Article 40
Part 2
by
Stephen M. Phillips
Flat 3, 32 Surrey Road South. Bournemouth. Dorset BH4 9BP.
England.
Website: http://www.smphillips.mysite.com
1

Figure 1
The 34 vertices of the 2dimensional Sri Yantra and their 34 mirror images
correspond to the 34 corners of the seven enfolded polygons outside their root edge and
their 34 mirror images in the other set of polygons. The 42 edges and their 42 mirror images
in the first three layers of triangles are the counterpart of 42 hexagonal yods on the edges
of one set of polygons and their mirror images in the other set. The 42 edges &
triangles in the fourth layer and their 42 mirror images are the counterpart of another 42
hexagonal yods on the edges of one set of polygons and their 42 mirror images in the other
set.
2

Correspondence between the geometrical composition of
the four layers of the 2d Sri Yantra and the boundary yods of the 14
polygons of the inner Tree of Life.
3

Figure 2
Just as 240 geometrical elements are needed to construct the 2dimensional
Sri Yantra, starting with the central bindu point, so 240 extra yods are needed to construct
the 19 triangles of the lowest Tree of Life from tetractyses and 240 extra yods are needed
to construct the sectors of the polygons in the inner Tree of Life from tetractyses.
4

The number 240 is a structural parameter of the Sri
Yantra, the Tree of Life and its inner, polygonal form.
5

Figure 3
When constructed from tetractyses, the first three Platonic solids have 240
hexagonal yods, as do the icosahedron and the dodecahedron. The number 240 is a structural
parameter of holistic systems like the five possible, regular polyhedra.
6
Figure 4
There are 13 semiregular polyhedra (Archimedean solids). They have 13 duals
– the Catalan solids – in which each vertex is replaced by a face and vice versa. The two
tables list the number of vertices, edges & triangles in their faces. The most complex
of the Catalan solids is the disdyakis triacontahedron. 2400 corners, edges & triangles
surround an axis through any two opposite vertices when its faces are divided into three
triangles and 1680 geometrical elements when its faces are single triangles. This is ten
times the corresponding numbers for the triakis tetrahedron, the simplest Catalan solid. The
disdyakis triacontahedron is the polyhedral counterpart of the inner Tree of Life, embodying
the structural parameter 240. As shown later, 168 and 1680 are also parameters embodied in
any manifestation of the Tree of Life blueprint.
8
Figure 4
Case A: triangular face as tetractys



Case B: triangular face as 3 tetractyses


C = number of corners
E = number of edges
F = number of faces 
N = number of corners, edges & triangles
surrounding the axis (case A)
N' = number of corners, edges & triangles surrounding the axis
(case B)


Tables of properties of the Archimedean and the Catalan
solids

N'

F

E

C

Archimedean solid

244

8

18

12

truncated tetrahedron

322

14

24

12

cuboctahedron

490

14

36

24

truncated cube

490

14

36

24

truncated octahedron

646

26

48

24

rhombicuboctahedron

802

38

60

24

snub cube

802

38

60

24

snub cube (chiral partner)

808

32

60

30

icosidodecahedron

882

26

72

48

truncated cuboctahedron

1228

32

90

60

truncated icosahedron

1228

32

90

60

truncated dodecahedron

1618

62

120

60

rhombicosidodecahedron

2008

92

150

60

snub dodecahedron

2008

92

150

60

snub dodecahedron
(chiral partner)

2458

62

180

120

truncated icosidodecahedron



Catalan solid

F

E

C

N

N'

triakis tetrahedron

12

18

8

168

240

rhombic dodecahedron

12

24

14



324

triakis octahedron

24

36

14

336

480

tetrakis hexahedron

24

36

14

336

480

deltoidal icositetrahedron

24

48

26



648

pentagonal icositetrahedron

24

60

38



816

pentagonal icositetrahedron
(chiral partner)

24

60

38



816

rhombic triacontahedron

30

60

32



810

disdyakis dodecahedron

48

72

26

672

960

triakis icosahedron

60

90

32

840

1200

pentakis dodecahedron

60

90

32

840

1200

deltoidal hexacontahedron

60

120

62



1620

pentagonal hexacontahedron

60

150

92



2040

pentagonal hexacontahedron
(chiral partner)

60

150

92



2040

disdyakis triacontahedron

120

180

62

1680

2400


2400 geometrical elements surround the axis of the disdyakis
triacontahedron constructed from triangles. This is 10 times that for the
triakis tetrahedron, the simplest Catalan solid. It illustrates how the number
240 characterizes holistic systems like the disdyakis triacontahedron.
9

Figure 5
The Tree of Life parameter 240 appears in superstring physics as the number
of nonzero roots of the Lie algebra of E_{8}, the superstring gauge symmetry group.
The parameter 168 appears as the number of nonzero roots of E_{8} that are not
nonzero roots of its exceptional subgroup E_{6}.
10
Figure 6
There are 260 vertices, edges & triangles in the 3dimensional Sri
Yantra. 168 geometrical elements are in the first three layers of triangles.
12

Geometrical composition of the 3d Sri Yantra.
13

Figure 7
As confirmation that the 2dimensional Sri Yantra is the counterpart of
seven overlapping Trees of Life, compare their geometrical compositions. The seven
overlapping Trees of Life are composed of 260 vertices, edges, triangles & tetrahedra.
The 3dimensional Sri Yantra has 260 vertices, edges & triangles. They are both
composed of 260 geometrical elements. The seven overlapping Trees of Life are a map of the
seven planes of consciousness. The number value 26 of YAHWEH, Godname of Chokmah, prescribes
these two maps of the seven planes.
14
15
Figure 8
Constructed from tetractyses, the seven enfolded polygons have 260 yods
outside their shared root edge. Each yod symbolizes one of the geometrical elements
composing the 3dimensional Sri Yantra. This demonstrates that the inner Tree of Life and
the Sri Yantra are equivalent representations of holistic systems.
16

The inner Tree of Life is composed of 260 yods outside its root
edge. This demonstrates its identity to the 3d Sri Yantra, which comprises 260
geometrical elements. Each yod symbolizes an element.
17

Figure 9
The 260 geometrical elements of the Sri Yantra comprise the eight elements
making up the central bindu point and innermost triangle and the 252 elements of the eight
layers of triangles. Their counterparts in the inner Tree of Life are the eight yods that
are either centres of polygons or Sephiroth of the Tree of Life and the 252 other yods
outside the shared root edge of the polygons.
18

3d Sri
Yantra Bindu +
innermost triangle:
4 vertices + 3 edges + 1 triangle
= 8 geometrical elements
4 layers of triangles:
84 vertices + 126 edges + 42 triangles
= 252 geometrical elements
Total = 260

Inner Tree of Life
8 yods () are either centres of polygons or locations of
Sephiroth of the outer Tree of Life;
has 252 coloured yods
Total = 260

The correspondence between the Sri Yantra and the inner Tree
of Life.
19

Figure 10
When their triangles are turned into tetractyses, there are 384 yods up to
the top of the seventh, overlapping Tree of Life. The 42 triangles of the Sri Yantra have
378 yods, whilst the central triangle has six hexagonal yods on its edges, a total of 384
yods. This numerical correlation is not an accident but indicates that the Sri Yantra and
the seven Trees of Life are isomorphic representations.
20

The Sri Yantra is equivalent to the lowest 7 Trees of Life
because it comprises as many yods as there are yods up to the top of these
trees.
21

Figure 11
According to Plato, the celestial sphere was designed in the proportions of
the squares of the numbers 1, 2 & 3. Arranged in the shape of the Greek letter lambda,
this set of seven integers (the socalled “Lambda”) is but two sides of a tetractys array of
10 integers (let us call it the “Lambda Tetractys”) that add up to 90. The four integers 1,
3, 9 & 27 on one side of the array add up to 40. The sum of the remaining integers is
50. The Sri Yantra is formed from five downwardpointing triangles expressing the Shakti
(feminine) aspect of creation and four upwardpointing triangles expressing its Shiva
(masculine) aspect. If each triangle is considered a tetractys, the number of yods in the
nine tetractyses is 90, which is the sum of the integers in the tetractys extension of
Plato’s Lambda. The four Shiva triangles/tetractyses have 40 yods and the five Shakti
triangles/tetractyses have 50 yods. The source of the Sri Yantra therefore conforms to the
Lambda Tetractys pattern, confirming its archetypal quality.
The four integers adding to 40 are all odd integers. The six integers adding
to 50 are all even. The Pythagoreans regarded even integers as female and odd integers as
male. This is consistent with the five triangles that embody the Shakti creative energy
(female principle) having 50 yods and the four triangles that embody the Shiva energy (male
principle of creation) having 40 yods. The division of the Lambda Tetractys into even and
odd integers matches precisely its counterpart as five Shakti triangles and four Shiva
triangles. The Lambda Tetractys is an arithmetic expression of the paradigm underlying
different sacred geometries.
22
Figure 12
As tetractyses, the nine primary triangles generating the Sri Yantra have 27
yods at corners and nine central yods, i.e., 36 yods. The sum of the integers at the corners
of the Lambda Tetractys is 36 (the largest of its integers is 27). The nine tetractyses have
54 hexagonal yods. The sum of the seven integers in the Lambda Tetractys arranged at the
corners and centre of a hexagon is 54. This further demonstrates that the Lambda Tetractys
arithmetically expresses the geometrical origin of the Sri Yantra. The integers 1 and 8 at
two corners of the Lambda Tetractys denote, respectively, the central yod of the unpaired
Shakti tetractys (the smallest, downward pointing, blue tetractys and the eight central yods
of the four pairs of Shiva & Shakti tetractyses forming Stars of David. The integer 27
at the third corner of the Lambda Tetractys is the number of yods at the corners of the nine
tetractyses.
24
Figure 13
The nine triangles with 27 vertices overlap to form the 3dimensional Sri
Yantra whose 43 triangles have 87 vertices. 60 new vertices are generated. This is
comparable with the Tree of Life when its 16 triangles with 10 vertices are turned into
tetractyses made up of 70 yods: 60 new yods appear.
26

60 new vertices are generated when 9 triangles with 27
vertices form the 3d Sri Yantra with 87 vertices in its 43 triangles.
Likewise, 60 yods are created by turning the 16 triangles of the Tree of
Life into tetractyses.
27

Figure 14
The four layers of triangles in the 3dimensional Sri Yantra have 84
vertices. This is the number of yods surrounding the centre of the 2ndorder tetractys. The
24 triangles of the outer two groups have 48 vertices. This is the number of hexagonal
(brown) yods in the seven tetractyses arranged in a hexagon that surround the centre. The
two inner groups of triangles have 36 vertices. 36 yods in the 2ndorder tetractys do not
belong to these tetractyses. These correlations show how the Sri Yantra is equivalent to the
2ndorder tetractys – a higher differentiation of the tetractys symbolizing the 10fold
nature of Divine Unity.
28

Correspondence between the 84 vertices in the 4
layers of triangles of the 3d
Sri Yantra and the 84 yods surrounding the centre of the 2ndorder
tetractys.
29

Figure 15
When the lowest Tree of Life is constructed from tetractyses, there are 84
yods up to the top of the lowest Tree of Life. They correspond to the 84 corners of the 42
triangles of the Sri Yantra. The third and fourth layers of triangles have 48 corners
corresponding to the 48 yods up to Chesed, the first Sephirah of Construction, and the first
and second layers have 36 vertices corresponding to the 36 yods between Chesed and the top
of the lowest tree.
30

Correspondence between the Tree of Life and the 3d
Sri Yantra.
31

Figure 16
336 yods lie on the edges of the 42 triangles of the Sri Yantra. 168 yods
form the edges of each half. 168 yods also lie on the edges of the 14 triangles in the
lowest layer.
32

336 yods lie on the 126 edges of the 42 triangles of the 3d
Sri Yantra. 168 yods lie on the edges of one half and 168 yods lie on the edges
of the other half. Remarkably, the same number of yods also lie on the edges of
the 14 triangles in the lowest layer of the Sri Yantra, whilst 168 hexagonal
yods lie on the edges of the 28 triangles in its first 3 layers.
33

Figure 17
When the 42 triangles of the Sri Yantra are converted into tetractyses, 168
yods lie on the edges of the 28 triangles in the first three layers. 168 yods lie on the
edges of the 14 triangles in the fourth layer.
34
Figure 18
336 yods lie on the edges of the 42 triangles of the 3dimensional Sri
Yantra. 168 yods lie on the edges of the 21 triangles in one half and 168 yods lie on the
edges of the 21 triangles in the other half.
36
Figure 19
The first (6+6) enfolded polygons of the inner Tree of Life have 42 corners
that do not coincide with Sephiroth of the outer Tree of Life. The eight corners that do
coincide are shown as white yods (although not a Sephirah, Daath can be formally treated
here as a Sephirah because it is Yesod of the next higher, overlapping Tree of Life). Each
set of six polygons have 168 yods (red or blue) that are not corners. Compare this with the
42 centres of triangles and the 168 yods on the edges of each half of the Sri Yantra. The
correspondence is complete if we include the seven hexagonal yods of the central triangle
(corresponding to the seven Sephiroth whose positions coincide with corners) and the bindu,
which corresponds to Daath.
38

Correspondence between the inner Tree of Life and
the 3d Sri Yantra
39

Figure 20
When the triangles of the Sri Yantra are each constructed from three
tetractyses, its outermost 14 triangles have 168 hexagonal yods on the edges of their 42
tetractyses.
40

The 14 outermost triangles of the Sri Yantra embody the
superstring structural parameter 168 as the number of hexagonal yods on the
edges of their 42 tetractyses.
41

Figure 21
The dodecagon is the seventh and last of the regular polygons in the two sets
that constitute the inner Tree of Life.
42
Figure 22
The dodecagon requires 168 extra yods when its sectors are divided into
three tetractyses. 14 yods are added per sector. Therefore, six sectors have 84 extra yods.
As the dodecagon is two hexagons rotated through 30°, the number 168 embodied in the
dodecagon divides naturally into 84 and 84. This is the counterpart of the 84 vertices of
the 42 triangles of the Sri Yantra and the 84 hexagonal yods on the edges of its outermost
14 triangles.
44

168 extra yods are needed to construct each of the sectors of the
dodecagon from three tetractyses.
45

