ARTICLE 61
by
Stephen M. Phillips
Flat 4, Oakwood House, 117119 West Hill Road. Bournemouth.
Dorset BH2 5PH. England.
Website: http://smphillips.mysite.com
Abstract
Sacred geometries embody the
number 216 because it is the gematria number value of Geburah, one of the 10
Sephiroth of the Kabbalistic Tree of Life. For example, 216 points & lines
surround the centre of the 3dimensional Sri Yantra, whilst 216 yods intrinsic
to the seven enfolded, regular polygons of the inner Tree of Life line their 47
sectors when the latter are tetractyses. This means that the 70 polygons
enfolded in every 10 overlapping Trees of Life have 2160 such boundary yods.
This, too, is a parameter of holistic systems, e.g., 2160 lines & triangles
surround the axes of the five Platonic solids when their vertices and centres of
faces are joined to their centres. This number is known in astronomy as the
number of years it takes for the axis of the Earth to rotate through
30° as the Sun moves through each of
the 12 astrological signs into which the celestial sphere is divided (a
socalled ‘astrological era’). The Earth’s axis rotates 360° in the 12stage
cycle of a Platonic Year of 12×2160 = 25,920 years. A rotation of 1° requires 72
years. The number 72 is the number value of Chesed, the Sephirah opposite
Geburah in the Tree of Life. As a geometrical symbol for the 12 signs of the
Zodiac, spaced 30° apart, the dodecagon is the seventh and last regular polygon
in the inner Tree of Life. The number of yods surrounding the centres of two
joined, Type A dodecagons is 140, which is the gematria number value of Masloth,
the Mundane Chakra of Chokmah. The number value 73 of Chokmah is the number of
yods in a Type A dodecagon. What is remarkable is that the Sphere of the Zodiac
is the astrological identification of Masloth! If, like a year and the zodiac,
an astrological era is 12fold, then the 2160 yods that surround the centres of
the Type B dodecagons enfolded in 12 overlapping Trees symbolise the 2160 years
of an era represented by these 12 Trees. The Chinese calendar can accommodate
both a 10fold and a 12fold cycle because it groups years within a 10year
cycle (10 Celestial Stems) and a 12year cycle (12 Earthly Branches). Curiously,
the number (1680) of oscillations of each whorl of the UPA remoteviewed by
Charles Leadbeater over a century ago is the same as the number of years during
which the Earth’s axis rotates through an angle equal within a discrepancy of
0.12% to its current angle of inclination of about 23½°.

1
Table 1. Gematria 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 




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, Orders 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. Numbers from the table are written in
boldface in the article.

2
1. The number 216 of Geburah in sacred
geometries
The inner form of the Tree of Life consists of two sets of seven
polygons:
triangle, square, pentagon, hexagon, octagon, decagon & dodecagon.
When their 47 sectors are tetractyses, the seven enfolded polygons contain
264 yods (Fig. 1). Of the 264 yods in the seven enfolded polygons, 47 hexagonal yods are at
the centres of tetractyses. This leaves 217 yods (41 corners & 176 hexagonal yods)
lining their sides (Fig. 2). One of these is the topmost corner of the hexagon. It coincides
with the lowest corner of the hexagon that is part of the inner form of the next higher,
overlapping Tree of Life. 216 yods that are intrinsic to each Tree



Figure 1. The seven enfolded polygons of the inner Tree of Life contain 264
yods.

Figure 2. 217 yods line the 47 tetractyses in the
7 enfolded polygons.

Figure 3. 105 intrinsic, boundary
yods are associated with the first 5 polygons (blue) and with the last 2
polygons (red).

shape the tetractyses making up each half of the inner form of successive Trees of
Life. 216 is the number value of Geburah, the sixth Sephirah of Construction,
counting from the base of the Tree of Life. The seven enfolded polygons have
36 corners, where 36 is the number value of ELOHA,
the Godname of Geburah. This is an example of the conjunction of the numbers of the same
Sephirah in the same sacredgeometrical context.
The number 217 measures another property of the inner Tree of Life. The
seven enfolded polygons have 47 tetractys sectors containing 264 yods, of which 41 are
corners and 223 are hexagonal yods. Outside the root edge are (223–2=221) hexagonal yods, of
which four yods lie on the vertical axis of the hexagon and are shared with the outer Tree
of Life (see next paragraph). This leaves (221–4=217) hexagonal yods outside the root edge
which are intrinsic to the seven enfolded polygons. The number 217 is the intrinsic
hexagonal yod population of the inner Tree of Life external to the root edge.
When the 16 triangles in the outer Tree of Life are tetractyses, seven yods
lie on the Pillar of Mercy. They coincide with the seven green yods on the vertical axis of
the hexagon. These are the only yods that the outer Tree shares with its inner form in which
each yod is the same type in both cases. The 217 yods on the sides of the 47 tetractyses
consist of these seven shared yods and 210 (=21×10) yods that are intrinsic to the
inner Tree. It shows how EHYEH, the Godname of Kether with number value 21,
prescribes those yods unshared with the outer Tree that shape the tetractyses
making up its inner form.
Tabulated below in Table 2 are the numbers of intrinsic yods outside the
root edge on the sides of the tetractyses in each polygon:
Table 2. Number of intrinsic boundary yods outside root edge in the 7
separate Type A polygons.
Root edge 
Triangle

Square 
Pentagon

Hexagon

Octagon

Decagon

Dodecagon 
2 + 2 = 4

11

17

22

16

37

46

57

Total =

103

103

103 intrinsic yods (coloured blue) line the 25 tetractyses in
the first five enfolded polygons and 103 intrinsic yods (coloured red) line the
22 tetractyses in the last two enfolded polygons. 103 is the number value of
SABAOTH ("Hosts"), part of the Godnames of Hod and Netzach (see Table 1). Two blue yods in
the root edge can be associated with the former set and two red yods can be associated with
the latter. This means that the 210 intrinsic yods divide into two equal sets of
105 yods (Fig. 3). It is easily verified that these two sets are unique — there are no other
combinations of polygons with 103 yods.
Let us next compare this property of the inner Tree of Life with the Sri
Yantra. The 3dimensional Sri Yantra consists of four layers of 42 triangles (21
triangles in each half) that surround the central triangle (coloured green) above them. Its
three corners represent the threefold Godhead, or trimurti (Hindi:
3
Figure
4. The 21 triangles in each
half of the 3d Sri Yantra surrounding the seven points & lines in the central triangle
and bindu comprise 105 points & lines.
त्रिमू्र्ति, translation:
"Trinity"), of Shiva, Brahma & Vishnu. A dot, or bindu,
representing the Absolute, the source of all manifestation, both physical and superphysical.
The central triangle comprises three corners & three sides. The 42 triangles comprise 84
corners (42 in each half) and 126 sides (63 in each half). Each half of the 3‑dimensional Sri
Yantra is shaped by (42+63=105) corners & sides (Fig. 4). Together with the seven green
points & lines making up the bindu and the central triangle, (105+105+7=217) points &
lines constitute the Sri Yantra. 216 points & lines surround the central point, 210
(=21×10) belonging to the 42 triangles.
We find that the same number (217) that measures the shape of
the sectors of the seven enfolded polygons quantifies those geometrical elements that
shape the Sri Yantra. Moreover, the seven yods in the inner Tree of Life shared with
its outer form correspond to the seven points & lines making up the bindu and central
triangle. It is remarkable that the set of seven enfolded polygons divide uniquely into two
subsets of complete polygons with 105 yods that correspond to the 105 points & lines in
the 21 triangles in each half of the Sri Yantra. Both sacred geometries also display
the division: 217 = 1 + 216.
These correspondences demonstrate the equivalence of the Sri Yantra
and the inner Tree of Life. Their geometrical dissimilarity hides the fact that they embody
the same numbers quantifying analogous properties. These
numbers are defining parameters of all holistic systems/sacred geometries.
2. How the number 217 determines the dimension
of E_{8}
As well as shaping the inner Tree of Life and the 3dimensional Sri Yantra,
the number 217 has both an arithmetic and a geometric significance visàvis the dimension
248 of E_{8}, the rank 8, exceptional Lie group that plays a pivotal
role in one of the two heterotic superstring theories.
Arithmetic The dimension of SO(32) and
E_{8}×E_{8}, the symmetry groups describing the anomalyfree interactions
between the two types of heterotic superstrings, is 496. As the third perfect number
(1), this number is the sum of its nine factors:
496 = 1 + 2 + 4 + 8 + 16 + 31 +
62 + 124 + 248.
Therefore, 248 is the sum of the eight smallest
factors of 496:
248 = 
(1+2+4+8+16) + (31+62+124) 
= 
31 + 217, 
where 217 = 31 + 62 + 124 =
7×31. As 31 = 2^{0} +
2^{1} + 2^{2} + 2^{3} + 2^{4},
62 = 2×31 and 124 =
2^{2}×31, 217 may be written as the following sum of powers of
2:
217 = 2^{0} + 2^{3} + 2^{4} +
2^{6} + 2^{7},
so that 216 = 2^{3} +
2^{4} + 2^{6} + 2^{7}.
Geometric
Constructed from 67 triangles, the 5tree contains
280 yods when they are tetractyses, where 67 is the
number of Binah and 280 is the number value of Sandalphon, the
Archangel of Malkuth (Fig. 5). There are 248 yods up to Chesed of the
fifth Tree of Life (see also here), where
248 is the number of Raziel, the Archangel of Chokmah. This SL
is the 31st SL, where 31 is the number value of EL,
the Godname of Chesed. Therefore, the 248 yods comprise
31 SLs (shown in Fig. 5 as black yods) and 217 hexagonal yods (shown
as red yods). Remarkably, as the number of corners of tetractyses containing
248 yods, the number 31 determines the number
217 both geometrically, when the tetractyses are combined, and arithmetically, because 217 =
31×7, i.e., 31 separate tetractyses have
217 hexagonal yods.
Figure 5
3.
The zodiacal age measured by sacred geometry
As Figure 2 shows, 217 yods line the sides of the 47 tetractyses making up
each half of the inner Tree of Life. As the topmost corner of the hexagon in the inner Tree of
Life coincides with the lowest corner of the hexagon in the inner form of the next higher,
overlapping Tree of Life, 216 boundary yod are intrinsic to the set of
seven polygons enfolded in successive Trees. 216 is the number value of
4
Geburah. The number of yods on the boundaries of
the 47n tetractyses in the 7n polygons enfolded in the ntree ≡ B(n) =
216n + 1, where "1" denotes the
shared corner of the hexagon. The 470 tetractyses in the 70 polygons enfolded in the
10tree are shaped by B(10) = 2160 yods that are intrinsic to
them. In fact, the 70 polygons enfolded in every
10 Trees are composed of 470 tetractyses lined by 2160 yods. What is the significance of
the emanation of 10 Trees? According to the discussion of the Cosmic Tree of Life (CTOL)
in many previous articles, 91 Trees of Life map the seven cosmic planes of consciousness.
These Trees should be regarded as emanating in 10 stages, each a cycle of 10 Trees, the
last Tree emanated in each stage being, as its source, the first Tree of the next stage.
The number 2160 represents a measure of each cycle, being the number of yods needed to
shape the inner form of the 10 Trees emanated in each stage. Astronomers have calculated
that the axis of the Earth rotates in a circle once every 25,920 years approximately (the
socalled 'Platonic Year'). In this precession of the equinox, the axis rotates through 30° about
every 2160 years, creating an astrological age that is dominated by one of the 12 zodiacal
signs (2). It makes the stars move west to east about one degree about every
72 years. These numbers are only
approximate because the lengths of the ages are decreasing with time as the rate of
precession is increasing. Therefore, no two ages are of equal length. With this
qualification, the astronomical number 2160 may be seen as a terrestrial counterpart of the
parameter 2160 associated with the 10‑fold emanation of CTOL. It may be regarded as an
example of the hermetic principle "As above, so below." Remarkably, the first four enfolded
polygons have 72 intrinsic yods on
the sides of their 17 tetractyses, the last three polygons having 144 such yods lining their
22 tetractyses, so that the 216
boundary yods intrinsic to each set of seven polygons naturally divide into a set of
72 and a set of 144 yods. The
number value of Chesed is 72 and
the number value of Geburah, the next
Sephirah, is 216, where
216 = 2^{3} + 2^{4}
+ 2^{6} + 2^{7}. Notice that this can be rearranged as
(2^{3}+2^{6}) + (2^{4}+2^{7}) = (8+64) + (16+128) = 72 + 144, which are the numbers of intrinsic yods
lining the tetractyses in, respectively, the first four and the last three enfolded polygons
of the inner Tree of Life. When
geometry is sacred, it always exhibits a beautiful harmony with the properties of
integers. The division 216 = 72 + 144 is found also in the 144 Polyhedron, which is
part of the Polyhedral Tree of Life (see here). Formed from
the disdyakis dodecahedron with 26
vertices, 72 edges &
48 faces by attaching tetrahedra to
its faces, it has (26+48=74) vertices, (72 + 3×48 = 216) edges and (3×48=144) triangular faces. Its 216 edges comprise the 72 edges of the disdyakis dodecahedron and the extra
144 edges of the added tetrahedra. The 144 Polyhedron has 432 geometrical elements
surrounding an axis passing through two opposite vertices. In terms of years, this number,
which plays a part in Hindu chronology concerning the four yugas, corresponds
to the period of 1/5 of an astrological age, or a 6° (1/60th circle) rotation of the Earth's
axis. Notice that 144 (=12^{2}) is the 12th Fibonacci number after 0 and the only nontrivial, square, Fibonacci
number.
Embodiment of the
number of Tiphareth
According to Table 1, 103 yods outside the root edge line the 22 tetractyses
in the decagon & dodecagon. This number does not include its centre, which the table
counted as a corner of the pentagon. Let us, instead, count it with the decagon. Including
the four yods in the root edge, there are 108 boundary yods in the last two polygons and 109
boundary yods in the first five polygons. The latter includes the corner of the hexagon
shared with the hexagon belonging to the polygons enfolded in the next higher Tree. The
number of boundary yods outside the root edge in the 5n polygons of the first five types
enfolded in the n‑tree ≡ b(n) = 108n + 1. There are (b(10)=1081) such yods shaping the 50 polygons of these types enfolded on either side of
the central pillar of the 10tree. This is the gematria number of Tiphareth, the Sephirah at
the centre of the Tree of Life! Although remarkable, the appearance of this number in the
inner form of the 10tree is not unexpected in view of the holistic character of this set of
Trees, as demonstrated in many previous articles available on this website by the way in
which the 10tree is prescribed by Godnames and embodies superstring structural and
dynamical parameters. Using the formula given above for B(n), there are also
(B(5)=1081) yods lining the 235
tetractyses in the 35 polygons of all seven types enfolded in the 5tree. This is discussed
here. Therefore, the
number of the Sephirah that divides the Tree of Life into two sets of five Sephiroth also
divides 10 Trees into two sets of five Trees because 1081 boundary yods belong to the inner form of the
lowest five Trees and 1081 yods
(one yod being shared with the former set) belong to the inner form of the next five
Trees.
The number of boundary yods outside the root edge
in the first (5+5) polygons enfolded in the ntree = 2b(n) = 2×(108n+1) =
216n + 2, where "2" denotes the top
corners of the two hexagons enfolded in the nth Tree that coincide with the lowest corners
of the hexagons enfolded in the (n+1)th Tree. The first (5+5) enfolded polygons have
50 sectors, showing how they are
prescribed by ELOHIM, the Godname of Binah with number value 50. The (50+50) polygons of the first five types enfolded in the
10tree have (50×10=500)
tetractyses with 2160 boundary yods outside their root edges that are intrinsic to them.
Compare this with the fact that the 70 polygons enfolded on either side of the 10tree
contain 2160 intrinsic boundary yods. It demonstrates the geometrical connection between the number values of Chesed,
Geburah and Tiphareth — successive Sephiroth in the Tree of Life. It also shows how the same
holistic parameters reappear in different holistic subsets of a holistic system, defining
their properties.
5
It is proved in #20
at Wonders of
Superstrings that, when the vertices and
face centres of the five Platonic solids are joined to their centres and their faces and all
internal triangles divided into their sectors, there are 2160 sides & triangles that
surround their axes passing through two opposite vertices and their centres. This means
that, on average, 216 lines and
triangles in each half of a Platonic solid surround its axis. Moreover, on average,
72 corners surround their axes. The
presence in the regular polyhedra of the same parameters as were found above in the inner form of
the 10tree is evidence of their analogous, holistic character.
4. Tree of Life basis of an astrological
age
We have just seen that the number 2160 is a measure of a holistic system,
being a property of the 70 polygons enfolded in the 10tree. The Platonic Year is divided
into 12 eras, or astrological ages, each of length 2160 years. This number measures a
12stage cycle of a complete rotation of the Earth's axis. Is it a property of the inner
form, or part thereof, of 12 overlapping Trees of Life? If coincidence could be discounted
as a plausible reason for its appearance, this would be an indication that the precession of
the equinox, although having a wellunderstood astronomical cause, conforms to the universal
pattern embodied in sacred geometry. Chance can be refuted by providing sufficient examples
of the number 2016 or 1081 appearing in 12 Trees of Life to make this factor highly
improbable. Figure 6 illustrates three



A Type B hexagon
has 91 yods. As its topmost corner is shared with the hexagon enfolded in the
next higher Tree, 90 yods are intrinsic to it, The n hexagons enfolded in the
ntree contain (90n+1) yods. The 12 hexagons enfolded in the 12tree have
1081 yods. This is the gematria
number of Tiphareth (תפארת). 
The
first four enfolded Type A polygons have 90 yods outside the root edge. The
righthand corner of the pentagon (black dot) coincides with the centre of the
decagon. 89 yods outside the root edge of these polygons belong solely to them,
although one yod (topmost corner of the hexagon) is shared with the hexagon
enfolded in the next higher Tree. Associated with each set of the first four
enfolded polygons are 91 such yods, one being shared. Associated with the
48 polygons of
the first four
types enfolded on either side of the central axis of the 12tree are (12×90 +
1= 1081). The topmost corner of
each hexagon enfolded in the 12th Tree is shared with the hexagons enfolded
in the 13th tree. 1080 yods are intrinsic to the 48
polygons in
each set of 84 polygons enfolded in the 12tree and do not belong to any of
the remaining 36 polygons. (1080+1080=2160)
intrinsic, unshared yods make up the first (4+4) polygons making up the inner
form of 12 Trees. 
The Type B
dodecagon has 181 yods. Surrounding its centre are 180 yods. Surrounding the
centres of the dodecagons enfolded in 12 Trees of Life are (12×180=2160)
yods. 
Figure 6
6
of them. It shows that the number of
years in an astrological age is embodied in 12
overlapping Trees of Life as the 2160 yods both intrinsic to the first four types of
polygons enfolded in their inner form and unshared with any of the remaining types of
polygons. It is also embodied in the last type of polygon making up the inner Tree of Life
as the 2160 yods that surround the centres of the Type B dodecagons enfolded in the 12tree. The sceptic's argument that this lacks
significance because it
Figure 7. As the number of Geburah, the 216 yods
surrounding the centres of the first 6 separate polygons consist of 108 yods on their sides
and 108 yods in their interiors.
is based upon cherrypicking ignores the fact
that the geometrical context supposedly picked merely to generate the number 2160 also
produces in various, natural ways the gematria number value
1081 of Tiphareth, the central Sephirah of the Tree of Life. What is
the likelihood of that happening by chance?
It is far too small to make the sceptic's vacuous dismissal plausible. Is it cherry
picking to point out, as was done on the previous page, the simple, mathematical fact that
2160 lines and triangles surround the axes of the five Platonic solids when their vertices
and facecentres are joined to their centres? Hardly. What is being encountered here is a
spectacular example of how the gematria numbers of the Sephiroth are parameters of holistic
systems. Is it coincidence that the first six separate polygons of the inner Tree of Life,
which is shown in many sections of this website to constitute a holistic subset of the set
of seven polygons, have 216 yods
surrounding their centres made up of 108 yods on their sides and 108 yods in their interiors
(Fig. 7)? This means that there is the same 1080:1080 division in yods in 10 such subsets as
there is in the 12 pairs of the first four polygons shown in Figure 6? Is it yet another
coincidence that this subset has 36
corners, where 36 is the number
value of ELOHA, the Godname of Geburah, whose number is 216? No. Instead, what we have here is one of the
patterns that characterises a holistic system reappearing in part of it because this part,
too, is holistic, exhibiting all the numbers of the Sephiroth in the four Kabbalistic
Worlds.
The embodiment of the number 2160 by subsets of
polygons belonging to the inner form of 12 Trees of Life suggests the representation by 12
Trees of Life of each 30 degree rotation of the earth's axis from one astrological age to
the next, the Platonic Year spanning a complete 360° rotation of the Earth's axis being
mapped by (12×12=144) Trees. The 12fold division of the year is not, as astronomers might
think, the product of early man noticing 12 full moons within one year — at least not for
the Chinese. Their zodiac, Sheng Xiao, was based on a 12year cycle, each year
being named after an animal (2013 is the year of the Snake, ending January 14, 2014).
Chinese astronomers divided the celestial sphere into 12 divisions in order to follow the
orbit of Jupiter, whose period is 11.6 years. They were unaware of the Earth's precessional
motion, the Greek astronomerastrologer Hipparchus being regarded by most academics as the
first to notice it around 127 B.C.E., although some scholars believe, controversially, that
he more likely rediscovered it from his studies in Egypt. The Chinese divided a year
into 12 periods and each day into 12 twohour periods, or shi (the 12 "Earthly Branches," 地支). The 12fold
division in the calendar seems to have been the product of astronomical observation. For the
Chinese, however, the phenomenon of precession did not influence it as they did not populate
the celestial sphere with constellations.
Here is hard, mathematical evidence for a sacredgeometrical
connection between the numbers 12 and 2160. The number 12 manifests elsewhere as the 12
roots of G_{2}, the smallest exceptional Lie group, as the 12 notes between the
tonic and octave found in the seven musical scales (see here) and as the 12
meridians of acupuncture (see Article 32). Perhaps, it is also
revealed by the hidden, 12fold division in the layout of Plato's books, which was recently
discovered by Dr Jay Kennedy (see news item #4 here). In view of such occurrences, it
should not seem so strange that the 12sided dodecagon and 12 dodecagons enfolded in 12
overlapping Trees should embody a number that measures the time for the Earth's axis to
rotate through 1/12th of a circle! What, however, is the Kabbalistic significance of 12
Trees, with each one mapping a 2½° rotation of the Earth's axis that, theoretically
speaking, takes 180 years? Malkuth of the 12th Tree is Kether of the 10th Tree, the
65th SL, which is prescribed by
ADONAI, the Godname of Malkuth, because its number value is 65. ADONAI can be said in this way to determine 12
Trees as well as 10 Trees. Constructed from tetractyses, 12 Trees contain
620 yods. 620 is the number value of Kether. The apex of the 12th
Tree is the 76th SL, where
76 is the number value of YAHWEH
ELOHIM, the Godname of Tiphareth. It is the 26th SL on the Pillar of Equilibrium, below which are
50 SLs on the two side pillars.
26 is the number value of YAHWEH
and 50 is the number value of
ELOHIM. The 12th Tree is the 80th
from the top of CTOL (for the meaning of CTOL, see Maps of reality),
where 80 is the number of Yesod.
These are a few examples of how Kabbalistic numbers determine 12 Trees.
The
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The Type A dodecagon
contains 73 yods.
This is the number of Chokmah, meaning "wisdom."

72 yods
surround the centre of the Type A dodecagon. This is the number of
Chesed.

140
yods surround the centres of 2
Type A dodecagons. This is the number of Masloth
, the Mundane Chakra of Chokmah.
Its astrological counterpart in Kabbalah is the Zodiac.

282 yods line the 72 tetractyses in 2 Type
B dodecagons. This is the number of Aralim, the Order of Angels of
Binah.





97 yods
either line sectors or are at centres of tetractyses in the Type B
dodecagon. This is the number of Haniel, the Archangel of
Netzach.

48 hexagonal
yods line the sides of the sectors of a Type A dodecagon. This is the
number of Kokab, the Mundane Chakra of Hod.

155 red or
blue hexagonal yods are associated with each Type B dodecagon. This is
the number of ADONAI MELEKH, the Godname of Malkuth.

168
yods other than its corners
surround the centre of the Type B dodecagon. This is the number value
of Cholem
Yesodeth, which is the
Mundane Chakra of Malkuth.

Figure 8. The wisdom of the
dodecagon.

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reason why this happens is that the
tetractysdivided Type A dodecagon is a representation of 12 overlapping Trees of Life, its
73 yods corresponding to the
73 SLs up to Chesed of the 12th
Tree. When it is Type B, the 180 yods surrounding its centre symbolise the 180 years that
elapse during 1/12th of the precession of the equinox through the 30 degree arc of an
astrological sign of the 12fold Zodiac, which is symbolised by the dodecagon. The 2160 such
yods surrounding the centres of the Type B dodecagons enfolded in 12 overlapping Trees
symbolise the 2160 years required for the Earth's axis to rotate through 30° to complete the
journey through an astrological sign. The complete precessional cycle is mapped by 144 Trees
— the counterpart of the 144 sectors of the dodecagons enfolded in 12 Trees. This number was
encountered in the discussion in the Polyhedral Tree of
Life subsection
of Sacred
geometry as the number of yods that line
the sides of the seven separate regular polygons making up each half of the inner Tree of
Life (see here). When they
become enfolded, the polygons are lined by 120 yods but there are 144 yods inside their
boundaries. This 120:144 distinction between the exterior and interior of the inner Tree of
Life manifests in 3dimensional space as the 120 faces of the disdyakis triacontahedron and
the 144 faces of what has been called the "144 Polyhedron," both polyhedra discussed in that
subsection as, respectively, the outer and inner forms of the Polyhedral Tree of Life.
Remarkably, there are 144 SLs on the Pillar of Equilibrium of CTOL below the bottom of the
73rd Tree! Equally remarkable is
the fact that 144 yods inside the Type B dodecagon surround its centre. This, of course, is
no coincidence, for the 73 yods in
the Type A dodecagon symbolise SLs, which can be represented by complete Trees of Life. One
may say, therefore, that the 72
yods surrounding its centre symbolise the 72 Trees below the 73rd Tree that have
(72×2=144) SLs on the central
pillar below its Tiphareth symbolised by the 144 internal yods, there being two such SLs
per Tree. The 144th SL on the Pillar of Judgement is Geburah of the 72nd Tree. It is the 432nd SL and emanates 145 SLs
on the central pillar and 143 SLs on the Pillar of Mercy.
What is significant is not so much the ancient
division of the celestial sphere into 12 segments containing constellations but that the
division of the precessional cycle into n equal stages conforms to a holistic pattern only
when n = 12. As the number of yods in an nsided, regular polygon = 15n + 1, the number of yods surrounding the centres of
the n nsided polygons enfolded in the ntree = n×15n = 15n^{2}. This equals 2160 only when n = 12. The
dodecagon is unique in being the only
polygon that embodies this number when the number of copies of the polygon is identical to
the number of its sectors. The first four enfolded polygons have the same yod population
(making allowance for their shared corners) only when both sets are considered. If the
centre were included, then n×(15n+1) = 2160. But this quadratic equation has no
integer solution for n, so only the yods surrounding the centre of the dodecagon provide a
valid, unique representation of the number 2160. But, as the polygonal representation of the
Tree of Life, it embodies other Kabbalistic numbers. Figure 8 shows how the dodecagon
embodies some of the gematria numbers of the 10 Sephiroth in the four Kabbalistic worlds, as
listed in Table 1. Notice in particular that 140 yods surround the centres of two joined, Type A
dodecagons, where 140 is the number
value of Masloth (3), the Mundane Chakra of Chokmah, the
Sephirah whose number 73 is the yod
population of a single dodecagon. This is
appropriate, given that it embodies the astrological age of 2160 years, because Kabbalists
assign the Sphere of the Zodiac to Masloth!
Is there any astronomical significance to a
rotation of Earth's axis by 2½° over a period of 180 years that corresponds to a complete
Tree of Life, the Platonic Year corresponding to 144 overlapping Trees of Life? The 180 yods
in a Type B dodecagon that surround its centre consist of the 72 yods in a Type A dodecagon and the 108 yods
added by transforming it into the next type. As a yod symbolises a year, the former number,
which is 2/5 of 180, signify a rotation of (2/5)×(5/2) = 1° over 72 years, whilst the latter encodes a further rotation
of 1½° over 108 years. Is there any astronomical evidence for the 30° rotation of Earth's
axis during an astrological age of 2160 years dividing into a rotation of 12° over 864 years
and a rotation of 18° over 1296 years (or 144° (10,368 years) & 216° (15,552 years) for the Platonic Year of 25,920
years? In other words, for the 360° rotation being a fivefold cycle that is divided in the
proportion of 2:3?
Before answering these
questions, the issue of numerology must be addressed. Firstly, the Moon's diameter is often
quoted as 2160 miles, although this is an approximation because it is not perfectly
spherical, the more accurate mean diameter
being 2159.2 miles. The precession of Earth's axis is well understood as due to the combined
gravitational, tidal force of the Sun and Moon acting on Earth's equatorial bulge, although
unequally on the part above and below the plane of its orbit to which it is tilted (a
difference that generates a torque continually twisting its axis in a circle). However, it
remains an amazing 'coincidence' that the length in years of an astrological age that this
torque causes and the diameter of the Moon measured in miles should be almost exactly
identical numbers! Of course, it has to be no more than that, a scientist will argue,
because there can be no causal connection between the rate of wobble of the Earth and the
size of a piece of rock either captured in the past by the Earth or ejected from it whilst
it was in a molten state. He will point out that the force of gravity between the Moon and
Earth that is partly responsible for the precession depends only on the mass and distance of
the former,
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not on its size, so the periodicity of the
rotation of Earth's axis cannot be related to the Moon's diameter. However, although
perfectly true, this may not be the point. If universal laws of nature applied to analogous
systems produce features patterned by the same set of numbers, why should we always need to
demand a physical explanation, the absence
of which necessarily means that the appearance of the number 2160 in different astronomical
contexts must be merely a coincidence? Perhaps nature works through subtle, as yet
undiscovered, mathematical laws of analogy or correspondence between systems, whatever the
difference in scale between them — laws that are even more fundamental than Newton's laws of
motion and gravity, but acting acausally instead of mechanistically. Secondly, the actual
period of the precession of the equinox is about 25,772 years, not 25,920 years. This
amounts to one degree of rotation of Earth's axis every 71.6 years, not exactly
72 years, and to an astrological
age of 2147.7 years, not 2160 years. Do these slight numerical differences invalidate
comparison with sacred geometry? Not at all, for many small, astronomical perturbations
are at work, making the actual figures deviate from the theoretical ideal. For example,
the gravitational pull of planets, particularly Jupiter, creates a small precessional
motion that is added to that caused by the Sun and Moon. Moreover, the actual rate of
precession is not constant but (at the moment) slowly increases over time. This, too, has
to be taken into account when comparing the differences between theoretical values based
upon sacred geometry and scientifically measured values. It is a clouded situation that
will be familiar to any scientist who has compared his experimental data with the
predictions of some theory that he is testing. If their discrepancies are too large on
average, statistically speaking, to be due to errors of measurement, he will conclude
that his data does not support the theory — but only if he has satisfied himself that he
eliminated or minimised all laboratory variables that might disturb his measurement. What
has to be assessed is whether various theoretical and measured values agree too closely
and too often to be plausibly due to chance. A discrepancy in the rate of rotation of
Earth's axis as small as 0.5% is hardly to be ignored. Despite this degree of agreement,
scientists will dismiss it because too many of them are locked into an ideology that
rejects regularities — even phenomena —
as real if science cannot provide a physical explanation for them. For example, this has
been (and continues to be for many astronomers) the fate of the TitiusBode law (see
Article 17). Because they reject
acausal explanations as unscientific, they remain unconvinced by the beautiful properties of
sacred geometries, however amazingly these embody astronomical parameters. Their narrow
philosophy of scientism will not permit them to accept the possibility that cosmic and
smallscale phenomena might exhibit the same, mathematical patterns because they
are governed by the same, nonmechanistic
principles, being realizations of the same cosmic Whole. For most scientists, there is no
overriding Whole, only unconnected fragments randomly scattered about in a universe
of chance events. Hence, they dismiss any evidence contradicting this as the
product of coincidence.
Let us return to the issue of whether a fivefold
structure can be discerned in either the Platonic Year or an astrological age. The number 5
suggests the relevance of the ancient teaching of the five elements. Western astrology,
however, relates the 12 astrological signs to the four physical elements of ancient Greek
philosophy, there being three signs associated with each element and no sign corresponding
to the fifth element Aether (Table 3):
Table 3. Assignment of the four physical elements
to the 12 astrological signs.
Aries 
Fire 
Taurus 
Earth 
Gemini 
Air 
Cancer 
Water 
Leo 
Fire 
Virgo 
Earth 
Libra 
Air 
Scorpio 
Water 
Sagittarius 
Fire 
Caprican 
Earth 
Aquarius 
Air 
Pisces 
Water 
The Chinese yearly
calendar does, however, have a 5fold character because it has five "seasons" or divisions
of the year (four traditional seasons and an intermediate, representing the change between
two successive seasons). In their correct order, the five Chinese elements (Wu Xing) are:
Wood, Fire, Earth, Metal & Water. Rather than substances or states of matter, these
words should be understood as metaphors for the five stages or phases of a cyclical process
(in this context the passage of a year). The words "Fire", Earth" & "Water" must not be
taken literally, nor must they be confused with the ancient names of the physical elements.
They are called 'elements' only through the influence of the western
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philosophy of the
elements. The association of Wood with Spring expresses the growth (sprouting) stage of a
life process, Fire associated with Summer represents the flowering or blooming phase,
Earth's association with Late Summer denotes the fruition, or ripening, stage, Metal's
association with Autumn denotes the harvesting, collecting, withering stage and Water
associated with Winter expresses the retreat, stillness or dormancy of life. There are six
Yang and six Yin Earthly
Branches.
Figure 9.
Correspondence of elements and seasons to the 12 Earthly Branches.
The 5fold division of
the 12 Earthly Branches is achieved by assigning a pair of branches (Yang & Yin) to each
of the four elements Wood, Fire, Metal & Water and two pairs
to the fifth element Earth (Fig. 9). A Yang branch is always followed by a Yin
branch and vice versa (Table 4):
Table 4. The 12 Earthly Branches & their elements.

12 Earthly Branches


Element

1

Rat

Yang

Water

2

Ox

Yin

Earth

3

Tiger

Yang

Wood

4

Rabbit

Yin

Wood

5

Dragon

Yang

Earth

6

Snake

Yin

Fire

7

Horse

Yang

Fire

8

Goat

Yin

Earth

9

Monkey

Yang

Metal

10

Rooster

Yin

Metal

11

Dog

Yang

Earth

12

Pig

Yin

Water

The years are grouped
within a 10year cycle called the "10 Celestial Stems". Each year corresponds to one of the
five elements (Yang or Yin forms). There is also a 12year cycle called the "12 Earthly
Branches" based upon 12 animal signs and a 60year cycle called the "stembranches" in which
the Celestial Stems and the Earthly Branches cycle run together so that a given animal sign
repeats itself five times over 60 years, once for each element every 12 years (for
comparison with the western calendar, see here). We see here parallels with how the
holistic parameter 2160 is embodied in different ways in both 10 and 12 overlapping Trees of
Life, as described above. Although the Chinese have a fivefold division in a year, it
refers, not to equal periods of time, but to types of temporal change in the life process, as manifested
within the four traditional seasons and in the transition from one to another. It is,
therefore, misconceived to look for some even, fivefold astronomical pattern within a year.
It does, however, exist in an astrological era and the Platonic Year because both are
exactly divisible by 60. The former is composed of (36×5=180) repetitions of each zodiac animal sign and
the latter comprises (12×180=2160) repetitions. We see that the ancient Chinese calendar
contains the same number 2160 when extended over a complete processional cycle! However, it
refers not to a period of time but to the number of times each animal sign is repeated in
this cycle.
The 180 yods surrounding the centre of a Type B
dodecagon symbolise the 180 years required for the Earth's axis to rotate through 2½°, or
1/144th of a circle. The 72 yods
surrounding the centre of a Type A dodecagon denote the 72 years that elapse during its rotation by 1°, or
1/360th of a circle. The extra 108 yods in a Type B dodecagon represent the 108 years during
which the axis rotates by 1½°, or 1/240th of a circle. In one year, the axis should rotate
through 1/72° = 50″, an angle that
corresponds to a yod, whilst
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Figure 10. Is it
just coincidence that the gematria number 140 of Masloth, the Mundane Chakra of Chokmah and the
Kabbalistic name for the 12fold Zodiac, is the number of turns in 1/12th of a
whorl of the UPA/superstring, whilst 168, the number of the Mundane Chakra of Malkuth
(physical universe) is what determines the number (1680) of turns in the whole
whorl? 
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it should rotate
through 50° in 3600
(=36×10×10) years. The number value
50 of ELOHIM, the Godname of Binah,
is the number of arcseconds through which the Earth's axis should rotate in one year (the
actual value is 50.3", a discrepancy of about 0.6% that is small enough to regard this
prediction as significant). The number value 36 of ELOHA, the Godname of Geburah, which is the
Sephirah directly below Binah in the Tree of Life, determines the time taken for it to
rotate 50°. The appearance here of
the numbers 50 and
36, as well as the numbers
72 and 216 elsewhere, where 72 is the number of Chesed and 216 is the gematria number of Geburah, is difficult to
dismiss as coincidence, given that Binah, Chesed & Geburah are successive Sephiroth in the Tree of Life.
Finally, the following amusing curiosity is
offered: how much does the earth's axis rotate during 1680 years, where 1680 is the number
of circularly polarised oscillations in each helical whorl of the UPA, as counted by C.W.
Leadbeater over a century ago when he used a form of remote viewing to describe subatomic
particles? This website proves beyond all reasonable doubt that this number is a parameter
so conspicuously and naturally embodied in sacred geometries that it renders
untenable the kind of vacuous criticism of cherrypicking that sceptics might resort to
in order to dismiss Leadbeater's work. So it is interesting to know what angle the Earth's
axis would rotate through in 1680 years about a line perpendicular to the ecliptic. Assuming
the actual value of the period of the precession of the equinox, i.e., 25,772 years, as
opposed to its idealised value of 25,920 years, the axis of the Earth rotates through an
angle of about 23.46733° in 1680 years. Compare this with its angle of tilt of about
23.43928° from the perpendicular to the plane of the Ecliptic. Earth's axial tilt varies
from 22.1° to 24.5° over a 42,000 year period. The tilt is currently decreasing. The
difference between the current angle of
tilt and the angle the axis would rotate through in 1680 years if its rate of rotation
remained constant is about 0.12%. This should be small enough to induce at least an
embarrassed smile in the sceptic before he hastily dismisses it as yet another coincidence!
The significance of the superstring structural parameter 1680 in the context of the Type B
dodecagon with 180 yods in 36
tetractyses surrounding its centre is that (180−36=144) of these yods line their 60 sides, i.e.,
(144−4=140) boundary yods are
outside the root edge, where 140 is
the gematria number value of Masloth (The
Sphere of the Zodiac), which is the Mundane Chakra of Chokmah (see Table 1).
(12×140=1680) yods
delineate the (12×36=432)
tetractyses making up the 12 Type B dodecagons enfolded in 12 Trees, whereas the remaining
480 yods either belong to their root edges or are hexagonal yods at the centres of these
tetractyses. This demonstrates the shapeforming character of the number 1680, as realised in
the 1680 circular turns of each helical whorl of the UPA/subquark superstring (see here). The number of
Masloth is the number of circular turns in
1/12th of a whorl of the UPA (Fig. 10). The 12fold aspect of the Zodiac has its counterpart
in each whorl of the subquark superstring, just as the five Chinese elements, or
stages of a life cycle, correspond to the five revolutions or twists in each whorl about the
axis of spin of the UPA. This accords with the Hermetic axiom: "As above, so
below."
References
1. A perfect number is an integer that is the sum
of all its divisors. For example, the number 6 is the first perfect number because 6 = 1 + 2
+ 3, where 1, 2 & 3 are its divisors, and 28 is the second perfect number because 28 = 1
+ 2 + 4 + 7 + 14, where 1, 2, 4, 7 & 14 are its divisors.
2. The zodiacal signs are the twelve 30° sectors
of the ecliptic and need to be distinguished from the 12 constellations of the zodiac, which
take up varying amount of ecliptic longitude, e.g., the constellation of Virgo takes up five
time as much longitude as the constellation of Scorpius. This means that the Sun is not in
each constellation for the same amount of time.
3. Masloth is
also written as Mazloth, with the Hebrew
letter zayin being used instead of samekh. Its gematria value is then 483. The present
geometrical context makes it clear that 'Masloth' is the right spelling, with the number 400
contracted to 4: MSLVTh = 40 + 60 + 30 + 6 + 400→4 = 140.
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