ARTICLE 29
by
Stephen M. Phillips
Flat 4, Oakwood
House, 117119 West Hill Road. Bournemouth. Dorset BH2 5PH. England.
Website: http://smphillips.mysite.com
Abstract
As, respectively, the first and last of the Catalan solids,
the triakis tetrahedron and the disdyakis triacontahedron are unique in having
numbers of edges and faces that differ by a factor of 10. This means that the
numbers of geometrical elements of any particular kind surrounding their axes
also differ by this factor. The tenfold multiplicity of the properties of the
disdyakis triacontahedron is evidence of its holistic character. The Godname YAH
with number value 15 picks out the truncated cuboctahedron — the 15th in the
families of Archimedean and Catalan solids — as the only one of them with 48
vertices. Surrounding its axis are 550 vertices, edges and triangles. This is
the number of Sephirothic emanations in the Cosmic Tree of Life that maps all
levels of reality. The counterpart of this property in the Platonic solids is
the 550 vertices, edges & triangles in their 50 faces. The Godname YAHWEH
determines the disdyakis triacontahedron as the 26th polyhedron. The Godnames
EHYEH and ADONAI prescribe the numbers of geometrical elements surrounding the
axes of the triakis tetrahedron and the disdyakis triacontahedron. The former is
built from 137 geometrical elements, showing how it embodies the reciprocal
of the fine structure constant that determines properties of atoms. Its
counterpart in the inner Tree of Life is the 1370 yods in 137 tetractyses that
are needed to construct it from tetractyses. When, instead, its internal
triangles are each constructed from three tetractyses, the triakis tetrahedron
has 168 elements surrounding its axis. It therefore embodies also the structural
parameter of the heterotic superstring. The disdyakis triacontahedron has 840
yods surrounding its axis. They symbolize the 840 circularly polarized
oscillations made by each helical whorl of the superstring as it winds 2½ times
around its axis. The polyhedron has 1680 geometrical elements surrounding its
axis. Their counterparts in the superstring are the 1680 oscillations in a
whorl. The numbers 168, 840 and 1680 have a natural representation in a
tetractys pattern of the first 40 odd integers after 1.

1
Article 28 showed that an isomorphism exists between the
disdyakis triacontahedron with 62^{1} vertices and the two sets of the last six polygons of the inner Tree
of Life whose 62 corners are unshared with its outer form. It allowed the
root structure of the superstring gauge symmetry group E_{8} and its subgroups
E_{7} and E_{6} to be correlated with the icosahedron and dodecahedron
within this polyhedron. This article will reveal further ways in which parameters of
particle physics are embodied in it. Three ways of constructing polyhedra with triangular
faces from tetractyses will be discussed (labelling of cases follows discussion in previous
articles):
Case B: Internal triangles divided into three tetractyses; polygonal faces
divided into three tetractyses;
Case A: internal triangles divided into three triangles; faces turned into one tetractys;
Case C: internal triangles turned into tetractyses; faces turned into tetractyses;
(The fourth possibility in which internal triangles are turned into tetractyses and faces
divided into three tetractyses need not be considered for the current purpose).
Table 2. Formulae for the three types of construction of polyhedra with
triangular faces.

Case C

Case A

Case B

Surface 



Number of vertices surrounding axis
= 
C–2

C–2

C+F–2

Number of edges surrounding axis = 
E

E

E+3F

Number of triangles surrounding axis
= 
F

F

3F

Subtotal = 
2E

2E

2E+6F

Interior 



Number of vertices surrounding axis
= 
0

E

E

Number of edges surrounding axis = 
C–2=E–F

C–2+3E=4E–F

C–2+3E=4E–F

Number of triangles surrounding axis
= 
E

3E

3E

Subtotal = 
2E–F

8E–F

8E–F

Total = 
4E–F

10E–F

10E+5F

Definitions
C = number of vertices of polyhedron.
E = number of polyhedral edges.
F = number of polyhedral faces.
C, E & F are related by Euler’s formula for a convex polyhedron:
C – E + F = 2.
m

=

number of triangular sectors of a face with m edges. 
n(m)

=

number of faces with m sides. 
L

≡

Σmn(m) = number of triangular sectors of
faces. 


^{m} 
The internal triangles formed by the centre of the polyhedron and the two
ends of an edge are turned into single tetractyses. Triangular sectors of faces are turned into
tetractyses.
Surface
Number of vertices in faces = C + F = 2 + E. 
Number of edges in faces = E + 
Σmn(m) = E + L. 


^{m} 
Number of triangles in faces = L. 
Number of vertices, edges & triangles = 2 + E + E + L + L = 2E
+ 2L + 2. 
Interior 
Number of vertices = 1.

2
Number of edges = C.
Number of triangles = E.
Number of vertices, edges & triangles = C + E + 1 = 2E – F + 3.
Total number of vertices, edges & triangles = 4E – F + 2L + 5.
The number ‘5’ denotes the five geometrical elements making up the axis (three vertices and two
edges). The number of geometrical elements in the surface of the polygon that surround the axis
≡ S = 2E + 2L. The number of internal elements surrounding the axis ≡ I = 2E – F. The total
number of elements surrounding the axis ≡ N = S + I = 4E – F + 2L.
E = 18 and F = 12 for the triakis tetrahedron and E = 180 and F = 120 for
the disdyakis triacontahedron, that is, these numbers are ten times as large in each case.
Table 2 indicates that the numbers of geometrical elements of each kind
surrounding the axis either inside or on the faces of a polyhedron with triangular faces
depends only on the value of E and F. This means that, for the disdyakis triacontahedron,
the number of internal or external geometrical elements of each kind is always ten times the
corresponding number for the triakis tetrahedron. The tenfold property is unique to this
pair of Catalan solids because no other pair has E and F differing by a factor of 10.
Table 3. List of values of S, I and N for the Archimedean and Catalan
solids.
Starting with the truncated tetrahedron (the polyhedron with the least
number of faces), and counting down these tables in a zigzag fashion across pairs of dual
polyhedra listed in order of increasing C, the 15th polyhedron picked out by
the Godname YAH with number value 15 is the truncated cuboctahedron and the
26th (and last) polyhedron picked out by the complete Godname YAHWEH with
number value 26 is the disdyakis triacontahedron (both shown in Table 3 with orange cells. We now know the significance of the latter: it is
the polyhedral counterpart of 10 overlapping Trees of Life. However, what is the
significance of the truncated cuboctahedron? Table 3 shows that 550 vertices, edges & triangles surround its axis,
where
550 =

55
55 55
55 55 55
55 55 55
55

and
55 =

1
2 3
4 5 6
7 8 9 10 .

3
The Decad (10) — the Pythagorean measure of perfection — determines the
number of geometrical elements in the truncated cuboctahedron. As discussed in Article
3,^{2} the map of all levels of reality, called the ‘Cosmic Tree of
Life’ (CTOL), consists of 91 overlapping Trees of Life, the seven lowest ones representing
26dimensional spacetime. CTOL has 550 Sephirothic
emanations.^{3} The truncated cuboctahedron is unique among the Archimedean and
Catalan solids in being made up of the same number of geometrical elements as there are
Sephirothic levels in the map of the spiritual cosmos.
The counterpart of this beautiful property in the Platonic solids is the
fact that they have 550 vertices, edges & triangles in their 50
faces.^{4} Its counterpart in the dodecahedron is the fact that, when constructed
from tetractyses, it has 550 hexagonal yods.^{5}
The number 550 is always embodied in objects that possess sacred geometry.
For this reason, it is no coincidence that the polyhedron is the 15th in the
sequence of Archimedean and Catalan solids, as prescribed by YAH.
According to Table 3, the disdyakis triacontahedron has 1320 geometrical elements
surrounding its axis, that is, 1260 geometrical elements other than the 60 vertices that
surround it. This is the number of yods in 126 tetractyses. Remarkably, 126 is the sum of
the number values of the four types of combinations of the letters A, H and I in EHYEH
(AHIH), the Godname of Kether:
A = 1, H = 5, I = 10

1.
2.
3.
4. 
A + H + I
AH + HI + AI + HH
AHI + HIH + AHH
AHIH 
= 16
= 42
= 47
= 21 

Total

= 126 
Just as remarkable is the fact that there are 1260 yods on the edges of the 360
tetractyses in the 120 faces of the disdyakis triacontahedron.^{6} This illustrates how EHYEH prescribes the disdyakis
triacontahedron.
The 1320 geometrical elements surrounding the axis of this polyhedron
comprise 660 (=66×10) elements and their mirror ages. As 66 is the 65th
integer after 1, the Godname ADONAI of Malkuth with number value 65 prescribes
the disdyakis triacontahedron. Similarly, it prescribes the triakis tetrahedron with 66
elements surrounding its axis.
We showed in Article 27 that the number of geometrical elements of a given
type surrounding the axis of the disdyakis triacontahedron is ten times the number of like
elements in the triakis tetrahedron for case A and case B. Inspection of Table 3 shows that
this is true also for case C. The triakis tetrahedron has 132 elements surrounding its axis,
which consists of five elements. The polyhedron is therefore built from 137 geometrical
elements. Three remarkable properties emerge:
Case A:168 elements surround its axis, where
168 is the number of roots of the superstring gauge symmetry group
E_{8} that do not belong to its subgroup E_{6};
Case B: 240 elements surround its axis, where 240 is the number of roots of E_{8};
Case C: it possesses 137 elements.
Physicists regard 137 as, perhaps, the most important number in physics
because, as the measure of the strength of the electromagnetic interaction between an electron
and an electromagnetic field, the fine structure constant e^{2}/ħc ≈ 1/137 determines
the very nature and size of atoms, as well as the chemistry of materials arising from their
mutual
4
bonding. The simplest construction of the triakis tetrahedron from
tetractyses (case C) requires 137 geometrical elements. The Pythagorean Tetrad determines this
number because 137 is the 33rd prime number, where 33 = 1! + 2! + 3! + 4!, and 33 is the 16th
odd integer after 1 that can be assigned to a 4×4 array (read across the rhombus):
The next simplest construction of the triakis tetrahedron (case A) require
168 geometrical elements surrounding its axis, where 168 is
the sum of the 12 odd integers after 1 that form the edges of a rhombus, four to a side:
The last construction (case B) requires 240 elements surrounding its axis,
where
is the sum of the 16 integers that can be assigned to a 4×4 array, starting
with the first four odd integers after 1 and adding multiples of them by 2, 3 & 4. It is
remarkable that the largest number in the 4×4 array of the first 16 highly
composite numbers* is 1680, which is the number of geometrical elements
surrounding the axis of the disdyakis triacontahedron in case A:
___________________________________
*An integer is highly composite if it has more factors than
all integers smaller than it.
5
If the first 16 factors of 1680 are arranged in a 4×4 array, 24 is the
largest one:
This means that 240 is the largest of the first 16 divisors of 1680
multiplied by 10:
This demonstrates that the numbers 168, 240 and 1680 have
an arithmetic connection as well as a geometrical one. It exists because these numbers are
groupdynamical and structural parameters of the E_{8}×E_{8} heterotic
superstring, as explained shortly.
The counterpart in the inner Tree of Life of the 240 geometrical elements
surrounding the axis of the triakis tetrahedron in case B are the 240 yods in the seven
separate regular polygons other than the 55 corners of their 48
sectors (Fig. 1). The inner form of ten Trees of Life consists of 70 separate polygons
with 2400 hexagonal yods and 550 corners of their 480 tetractyses.
The 550 elements shaping the truncated cuboctahedron in case C correspond to
the 550 corners that shape the polygons. The 2400 elements shaping the disdyakis
triacontahedron in case B correspond to the 2400 yods other than these corners. As
2400 = 49^{2} – 1 = 3 + 5 + 7 +…+
97,
2400 is the sum of the 48 odd integers after 1. Their
average value is 50, the number value of ELOHIM, Godname of Binah.
49 is the number value of EL CHAI, the Godname of Yesod. The physical meaning
of the number 240 is the 240 gauge fields of E_{8} associated with its 240 nonzero
roots. As each gauge field has 10 spacetime components, the 240 fields have 2400 spacetime
components. Each one is symbolised by a hexagonal yod in the 70 separate polygons of the inner
form of ten Trees of Life.
6
7
For case A, there are 1680 geometrical elements surrounding the axis of the
disdyakis triacontahedron. They are degrees of freedom that appear in the subatomic world as
the 1680 circular turns in each “whorl” of the basic unit of matter described paranormally by
Annie Besant and C.W. Leadbeater^{7} and interpreted by the author as circularly polarised
oscillations of a standing wave (Fig. 2). Ten of these constitute the closed, E_{8}×E_{8}
heterotic superstring. Three socalled “major” whorls are thicker than the seven “minor”
ones.
The counterpart in the inner Tree of Life of the 137 geometrical elements
needed to construct the triakis tetrahedron is the fact that 1370 yods are needed to build the
two sets of seven enfolded polygons when their 94 sectors are divided into three tetractyses
(Fig. 3). They are in 282 tetractyses, where
282 is the number value of Aralim,(“thrones”), the Angelic Order assigned to Binah. The fact that yods in 137
tetractyses fill the inner Tree of Life proves the number 137 to be archetypal, as shown by
its ubiquitous presence in atomic, nuclear and particle physics. The
correspondences:
1370 yods of inner Tree of Life 1370 geometrical elements of ten triakis
tetrahedra
1320 elements of disdyakis triacontahedron 1320 geometrical elements surrounding axes of ten triakis
tetrahedra
show that the disdyakis triacontahedron is equivalent to ten
triakis tetrahedra (Fig. 4), whose number of geometrical elements is equal to the number of yods
making up the inner Tree of Life. Each yod symbolizes one of these elements. This is
further
8
evidence that the disdyakis triacontahedron is the polyhedral counterpart of
the inner Tree of Life, as discussed in Articles 2224.^{8}
Consider those Catalan solids whose faces are triangular as built from
tetractyses, with the interior triangles regarded as single tetractyses (case C). The formulae
for the various types of geometrical elements composing the solids are shown below:
Number of vertices ≡ V = C + 1. Number of vertices surrounding axis ≡ V' = C
– 2.
Number of edges ≡ e = C + E. Number of edges surrounding axis ≡ e' = C + E – 2.
Number of triangles ≡ T = E + F. Number of triangles surrounding axis = E + F.
Total number of geometrical elements ≡ N = 2C + 2E + F + 1 = C + 3E + 3.
Number of geometrical elements surrounding axis ≡ N' = C + 3E – 2.
Table 4 lists the numbers of elements of each type (Catalan solids without
triangular faces have dashes in cells):
Table 4. Numbers of geometrical elements in the Catalan solids.
Catalan solid

V

V'

e

e'

T

N

N'

triakis tetrahedron 
9

6

26

24

30

65

60

rhombic dodecahedron 














triakis octahedron 
15

12

50

48

60

125

120

tetrakis hexahedron 
15

12

50

48

60

125

120

deltoidal icositetrahedron 














pentagonal icositetrahedron 














rhombic triacontahedron 














disdyakis dodecahedron 
27

24

98

96

120

245

240

triakis icosahedron 
33

30

122

120

150

305

300

pentakis dodecahedron 
33

30

122

120

150

305

300

deltoidal hexacontahedron 














pentagonal hexacontahedron 














disdyakis triacontahedron 
63

60

242

240

300

605

600

Table 3 indicates that, when their triangular faces are divided into three
tetractyses, 240 geometrical elements inside the disdyakis triacontahedron surround its axis
and 24 internal elements surround the axis of the triakis tetrahedron. Table 4 shows that, when their faces are single tetractyses (case C), the
triakis tetrahedron is built from 30 tetractyses with 24 edges and the disdyakis
triacontahedron is constructed from 300 tetractyses with 240 edges. For case B, the total
number of geometrical elements surrounding their axes are, respectively, 240 and 2400. The
counterpart of this pattern in the heterotic superstring shown in Fig. 2 are the 240 gauge
charges corresponding to the 240 roots of the gauge symmetry group E_{8} that are
spread around each of the ten whorls of the UPA, 24 to a whorl. The disdyakis
triacontahedron is the polyhedral counterpart of the heterotic superstring and the triakis
tetrahedron is the polyhedral counterpart of a whorl, its 24 shapedetermining
edges surrounding its axis being the geometrical counterpart of the 24 gauge charges carried
by each whorl of the UPA.
This analogy can be extended to the very dimensions of spacetime predicted
by string theory. Table 4 indicates that the triakis tetrahedron has 26 edges,
showing how it is prescribed by YAHWEH with number value 26. Two of these
edges form the central axis, leaving 24 edges surrounding it. The former correspond to the
longitudinal dimension (distance measured along the length of a string) and to the time
dimension, whilst the latter are the counterpart of the 24 dimensions of
26dimensional spacetime
9
that are transverse to the string. The number 26 is related
to the number 24 as
where 24 =1×2×3×4. Appropriately, the Godname ADONAI of Malkuth (the
physical aspect of the Tree of Life) prescribes the triakis tetrahedron as the
polyhedral form of the fundamental component of the superstring — the whorl — because its
number value 65 is the number of geometrical elements from which this Catalan solid is built (see Table 4). The counterpart of this in the Tree of Life are the
65 Sephirothic emanations in the lowest ten Trees of Life belonging to CTOL
(Fig. 5).
Below their top are 1680 yods contained in 385 tetractyses (Fig. 6), where
385 = 
1^{2}
2^{2 } 3^{2}
4^{2} 5^{2 } 6^{2}
7^{2} 8^{2} 9^{2}
10^{2} .

This demonstrates how ADONAI prescribes both the ten trees representing the
10dimensional spacetime of superstrings and the 1680 circularly polarised oscillations of
each whorl of the heterotic superstring, their counterpart in the disdyakis triacontahedron
being the 1680 geometrical elements surrounding its axis in case A.
10
11
The disdyakis triacontahedron in case C has 240 edges surrounding its axis.
They are symbolized in the lowest Tree of Life in CTOL as the 240 extra yods generated by
conversion of each of its 19 triangles into three tetractyses (Fig. 7). The number 240 expresses in both contexts the number of degrees of
freedom needed to form the object, given in the former its essential 11 Sephirothic points
and in the latter the axis of the polyhedron made up of five geometrical elements (three vertices & two
edges). A yod is at the centre of each of the 300 triangles inside and on the
faces of the disdyakis triacontahedron, which has 60 vertices surrounding
its axis. Each of the 240 edges has two hexagonal yods between its ends. The number of yods
surrounding the axis of the disdyakis triacontahedron in case C = 300 + 60 + 240×2 = 840 =
84×10, where
84 = 1^{2} + 3^{2} + 5^{2} + 7^{2}
and
10 = 1 + 2 + 3 + 4.
This demonstrates how the Tetrad Principle determines the yod population of
this polyhedron as the number of tetractyses with the same number of yods. The next level of
differentiation of the tetractys — the 2ndorder tetractys shown in Fig. 8 — has 84 yods surrounding its centre. The meaning of this is that a
holistic system patterned or structured according to the Tree of Life blueprint needs 84 degrees of freedom to manifest at the level symbolised by
the (○) yod at the centre of the 2ndorder tetractys.
We saw in Article 27^{9} that the polyhedral example of this is the tetrahedron, which in
case B requires 30 triangles with 40 edges and 15 vertices, that is, 85
geometrical elements. 84 of which surround its centre. The 15 yods at
corners of
12
the 10 tetractyses in the 2ndorder tetractys symbolize the
15 vertices and the 70 hexagonal yods symbolize the 30 tetractyses and 40
edges. Weighted with the number 10 (the Pythagorean Decad and measure of Wholeness), the 84
yods surrounding the centre of the 2ndorder tetractys generate the number 840. It is the
number of yods surrounding the axis of the disdyakis triacontahedron when its interior
triangles and faces are turned into tetractyses. The yod at its centre symbolizes this
axis.
The number 840 manifests in the heterotic superstring as the 840 circular
turns made by each helical whorl as it winds in an outer circuit of 2½ revolutions, making the
same number of turns as it returns to its starting point after winding another 2½ times around
the spinaxis of the superstring (Fig. 2). As
29^{2} – 1 = 840 = 3 + 5 + 7 + … + 57,
the number 840 is the sum of the first 28 odd integers after 1. This means
that the number 8400 can be thought of as the sum of ten identical sets of 28 odd integers,
that is, as the sum of 280 odd integers. There are 8400 circular turns in the
ten whorls as they wind 2½ times in either the inner or the outer half of the superstring. The
number value 280 of Sandalphon, Archangel of Malkuth, determines the number of
turns in 2½ revolutions of all ten whorls and the number value 168 of
Cholem Yesodeth, the Mundane Chakra of Malkuth — the same Sephirah — is the
number of turns in a halfrevolution of each whorl. As
41^{2} – 1 = 1680 = 3 + 5 +7 +... + 81,
1680 is the sum of the first 40 odd integers after 1. As
13^{2} – 1 = 168 = 3 + 5 + 7 +… + 25,
168 is the sum of the first 12 odd integers after 1. These
properties allow the number 1680 to be represented as a tetractys array of quartets of
successive odd integers:
The sum of the ten quartets of odd integers is 1680. The sum of the seven
quartets of odd integers shown shaded is 840, as is the sum of the quartets of integers at the
corners. The 3:7 division of the tetractys array manifests in the heterotic superstring as the
840 circular turns in the inner or outer halves of each helical whorl.
The sum of the quartet of integers at its centre is 24. This is the
number of gauge charges of the superstring gauge symmetry group E_{8} that are spread
around each whorl of the heterotic superstring. The sum of the first three quartets of integers
is 168, the number of turns in a halfrevolution of a whorl, and the sum of
the first seven quartets is 840, the number of turns in 2½ revolutions, that is, in half a
whorl. The sum of all 10 quartets is 1680, which is the number of turns in a whorl. The sum of
the last three quartets of integers at the corners of the array is 840. The distinction between
hexagonal yods and yods at corners of a tetractys creates the two halves of the whorl.
Such a beautiful property of the odd integers connecting them to the
threedimensional structure of the superstring cannot be due to coincidence. Rather, it serves
to demonstrate the power of the insight expressed in the Pythagorean statement that “form
is number.”
29 is the tenth prime number in the tetractys array of such
numbers:
13
2
3 5
7 11 13
17 19 23 29 .
This illustrates once again the power of the tetractys to generate numbers
that in turn determine other numbers of universal significance, such as the superstring
structural parameter 1680 and the number 240 of gauge charges corresponding to the 240 roots of
the gauge symmetry group E_{8}:
240 =

24
24 24
24 24 24
24 24 24 24 .

Indeed, this is not merely a trivial way of representing a factor of 10. The
E_{8}×E_{8} heterotic superstring is the physical manifestation of this
Pythagorean symbol of holistic systems, each of its ten whorls carrying 24 gauge charges
associated with these roots. The superstring exists in 10dimensional spacetime, which is
symbolized by a tetractys. The three yods (o) at the corners denote the three largescale
dimensions of space, the six yods () at the corners of a hexagon symbolize the six compactified
dimensions and the yod (□) at its centre denotes the
dimension of time.
Truly, one can now understand the meaning of the oath sworn by the followers
of Pythagoras to their master:
“I swear by the discoverer of the tetractys,
Which is the spring of all our wisdom,
The perennial fount and root of Nature.”
References
^{1} Numbers written in boldface throughout
this article are the gematria number values of the ten Sephiroth, their Godnames,
Archangels, Orders of Angels & Mundane Chakras. They are listed in Table 1:
Table 1. The number values of the ten Sephiroth in the four Worlds.

SEPHIRAH

GODNAME

ARCHANGEL

ORDER OF ANGELS

MUNDANE CHAKRA

1 
Kether
(Crown)
620 
EHYEH
(I am)
21 
Metatron
(Angel of the
Presence)
314 
Chaioth ha Qadesh
(Holy Living Creatures)
833

Rashith ha Gilgalim
First Swirlings.
(Primum Mobile)
636 
2 
Chokmah
(Wisdom)
73 
YAHWEH, YAH
(The Lord)
26,
15

Raziel
(Herald of the Deity)
248 
Auphanim
(Wheels)
187 
Masloth
(The Sphere of the Zodiac)
140 
3 
Binah
(Understanding)
67 
ELOHIM
(God in multiplicity)
50

Tzaphkiel
(Contemplation of God)
311

Aralim
(Thrones)
282

Shabathai
Rest.
(Saturn)
317 

Daath
(Knowledge)
474 




14
4 
Chesed
(Mercy)
72 
EL
(God)
31 
Tzadkiel
(Benevolence of God)
62 
Chasmalim
(Shining Ones)
428

Tzadekh
Righteousness.
(Jupiter)
194 
5 
Geburah
(Severity)
216

ELOHA
(The Almighty)
36

Samael
(Severity of God)
131

Seraphim
(Fiery Serpents)
630

Madim
Vehement Strength.
(Mars)
95 
6 
Tiphareth
(Beauty)
1081

YAHWEH ELOHIM
(God the Creator)
76 
Michael
(Like unto God)
101

Malachim
(Kings)
140

Shemesh
The Solar Light.
(Sun)
640 
7 
Netzach
(Victory)
148

YAHWEH SABAOTH
(Lord of Hosts)
129

Haniel
(Grace of God)
97 
Tarshishim or
Elohim
1260

Nogah
Glittering Splendour.
(Venus)
64 
8 
Hod
(Glory)
15

ELOHIM SABAOTH
(God of Hosts)
153

Raphael
(Divine Physician)
311

Beni Elohim
(Sons of God)
112

Kokab
The Stellar Light.
(Mercury)
48 
9 
Yesod
(Foundation)
80

SHADDAI EL CHAI
(Almighty Living
God)
49,
363

Gabriel
(Strong Man of God)
246

Cherubim
(The Strong)
272

Levanah
The Lunar Flame.
(Moon)
87 
10 
Malkuth
(Kingdom)
496

ADONAI MELEKH
(The Lord and
King)
65,
155

Sandalphon
(Manifest Messiah)
280 
Ashim
(Souls of Fire)
351

Cholem Yesodeth
The Breaker of the
Foundations.
The Elements.
(Earth)
168 
The Sephiroth exist in the four Worlds of Atziluth, Beriah, Yetzirah
and Assiyah. Corresponding to them are the Godnames, Archangels, Order of Angels and
Mundane Chakras (their physical manifestation). This table gives their number values
obtained by the ancient practice of gematria, wherein a number is assigned to each letter
of the alphabet, thereby giving a number value to a word that is the sum of the numbers of
its letters.
^{2}^{} Phillips, Stephen M. Article 5: “The Superstring as the Microcosm of
the Spiritual Macrocosm,” ( WEB, PDF).
^{3} ^{}The number of Sephirothic emanations in n overlapping Trees of Life ≡
N(n) = 6n + 4. N(91) = 550.
^{4 }Phillips, Stephen M. Article 3: “The Sacred Geometry of the Platonic
Solids,” ( WEB, PDF), p. 11.
^{5 }Ibid, p. 10.
^{6 }Phillips, Stephen M. Article 27: “How the Disdyakis Triacontahedron
Embodies the Structural Parameter 1680 of the E _{8}×E _{8} Heterotic
Superstring.” ( WEB, PDF), p. 18.
^{7 }Besant, Annie and Leadbeater. C.W., Occult Chemistry,
Theosophical Publishing House, Adyar, Chennai. India, 1951.
^{8 }Phillips, Stephen M. Article 22: “The Disdyakis Triacontahedron as
the 3dimensional Counterpart of the Inner Tree of Life;” Article 23: “The ‘Polyhedral
Tree of Life;” Article 24: “More Evidence for the Disdyakis Triacontahedron as the
3dimensional Realisation of the Inner Tree of Life and its Manifestation in the
E _{8}×E _{8} Heterotic Superstring.” ( WEB, PDF).
^{9 }Ref. 6, pp. 23.
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