The Masonic Royal Arch Companions Jewel and the Platonic Solids.


High PriestCompanion Captain of the Host, are you a Royal Arch Mason?

CaptainI am, that I am.

High PriestHow shall I know you to be a Royal Arch Mason?

CaptainBy Three Times Three.

The Triple Tau is regarded as one of the defining symbols of Royal Arch Freemasonry.

‘The Triple Tau is also referred to within Royal Arch Masonry as”The Key.”

The Tau (T) being the 19th letter of the Greek alphabet. In the ancient world it was regarded as symbolising life itself, as conversely,the Theta,the 8th letter of the Greek alphabet, was held to symbolise death. It has been suggested by certain commentators,that these two symbols gave rise to the modern plus and minus symbols.

The Tau is often regarded as being a very early form of the cross, and is associated with  St. Anthony within Christian symbology.


The cross with the crosspiece at the top of the upright is known as the Cross of St. Anthony or as the Crux Commissa. This cross is also known as the Tau Cross, because it looks like the Greek letter tau which is the same as the T in our alphabet. In this form, the cross symbolizes the triumph of Man’s spiritual nature over his physical nature.

the Triple Tau, is  a Trinity symbol. Christians interpreted the symbol as “Holiness supporting Trinity”.  it is also said to mean Clavis ad Thesaurum – “A key to the treasure” – and Theca ubi res pretiosa – “A place where the precious thing is concealed.” The Triple Tau is a significant symbol, or logo, of the Royal Arch Mason. It is the jewel signifying the Mason who has reached either the seventh degree of the York Rite or 13th degree of the Scottish Rite.

The origins of the letter Tav

The Hebrew form of the word Tau, pronounced tav, suggests a marking or an etching. In the ancient world, a warrior who had returned from battle with honour was permitted to attach a T to his name.

In an old Masonic Royal Arch lecture it is explained that persons acquitted of a crime, or returning unhurt from battle could use the T as a sign. In the 26th degree of the Scottish Rite, a Tau is put on the candidate’s forehead after the candidate has been purified with water on the head, to ritually mark him.

The earliest symbol for Tav meant ‘A wound’.The triple Tau therefore can be held to represent 3 wounds; as reflected in the case of the murdered (And raised) Master Mason; Hiram Abiff-illustrated within the 3rd degree legend and of course, in the case of the three wounds inflicted by the nails used in the crucifixion of Jesus.

Triple Tau – Three Taus or T and H?:

R.A. Jewel 2

It has been said that three Taus come together to form the Triple Tau,. Others say the Triple Tau is originally the coming together of a T and a H, forming , meaning Templum Hierosolyma, or the Temple of Jerusalem. Royal Arch records dating from 1767 show this symbol. In addition to meaning Templum Hierosolyma (The Temple of Jerusalem), it is also said to mean Clavis ad Thesaurum – “A key to the treasure” – and Theca ubi res pretiosa – “A place where the precious thing is concealed.”
The jewel incorporates the double triangle, also known as the “Seal of Solomon” and contains upon it the following inscriptions:
“Nil nisi clavis deest”Nothing is wanting but the key
“Si talia jungere possis sit tibi scire satis”If thou canst comprehend these things, thou knowest enough
“Invenimus cultor dei civis mundi” – We have found the worship of God, O citizen of the world
“Deo, regi, et fratribus, honor fidelitas, benevolentia” – For God, king, and brethren; honour, fidelity, and benevolence

The Platonic Solids and the Jewel:

As we have touched upon the 5 Platonic solids in some depth previously in our article on the 24 reduced Fibonacci numbers and the Platonic solids, we had noted that Plato observed that the study of the universe involved the analysis of different volumes, as all that is in this world, from the smallest atoms to the largest items, consist of volume. When he studied each shape (triangle, square etc) he concluded that only 5 shapes remain completely equal regardless of the angle they are viewed from. These shapes we know as “The Five Platonic Solids” and are described in detail in his ‘Timaeus.’ The five solids represented the four base elements of this world (fire, air, water, earth) plus the fifth, being heaven, served to represent the universe as a whole.

1.solids chart

Click to expand.

Mathematicians have long understood that these five polyhedra are the only geometric constructs that are able to equally divide three-dimensional space, and this understanding represented the essence of ancient geometric and esoteric knowledge (a sphere also may equally divide space, but as it has no faces, edges, corners or degrees, it was not considered to be a solid).

The Seal of Solomon and the five elements:

On a cursory examination, we would not notice the five Platonic shapes present within the Seal of Solomon, but when we count the number of right-angles, their presence becomes apparent. We note that the number of right-angles in the Triple Tau (The key), and a multiple of it, are equal to combinations of the triangles in the Seal of Solomon. Hence the Triple Tau, or key, “unlocks” the Seal of Solomon to reveal the five Platonic shapes, just as our 24 reduced Fibonacci numbers placed in a circle also generate the five solids by way of their interaction.

Clearly this Masonic Royal Arch key serves to unlock exactly the same secret we have discovered within the 24 reduced Fibonacci numbers.

The Triple Tau and the 90 degree Right-Angles.

Examining the form of the triple Tau,we can note that it is comprised of 8 x 90 degree angles, which is in turn equal to a value of 720 degrees.
Therefore, the number of degrees in a Triple Tau is equivalent to 8 x 90 degrees = 720 degrees.

”It contains eight right angles, and is used as a measure or mnemonic whereby the Platonic Solids can be calculated.
Taken alone, it is com­mensurate with the Tetrahedron, the sides of which, being four equilateral triangles, are together equal to eight right angles, because the interior angles of any triangle are together equal to two right angles. It is said that this solid was used by the Platonists as a symbol of the element Fire.

Two of these Keys are equivalent to the Octahed­ron, which contains sixteen right angles, and was con­sidered to represent Air. Three Keys are commensu­rate with the Cube, the sides of which contain twenty-four right angles; this figure was supposed to typify Earth, because it is of all these figures the firmest and most immovable upon its basis.

Five of these Keys give us forty right angles, which are equal in amount to those contained in the twenty equilateral sides of the Icosahedron. This solid was taken to express the element Water.
The remaining Platonic Solid, called the Dode­cahedron, has for its sides twelve regular pentagons.
It is a rule in geometry that the interior angles of any rectilinear figure are equal to twice as many right angles as the figure has sides less 4 right angles; thus the interior angles of a pentagon are 10 – 4 = 6 right angles; therefore the dodecahedron is contained by  seventy-two right angles, and consequently is represent­ed by nine Keys. So it will be seen that this Key is the greatest common measure of all these Platonic Solids, and that is why on the scroll round it in the Jewel of  the Holy Royal Arch Degree we find the Latin phrase: Nil nisi clavis deest, “Nothing is wanting but the key”, teaching us on the one hand that without the inner knowledge all these symbols are but lifeless, and on the other that, great as is the teaching given, there is yet more to be found as we move along on the path of Masonic progress
There is a method by which, by sub-dividing the triangles and the Seal of Solomon into smaller triangles and adding up the total number of degrees formed by all their angles, we can yet again work out the number of right angles equivalent to those of the Platonic solids.

This process is complicated, and is of little practical value, so I do not give it here; although it is true that the Platonic Solids have a profound meaning in connection with that process of Divine Creation, upon which the Degree of the Holy Royal Arch contains such priceless teaching.”




Three Times Three;

H.Meij; in his ‘The Tau and the Triple Tau’ informs us that;

We might also note that the Seal of Solomon, as shown in the Royal Arch Companion’s jewel, is actually made up of three triangles, which we can mark as follows:

A-B-C, D-E-F, and G-H-I.

3 Triangle Grid

With the Royal Arch ritual the following is explained:
“The equilateral or perfect Triangle is an emblem of the three essential attributes of Deity, namely, Omnipresence, Omniscience, and Omnipotence; and as the three equal sides or equal angles form but one triangle, so these three equal attributes constitute but one God”

From this we can deduce that one triangle shown in the jewel, is actually comprised of three triangles (triangles a, b, and c), which also form a fourth triangle in the center (triangle d):
3angle 1

Such a triangle, when approached from a geometrical value of its angles, is equal to 60 x 12 = 720 (because there are 4 triangles, each triangle being equilateral, has three 60 degree angles each)

Combine the Triple Tau and the Key of Solomon:
Now we have all the prerequisites to proceed to reveal the five Platonic shapes embedded in the Companion’s jewel with the help of the “Key”, or Triple Tau. You will notice that:
Triangle GHI = 1 x  triple Tau.

(We have already noted that it consists of 8 right angles of 90 degrees each. )

Hence = 8 x 90 = 720 degrees. Triangle GHI shows 4 equilateral triangles, which we showed above is also equal a geometrical value of 720, which in turn equals the total degrees of a Tetrahedron, symbol of Fire.
Triangles ABC DEF = 2 x  Triple Tau= 1440 degrees = the degrees in an Octahedron, which is the emblem of Air.
Triangles ABC DEF GHI = 3 x  Triple Tau= 2160 degrees = the degrees in a cube (Hexahedron), which is the emblem of Earth.
Triangles DEF is can also be divided into 4 smaller triangles by GHI, add ABC. These 5 triangles = 5 x Triple Tau = 3600 degrees = the degrees in an Icosahedron, which is the emblem of Water.
We have now found the four elements. What remains is the last, “Heaven.” We find that the intersection of triangles ABC and DEF, form six smaller triangles around the circumference of the jewel, whose base rests on the central triangle of GHI. As one triangle is 180 degrees, and there are four equal triangles in one (see above), means that one triangle on the circumference is 180 x 4 = 720.
There are six triangles on the circumference, so 6 x 720 = 4320. Add to this the revolving central triangle GHI (720) and you obtain 4320 + 720 = 5040, which is equal to the degrees of a Dodecahedron, which is the emblem of Heaven,the quintessence.

By way of illustration;

Each of the following geometrical forms are two dimensional representations of three
dimensional forms, i.e.three dimensions folded out into two dimensions.

Using the previously mentioned model of;

3angle 1

We find the following;

As each equilateral triangle is comprised of three angles of sixty degrees, in total one hundred and eighty degrees,which is equal to two ninety degree angles. Looking at the above diagram each of the four triangles is equivalent to two right angles.


Tetrahedron (fire)
1 times 8 right angles = 8 right angles


Octahedron 1 (air)
8 right angles.

1.octahedron 2

Octahedron 2

2 times 8 right angles.
16 right angles in total in the Octahedron.


Cube 1 (earth)

1 times 8 right angles

1.Cube 2

Cube 2

1 times 8 right angles

1.Cube 3

Cube 3
1 times 8 right angles
8 + 8 + 8 right angles.

There are 24 right angles in the cube.

1.Icos 1

Icosahedron 1 (water) 
1 times 8 right angles

1.Icos 2

Icosahedron 2
1 times 8 right angles

1.Icos 3

Icosahedron 3

1 times 8 right angles

1.Icos 4

Icosahedron 4

1 times 8 right angles

1.Icos 5

Icosahedron 5
1 times 8 right angles
8 + 8 + 8 + 8 + 8
40 right angles in the Icosahedron.


Dodecahedron 1
7 times 8 right angles = 56


Dodecahedron 2
(exterior angles of the triangles)
Equivalent to 16 right angles

72 right angles comprise the dodecahedron.

The exterior angle of every triangle formed by one of its sides is equal to the sum of two interior and opposite angles.
Every angle in a equilateral triangle is equal to one third of two right angles.

Paul Bevan and Roz Polden.

With thanks to;

C.W.Leadbeater; ‘The Hidden Life In Freemasonry’.

H.Meij; ‘The Tau and the Triple Tau’.

Malcolm C. Duncan; ‘Duncan’s Masonic Ritual and Monitor.


An Analysis of the prime number cross and its relationship to other models of reality; Part 2

Part 2;

The Prime Number Cross and The Tarot

Paul Bevan and Roz Polden.

The Fool-Shin

The french occultist Gerard Encausse,writing as ‘Papus’ in his book ‘Tarot of the Bohemians’ presents us with an unusual ordering of the 22 tarot trumps,one which does not follow any of the widely accepted systems of tarot attribution,yet on closer examination we found that his schema falls quite conclusively into this same 147,258,369 modelling we have shown to be present both within the 24 reduced Fibonacci numbers and the prime number cross.

Some time back we came across an ancient Persian Alchemical text by name of;

‘The mystic rose from the garden of the king’

Upon studying this document and brooding over its somewhat arcane and allegorical content,we felt that there could be a hint of  a suggestion that it might offer some very intriguing possibilities and might likely provide further illumination in terms of our current understandings of this ‘forgotten’ knowledge.

The narrative of the book describes and follows an ascent through the levels of a tower;

”A temple built like a tower…”

The tower contains seven levels,each level has three chambers.
And goes on to state that;

”At the top is one singular chamber.”

Arranging Encausse’s tarot attributions,which he divides into what he refers to as being ‘terniaries’-groups of three,by placing these into the form suggested by the tower mentioned in this alchemical text we arrived at the following arrangement;

tarot tower one

(Click on image to enlarge)

Surprisingly,by way of its integral allegorical structure and the numeric values ascribed to each individual card by Papus, this arrangement appeared to invoke our precise same 1,4,7-2,5,8-3,6,9 sequence by applying reduction.

tarot tower values

(Click to enlarge)

Following the Hebrew letter values attributed to each card in Papus’ system,we arrive at the above construct.
Using the Mod. 9 formula,we noted that each of the seven levels of the tower were depicted as triangles,
The ascribed letter value of each of the three cards within each triangle adds up repeatedly to 6.








7 times 6


Life,the universe and everything.

The one exception is the eighth level which is comprised of the card ‘The Universe’ which has a letter value of 400 and is represented by the letter ‘Tav’-The final letter of the Hebrew alefbet.

What is interesting here is that on the left-hand side of the tower,the sequence of 147 is visible via base 9 reduction.Similarily on the right hand side,we note the 258 sequence is also present.
In the middle,as always,we have the 369 vector.

This same sequencing we see here also mirrors the given values of the 22 Hebrew letters;

tarot tower letters


In the 2nd degree of freemasonry,the steps taken by the candidate fall into 3 groups of 3,5 and 7-

Might this be representing a knowledge of something that might well fall in with our above arrangement?

As a final thought;

The Masonic Dictionary refers to a ladder of Seven rungs,not entirely unlike our Tarot tower;

”Thus, in the Persian Mysteries of Mithras, there was a ladder of seven rounds, the passage through them being symbolical of the soul’s approach to perfection. These rounds were called gates, and, in allusion to them, the candidate was made to pass through seven dark and winding caverns, which process was called the ascent of the ladder of perfection Each of these caverns was the representative of a world, or  state of existence through which the soul was supposed to pass in its progress from the first world to the last, or the world of truth. Each round of the ladder was said to be of metal of measuring purity, and was dignified also with the name of its protecting planet.”

An Analysis of the prime number cross and its relationship to other models of reality; Part 1

An analysis of the prime number cross
and its discernable connection with Phi,Fibonacci,Qabalah,Tarot and Ed Leedskalnin’s Coral Castle.

Or; all the math they never taught you about in school.

Paul Bevan and Roz Polden 2013.


According to Dr Peter Plichta a German chemist, the ancient Egyptians were aware of a hidden pattern buried away within the prime number sequence. By placing the numbers from 1 to 24 into a circle,as we did previously with the 24 reduced Fibonacci numbers and moving in a  clockwise direction, then placing the next 24 numbers of the sequence running concentrically around it, repeating this manouvre, we discover that the prime numbers fall on the diagonals which in turn appear to form the image of a Templar cross.



Contained within his prime number cross are the numbers from 1 to 144
Within this series of the first 144 numbers there are 34 prime numbers.

On Plichta’s diagram we note that only 32 primes fall into the cross.

The primes 2 and 3 are for some reason, excluded from this Templar cross patterning.

Taking these primes which fall within the cross;



Their total value is 2124 which reduces to 9.
The numbers 2 and 3 are the excluded exceptions
2 plus 3=5
Taking the full prime sequence up to 144

Their total value is 2129 which in turn reduces to 5.

Reducing the numbers on the prime cross to a single digit by mod 9
reveals the following array-and it is a familiar one also-all the the numbers fall into 3 distinct sequences alternating as follows;
1-4-7  2-5-8  3-6-9
Which in turn break down further to a single digit pattern

Prime Cross 963

3-6-9 patterning with prime number cross.

(Click image to enlarge.)

This is exactly the same patterning as we have witnessed so far within the repeating 24 Fibonacci sub-code

and the 3 groupings of the prime numbers divisable by 1,2 and 3.

Or even by adding the single numbers together;
Counting down;

1-1-1 times 8
(The pattern occurs 8 times in the prime cross)
(8-8-8=24-Indicative of time perhaps?)
Applying the same rule as above;
3 nines

Toroidal ‘S’ curves are also visibly present within the prime number cross sequence.
(Starting from the 1 position in the cross)
Note; all chains in this progression break down by mod 9 to the 3-9-6 sequence.

Prime Torus

The last two numbers of a chain are always the first two numbers of the second (highlighted in red)
The commencing number in the first line (18) is the same as the final number in the last line.
(Highlighted in blue)
This pattern repeats throughout the cross,turning on each 9th chain.

Prime Torus Numbers

Also there would appear to be another sequence occuring in the last two numbers of each chain;

The first four seem to follow a 2,4,6,8 sequence
The next five follow a 1,3,5,7,9 pattern.

Patterns are also visible within the array of numbers if we read them in straight lines from inner to outer;
this continues over in the opposite line with a chirality of 471471
The same patterning  occurs within all the number stands throughout the prime number cross.

There are six concentric circles in the cross within which the numbers are distributed.
(Inner to Outer)
(9 units;value-100=1)
(6 units;value-228-12=3)
(6 units;value-376-16=7)
(4 units;value-324=9)
(6 units;value-620=8)
(3 units;value-403=7)

1 3 7 9 8 7

Part 2 to follow.