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.