a surface of genus 3, i.e., the 3torus. In fact, this is the
maximum number of symmetries for a surface of this genus. This Riemann surface can be
represented in the hyperbolic plane by the Klein Configuration. For the {7,3} tiling, it has
168 red, hyperbolic triangles denoting the 168 automorphisms and 168 blue triangles denoting
the 168 antiautomorphisms. The 168 red or blue triangles are grouped 24 to each o seven
sectors, forming 24 heptagons. Three heptagons meet at each of its 56 vertices. Each sector has
two slices. Each of the 14 slices shown numbered has 12 red triangles and 12 blue triangles.
The 168 automorphisms belong to the group PSL(2,7). The 168 automorphisms and 168
antiautomorphisms belong to the doublecover group SL(2,7).
2

The Klein configuration is the mapping on the hyperbolic
plane of the 168 automorphisms (red hyperbolic triangles) of the Klein
quartic. The 168 blue triangles denote its 168 antiautomorphisms.
3

Figure 2
In their book Occult Chemistry, published in 1908, Annie Besant and
C.W. Leadbeater recorded their observations of what they believed were atoms of all the
elements. The basic unit of matter, or “ultimate physical atom” (UPA), has two varieties, one
the mirror image of the other. In the positive type, the ten closed curves, or “whorls,” spiral
clockwise 2½ times around the axis about which the particle spins, then wind back 2½ times in a
narrower helix back to the top of the particle. Each of the ten helices is a closed curve with
1680 turns. There are 336 turns in each of the five revolutions of each whorl, that is, 168
turns in a halfrevolution. The ten whorls make 3360 turns in each revolution. The author
proved that these particles are constituents of up and down quarks and has interpreted them as
E_{8}×E_{8}' heterotic superstrings.
4
5
Figure 3
The numbers 84, 168 and 336 appear in the Sri Yantra. Its 42 triangles have
84 vertices (black yods), 84 (red) hexagonal yods on the edges of its 14 outermost triangles
and 168 (blue) hexagonal yods on the edges of the 28 triangles in its first three layers. 336
yods therefore line its 42 triangles, delineating its shape. 168 yods mark out each
half. The Sri Yantra therefore represents the number of turns in one revolution of each helical
whorl of the UPA. If one assigns the number 10 (the Pythagorean Decad symbolized by the
tetractys) to each yod, the Sri Yantra generates the number 3360. This is the number of turns
in one revolution of all ten whorls of the UPA. If one assigns the number value 50 of the
Godname ELOHIM to each yod, the Sri Yantra generates the 16800 turns in all ten whorls of the
UPA, a heterotic superstring. Created out of the number value of ELOHIM, the Godname of the
third member of the Supernal Triad, the Sri Yantra generates the form of the
fundamental subatomic particle making up the atoms of the elements. The Godname YAHWEH of the
second member of the Supernal Triad with number value 26 prescribes the 26 dimensions of
spacetime from which the 10dimensional superstring emerges.
6
7
Figure 4
The I Ching table, used for thousands of years by the Chinese for purposes
of divination, is an 8×8 array of 64 hexagrams, each a pair of trigrams. There are eight
hexagrams in its diagonal and 28 hexagrams (56 trigrams with 168 lines and broken lines) on
either side of it. The table is equivalent to the Klein Configuration because the 168 red lines
and broken lines of the 56 trigrams on one side of the diagonal correspond to the 168 red
hyperbolic triangles denoting the 168 automorphisms, whilst the 168 blue lines and broken lines
of the 56 trigrams on the other side of the diagonal correspond to the 168 blue hyperbolic
triangles denoting the 168 antiautomorphisms.
8
9
Figure 5
In the {3,7} tiling of the Riemann surface of the Klein quartic, 56
triangles with 168 vertices tessellate completely the hyperbolic plane. The vertices denote
the 168 automorphisms of the Klein quartic. The triangles correspond in the I Ching table to
the 56 red trigrams on one side of the diagonal with 168 lines and broken lines, each one
corresponding to an automorphism of this equation wellknown to mathematicians.
10
11
Figure 6
The {3,7} tiling onto the 3torus of the 168 automorphisms of the Klein
quartic represented by the 168 vertices of the 56 triangles of the Klein configuration requires
seven colours to colour the 56 triangles so that no two triangles sharing an edge have the same
colour. The 3torus may be deformed into a tetrahedral structure formed by sticking the 12
square faces of six square antiprisms onto the 12 square faces of four triangular prisms and
then twisting each antiprism. This creates 56 triangles (eight triangular faces of the four
prisms + 48 triangular faces of the six square antiprisms). The 56 triangular faces define the
56 vertices of seven cubes. As a cube has 24 different rotations, the 168 automorphisms of the
Klein quartic correspond to seven copies of 24 symmetries of the octahedral group. Its 168
antiautomorphisms are represented by the 168 vertices of the 56 triangular faces of the
tetrahedral structure after it has been turned inside out. These triangles, too, define the 56
vertices of seven cubes that generate seven copies of the 24 symmetries/inversions of the
octahedral group. These make up the 168 antiautmorphisms of the Klein quartic.
12
13
Figure 7
The 168 automorphisms of the Klein quartic belong to PSL(2,7). This group is
isomorphic to SL(3,2), whose 168 symmetries are displayed by the Fano plane, the simplest
projective plane. Implicit in its geometry is a Golden Rectangle, the ratio of whose adjacent
sides is the Golden Ratio φ = 1.6180..., and a Golden Rhombus, the lengths of whose diagonals
are in the same proportion. The 60 edges of a rhombic triacontahedron form 30 Golden Rhombi
that are the bases of pyramids with four faces, creating the 120 faces of the disdyakis
triacontahedron. This shows how the ideal, aesthetically pleasing proportion of the Golden
Ratio, used throughout history by artists and architects, manifests in the form of the
disdyakis triacontahedron. Beauty is exhibited in the shape, as well as in the mathematical
properties, of the polyhedral version of the inner Tree of Life.
14
The Fano
plane has the 168 symmetries of SL(2,3), which is isomorphic to
PSL(2,7), the group of symmetries of the Klein quartic.
The
Golden Rhombic shape of the faces of the rhombic triacontahedron
underlying the disdyakis triacontahedron is implicit in
the
geometry of the Fano plane, which represents the algebra of the
octonions.

15
Figure 8
A continuous, logical link connects the (2,3) torus knot to the quantitative
description given in 1908 by Annie Besant and C.W. Leadbeater of the form of the heterotic
superstring constituent of up and down quarks.
16
17
Figure 9
The polyhedral inner form of the Tree of Life is the 144 Polyhedron, which
has 74 vertices, 216 edges and 144 faces. It generates another polyhedron with 62 vertices, 180
edges and 120 triangular faces. The latter is the disdyakis triacontahedron and the former is
the disdyakis dodecahedron with tetrahedra added to its 48 faces. Their (24+24=48) peaks
correspond to the 24 rotational symmetries of the octahedral group and the 24
rotations/inversions. This is a subgroup of SL(2,7), and seven copies of it define the 336
symmetries of SL(2,7), the doublecover group of PSL(2,7), which is isomorphic to
SL(2,7)/Z_{2} and describes the 168 automorphisms of the Klein quartic. This
symmetry manifests in the 168 edges of the disdyakis triacontahedron above and below the
equator that is perpendicular to the axis joining two diametrically opposite A vertices of this
polyhedron. The centre of PSL(2,7) is Z_{3}, the cyclic group of order 3 that is
isomorphic to the three primitive roots of 1, namely, 1, exp(2πi/3) & exp(4πi/3). The fact that the dimension of SL(2,7) is the
number of edges above and below the equator of the disdyakis triacontahedron is evidence that
PSL(2,7) is embodied in this polyhedron as a fundamental symmetry.
The algebra of the seven unit imaginary octonions is represented by the Fano
plane, which has the symmetry of SL(3,2), a group that is isomorphic to PSL(2,7). It can
alternatively be represented by assigning them to the vertices and centre of an octahedron.
This suggests a connection between the disdyakis triacontahedron and the octonions. It is to be
expected because the octonions form a basis of E_{8}, the superstring gauge symmetry
group (see Figs. 7 & 8).
18
19
Figure 10
If a Yang (unbroken) line of a trigram denotes a face of a cube orientated
along one of the three perpendicular, positive directions and a Yin (broken) line denotes a
face facing a negative direction, the eight trigrams symbolize the sets of three perpendicular
faces that intersect at the eight corners of a cube. As a pair of different trigrams, a
hexagram defines the straight line joining two corners of a cube. The pairs of identical
trigrams in the eight hexagrams in the diagonal of the I Ching table define the eight corners
themselves. The ordering of pairs of trigrams signifies the directions of the lines regarded as
arrows. This means that the hexagrams below the diagonal signify arrows connecting different
corners that point in the opposite direction to those connecting corners signified by hexagrams
above the diagonal. The 28 hexagrams above the diagonal have 168 lines/broken lines denoting
the 168 faces (84 positive, 84 negative) defined by the endpoints of the 28 lines joining
different corners. Each combination of three faces appears seven times, creating seven copies
of each corner, i.e., 56 copies of the eight corners, totalling 64 corners. These are the
counterparts of the 56 hyperbolic triangles with 168 vertices in the {3,7} tiling of the
automorphisms of the Klein quartic on the hyperbolic plane, each triangle in fact defining one
of the corners of seven cubes. The 56 hyperbolic triangles mapped onto a 3torus turned
insideout, whose 168 vertices denote the 168 antiautomorphisms of the Klein quartic,
similarly correspond to the 56 trigrams with 168 lines/broken lines in the 28 hexagrams below
the diagonal, each trigram defining a corner of seven copies of a cube  the seven cubes whose
56 corners are defined by these 56 triangles. The Yang/Yin nature of each line/broken in the I
Ching table signifies whether the faces of the cube are orientated towards the positive or
negative directions of each perpendicular axis. These 168 bipolar degrees of freedom manifest
in the disdyakis triacontahedron as the 168 edges other than the 12 edges in its equatorial
plane perpendicular to an axis joining two diametrically opposite A vertices. Regarded as
arrows that can point in two opposite directions, the edges of the polyhedron point in 168
directions above the equatorial plane and 168 directions below it. The 168 pairs of oppositely
directed edges are the counterpart of the 168 automorphisms and the 168 antiautomorphisms of
the Klein quartic and the 168 lines and 168 broken lines in the 56 offdiagonal hexagrams of
the I Ching table.
20
21
Figure 11
In its {7,3} tiling, the Klein configuration (KC) is divided into seven
identical sectors. A sector is composed of two halfsectors, each with 12 hyperbolic triangles,
so that KC is divided into 14 sectors with 168 triangles. Compare this with the 14 triangles in
the fourth layer of the Sri Yantra. When each triangle is constructed from three tetractyses,
there are 12 hexagonal yods on their six edges. This means that (14×12=168) hexagonal yods line
on the (14×6=84) edges of the (14×3=42) tetractyses comprising the 14 triangles. KC is
isomorphic in this sense to the last layer of triangles of the Sri Yantra. To establish such
isomorphism, however, we need to consider only each triangle as a tetractys, for 168 yods
symbolizing the 168 automorphisms line the 63 edges of the 21 triangles in one half of the Sri
Yantra and 168 yods symbolizing the 168 antiautomorphisms line the 63 edges of the 21
triangles in its other half. Unlike, however, in the case of the disdyakis triacontahedron, one
half of the Sri Yantra is not the exact mirror image of its other half.
22
23
Figure 12
It was shown in Part 2 (pp. 21, 22) that the Sri Yantra and the lowest seven
overlapping Trees of Life are equivalent. Here is displayed the isomorphism between the Sri
Yantra and the inner form of seven Trees of Life – or rather, the first six polygons enfolded
in each tree, as these two sets of polygons constitute a Tree of Life pattern in themselves.
There are 168 corners associated with the 42 polygons enfolded in seven overlapping Trees of
Life on each side of its central pillar. They correspond to the 168 yods lying on edges of the
21 triangles in each half of the Sri Yantra. The 42 (black) vertices associated with each set
of 21 triangles correspond to the 42 (black) corners associated with the squares and hexagons
in each set of six polygons. The 42 (red) hexagonal yods on edges of each set of seven
triangles in the fourth layer correspond to the 42 (red) corners of the octagons outside their
shared edges in each set of polygons. The 84 (blue) hexagonal yods on the 42 edges of the 14
triangles in each half of the first three layers correspond to the 84 (blue) corners of the
triangle, pentagon & decagon in each set of polygons outside their root edges.
24
25
Figure 13
Of the 384 yods in the tetractyses forming the lowest seven Trees of Life up
to the top of the seventh tree, 48 (red) yods are in the lowest tree up to the level of Chesed,
the first Sephirah of Construction. The counterpart of this in the Sri Yantra is that there are
48 (red) yods which are either centres of triangles or hexagonal yods on edges of the central
triangle. The 336 (black) yods on the edges of the 42 triangles correspond to the 336 (black)
yods in the lowest seven trees above Chesed of the lowest tree.
26
27
Figure 14
This displays the corresponding features of the inner Tree of Life, the I
Ching table and the Sri Yantra as isomorphic representations of holistic systems.
1. The six green yods either at the external corners of the triangles or at
the topmost and lowest corners of the hexagons coincide with Sephiroth. They correspond to the
six lines of the pair of Heaven trigrams in the top lefthand corner of the table and to the
six green hexagonal yods on the edges of the central triangle of the Sri Yantra.
2. The 21 black yods denoting corners of one set of the first six polygons
that lie outside their shared edge correspond to the 21 black lines/broken lines in the upper
trigrams of the seven remaining diagonal hexagrams and to the black centres of the 21 triangles
in one half of the Sri Yantra. The 21 white yods denoting external corners of the other set of
polygons correspond to the 21 white lines/broken lines in the lower trigrams of the seven
hexagrams on the diagonal of the table and to the white centres of the 21 triangles in the
other half of the Sri Yantra.
3. The 168 red yods in one set of six polygons that are not corners
correspond to the 168 red lines/broken lines in the 28 offdiagonal hexagrams of half of the
table and to the 168 red yods on the 63 edges of the 21 triangles in one half of the Sri
Yantra. The 168 blue yods in the other set of six polygons that are not corners correspond to
the 168 blue lines/broken lines in the 28 offdiagonal hexagrams of the other half of the table
and to the 168 blue yods on the 63 edges of the 21 triangles in the other half of the Sri
Yantra.
28
29
Figure 15
192 yods are associated with each set of the first six enfolded polygons of
the inner Tree of Life. They are intrinsic to that set because none of them is shared with the
six polygons enfolded in the next higher Tree of Life, which also have 192 such yods. The 192
yods associated with each set of six polygons correspond to the 192 lines/broken lines in each
half of the I Ching table.
30
31
Figure 16
Considered as tetractyses, the 21 triangles in one half of the Sri Yantra
have 21 black centres and 21 white pairs of vertices, i.e., 21 triplets of one white yod and
two black yods. They also have 21 purple triplets of hexagonal yods and 21 brown triplets of
hexagonal yods, each pair of triplets forming a Star of David. The 189 yods associated with the
21 tetractyses in each half of the Sri Yantra comprise three sets of 21 triplets of yods, i.e.,
63 triplets.
The 21 centres of tetractyses in each half of the Sri Yantra comprise 12
centres of the tetractyses in the third and fourth layers and nine centres of tetractyses in
the first and second layers. The significance of this will be discussed on pages 41 & 42.
32
33
Figure 17
Selection of successive notes of the Pythagorean scale as the starting note
(tonic) generates seven possible musical scales. These sequences of intervals (T) and leimmas
(L), the counterpart of the modern semitone, define the musical modes of the Roman Catholic
Church. The four “authentic modes” are the Dorian mode (D scale), the Phrygian mode (E scale),
the Lydian mode (F scale) & the Mixolydian mode (G scale). They have four “hypo” modes
separated by the interval of a perfect fourth from their authentic counterparts – the
Hypodorian (A scale), the Hypophrygian (B scale), the Hypolydian (C scale) & the
Hypomixolydian (D scale). In terms of notes, the lattermost is identical to the Dorian,
differing in the choice of the ‘dominant’ and ‘reciting note.’
The table displays the ‘tone ratios’ of the notes in the seven musical
scales. These are the frequencies or pitches of the notes relative to that of the tonic. The
Pythagorean musical scale is the C scale (Hypolydian mode). Tone ratios of notes belonging to
this scale are written in black; nonPythagorean tone ratios are written in red. The seven
scales have 26 Pythagorean notes between the tonic and the octave, showing how YAHWEH, the
Godname of Chokmah with number value 26, prescribes the seven musical scales. Their notes have
14 different tone ratios, i.e., there are 12 distinct types of notes between the tonic and
octave. The sequence of 14 notes is split into the first seven, primary notes and their seven
“complements” (notes whose tone ratios are the interval between its corresponding primary note
and the octave). They comprise the eight notes of the Pythagorean scale and six nonPythagorean
notes. The 12 types of notes between the tonic and octave comprise six Pythagorean notes and
six nonPythagorean notes.
34
35
Figure 18
There are 28 intervals between the eight notes of a musical scale. Excluding
the octave, there are (7×27=189) intervals between the notes of the seven varieties of scales.
They all have the values of the tone ratios of the 12 types of notes between the tonic and the
octave found in the seven scales. The second table lists the number of intervals of each type.
The number in the brackets next to each one is the number of times the note with that
tone ratio appears in the scales. Some of the notes and intervals can be paired with their
complements. Their numbers are listed in the third table, together with the numbers of
intervals without complements. There are 21 notes and 42 intervals that have complements. They
form two sets of 63 intervals, one set paired with its complementary set, creating 63 pairs.
There are 63 unpaired intervals. The 189 intervals therefore divide into three sets of 63
intervals, that is, 63 triplets, each triplet comprising a pair of notes or intervals and an
unpaired interval. They comprise 21 notes made of the second, third & fourth notes of the
seven scales and 168 intervals made up of the 21 complements of these notes, 42 intervals and
their 42 complements and 63 unpaired intervals.
36
37
Figure 19
Between the notes of the seven scales, there are 189 rising intervals below
the octave. They also have 189 falling intervals (this is the interval between the lower note
and the higher note. It is the reciprocal of the corresponding rising interval). So there are
378 rising and falling intervals other than the octave. As the seven scales constitute a
holistic system, their patterns of intervals are encoded in the inner form of the Tree of Life.
The two sets of the first six enfolded polygons have 384 yods that are intrinsic to them. Six
of them coincide with Sephiroth or Daath, leaving 378 yods that do not belong to the outer form
of the Tree of Life. The 189 yods in one set of polygons denote rising intervals. Their mirror
images in the other set denote falling intervals.
As evidence that this is not a coincidence, the yod populations of pairs of
polygons correlate exactly with the numbers of different classes of intervals. The 21 corners
of polygons that are outside their shared edge and which do not coincide with Sephiroth of the
Tree of Life symbolize the 21 notes made up of the second, third & fourth notes of each
scale. Their mirror images in the other set of polygons denote the complements of these notes
(not necessarily in the same scale, of course). The 21 corners comprise 12 corners of the
square, hexagon & decagon, and nine corners of the pentagon & octagon. The 42 yods in
the square & hexagon symbolize the 42 intervals that are not notes. The 63 yods in the
triangle & decagon denote the 63 complements of the notes and intervals. The 63 yods in the
pentagon & octagon denote the 63 intervals lacking a complement.
This is the Tree of Life basis of the seven types of musical scales as a
holistic system.
38

Tree of Life representation of the three sets of 63 rising
& falling intervals between the notes of the seven musical scales.
39

Figure 20
This correlation between the intervallic structure of the seven musical
scales and the sacred geometry of the inner Tree of Life extends to the tetractystransformed
Sri Yantra as well. The 21 notes made up of the first three notes above the tonic in each scale
determine the seven scales collectively because the 21 remaining notes below the octave are
their complements and therefore are defined by them. They are symbolized as rising intervals by
the yods at the centres of the 21 triangles/tetractyses in one half of the Sri Yantra, the
centres of the 21 tetractyses in the other half denoting their corresponding 21 falling
intervals (note: not their complements) . The tips of the 21 triangles denote the 21
complements of the notes. The tips of the 21 triangles in the other half of the Sri Yantra
denote their falling interval counterparts. The 42 intervals and their complements are
symbolized by the 42 hexagonal yods on each of the two edges of each triangle forming its tip.
Their corresponding falling intervals are symbolized by the counterparts of these yods in the
other half of the Sri Yantra. The 63 intervals without complements are symbolized by the 63
yods on the bases of the 21 tetractyses in one half, their falling interval counterparts being
denoted by the 63 yods on the bases of the 21 tetractyses in the other half of the Sri
Yantra.
The centres of the 21 tetractyses in either half of the Sri Yantra comprise
the centres of the 12 tetractyses in the third and fourth layers and the centres of the nine
tetractyses in the first and second layers. This 12:9 differentiation is the counterpart of the
distinction between the 12 notes above the tonic made up of the second, third & fourth
notes in the four authentic modes and the nine notes above the tonic made up of the second,
third & fourth notes in the three plagal modes (the fourth, plagal mode is not a distinct
octave species, the Hypomixolydian mode having the same sequence of notes as the Dorian). The
uppermost first and second layers of the Sri Yantra therefore correlate with the three plagal
modes that have different sets of notes, whilst its third and fourth layers correlate with the
four authentic modes.
40
41
Figure 21
Arranged in a Star of David in each tetractys of the Sri Yantra, the two
triads of hexagonal yods correspond to the two trigrams in each hexagram of the I Ching table.
The six green, unbroken lines of the two Heaven trigrams at the upper lefthand corner of the
table correspond to the six hexagonal yods arranged as two triangles in a Star of David in the
central triangle (see Fig. 14). The (21+21) black lines/broken lines of the seven remaining
hexagrams in the diagonal correspond to the centres of the two sets of 21 tetractyses. The
84 white lines/broken lines of the 14 hexagrams containing the Heaven trigram correspond to
the 84 corners of the 42 tetractyses. Each category ‘marks out’, so to speak, the boundary
of their respective systems. The 21 purple trigrams on one side of the diagonal correspond
to the 21 triplets of purple, hexagonal yods in one half of the Sri Yantra. The 21 purple
trigrams on the other side of the diagonal correspond to the 21 triplets of purple,
hexagonal yods in the other half of the Sri Yantra. Similarly for the brown, hexagonal yods.
The I Ching table is a nongeometrical version of the Sri Yantra.
42
43
Figure 22
Displayed here is the detailed correspondence between different types of
trigrams in the I Ching table and the triplets of hexagonal yods in the tetractystransformed
triangles of the Sri Yantra. Lines/broken lines and their counterpart yods have the same
colour.
44

Correspondence between the I Ching table and the Sri
Yantra.
45

Figure 23
The seven separate, regular polygons constituting the inner form of the Tree
of Life comprise 295 yods when their 48 sectors are turned into tetractyses. In other words,
starting with the seven polygons divided into their sectors, (295487=240) more yods are
needed to transform their sectors into tetractyses. There are 48 centres of tetractyses. This
leaves (24048=192) hexagonal yods arranged at the corners of sixsided polygons (i.e., at the
tips of Stars of David). 192 yods are similarly arranged in the other set of polygons. In terms
of the formal equivalence between the Tree of Life and the tetractys, the six yods at the
corners of a sixsided polygon (it does not need to be a hexagon, of course) symbolize the six
Sephiroth of Construction above Malkuth. These two sets of 192 hexagonal yods arranged at the
corners of triangles are the Tree of Life counterpart of the 192 lines/broken lines grouped in
trigrams in each half of the I Ching table. The 24 red lines/broken lines in the upper trigrams
of the eight diagonal hexagrams correspond to the 24 red, hexagonal yods in one of the
hexagons. The 24 blue lines/broken lines in the lower trigrams of these eight hexagrams
correspond to the 24 blue, hexagonal yods in the hexagon belonging to the other set of
polygons. As 24 = 4×3×2 and as each sector of a polygon contributes four of these hexagonal
yods, the counterpart of the two sets of four diagonal trigrams are the four hexagonal yods per
sector multiplied, firstly, twice (a hexagon is two equilateral triangles rotated by 60°) and
then thrice (pairs of hexagonal yods are arranged at each corner of a triangle). The trigrams
are expressing the three fold, rotational symmetry of an equilateral triangle – a sector of a
hexagon. The eightfold nature of trigrams corresponds to the fact that there are eight
hexagonal yods on the edges of a pair of adjacent sectors in the hexagon. These are basic
because the rotation of each one by 120° about the centre of the hexagon generates all its
remaining yods.
46
47
Figure 24
Divided into their sectors, the seven separate polygons have 48 corners, 96
edges and 48 triangles surrounding their centres, i.e., 192 geometrical elements. They
correspond to the 192 lines/broken lines in one diagonal half of the I Ching table. The 192
geometrical elements in the other set of seven polygons of the inner Tree of Life correspond to
the 192 lines/broken lines in the other half of the table. The 12 lines and 12 broken lines in
the upper trigrams of the eight diagonal hexagrams correspond to the 12 edges and 12
corners/triangles of the sectors of the hexagon. Similarly, the 12 lines and 12 broken lines in
the lower trigrams correspond to the 12 edges and 12 corners/triangles of the sectors of the
hexagon in the other set of polygons. The 384 lines and broken lines in the table express the
number of geometrical elements needed to construct the two sets of seven polygons making up the
inner form of the Tree of Life. They symbolize the independent ‘bits of information’ needed to
build a holistic system.
48

The 384 lines & broken lines of the I Ching table
denote the 384 geometrical
elements composing the 14 regular polygons of the inner Tree of
Life.

49
